"STRAlEGIC PRICING OF DIFFERENTIATED CONSUMER DURABLES IN A DYNAMIC DUOPOLY

A NUMERICAL ANALYSIS'

by Fernando NASCIMENTO*

Wilfried R. VANHONACKER**

N° 88 / 63

* Fernando NASCIMENTO, Assistant Professor or Marketing, Catholic University of Portugal, Lisbon, Portugal.

** Wilfried R. VANHONACKER, Associate Professor of Marketing, INSEAD, Fontainebleau, France

Director of Publication :

Charles WYPLOSZ, Associate Dean for Research and Development

Printed at INSEAD, Fontainebleau, France

Strategic Pricing of Differentiated Consumer Durables

in a Dynamic Duopoly: A Numerical Analysis

* Fernando Nascimento

and **

Wilfried R. Vanhonacker

Revised October 1988

Assistant Professor of Marketing, Catholic University of Portugal,

Lisbon, Portugal.

** Associate Professor of Marketing, INSEAD, Fontainebleau, France.

Strategic Pricing of Differentiated Consumer Durables

in a Dynamic Duopoly: A Numerical Analysis

ABSTRACT

Under different modes of competitive pricing behavior, profit maximizing

price trajectories are derived for durable products in a dynamic duopoly.

Open-loop cooperative and non-cooperative pricing behavior is analyzed

within a comprehensive model where sales of differentiated products are

described by interlocked diffusion processes with realistic demand charac-

teristics. Because of analytic complexity, the optimal trajectories implied

by the control and differential game problems are derived numerically across

an extensive set of plausible market scenarios. Manipulation of initial

market conditions enables derivation of optimal competitive pricing as a

function of timing of entry.

Key Words: PRICING, DUOPOLY, DIFFUSION, CONTROL AND GAME THEORY,

COMPETITION.

1.

1. INTRODUCTION

Strategic pricing of consumer durables has been investigated extensi-

vely. Recognizing demand as well as cost dynamics, a body of literature has

emerged which provides a coherent set of normative pricing guidelines.

Relying on the equilibrium concept in a monopolistic environment, the majori-

ty of this research does not recognize the implications of competitive

behavior. As most aspects of business have become increasingly competitive,

existing normative guidelines need to be supplemented with insights regarding

pricing in a competitive environment. Some fruitful attempts have been made

recently and a set of new insights are emerging. However, these insights

remain confined to a single and specific mode of competitive behavior.

Recognizing that firms can and do behave in a variety of ways, this research

extends the normative pricing literature by explicitly focusing on differen-

tial conduct in a dynamic duopoly.

The importance of competitive effects on optimal prices was recognized

early on by Spence (1981). Using a calculus-of-variation approach, he inves-

tigated the impact of competitive behavior on prices in the framework of a

simple demand model with cost dynamics. Thompson and Teng (1984) considered

both advertising and pricing decisions in a dynamic duopoly. Their price

mechanism was modeled as a single selling price decided by the largest com-

petitor. Diffusion characteristics and learning effects were incorporated by

Rao and Bass (1984), who considered a more realistic demand model for a

market of undifferentiated products. Within a similar demand framework,

Clarke and Dolan (1984) studied differentiated product markets and evaluated

basic pricing rules in a simulation framework. Wernerfelt (1985) modeled the

"gaming" aspect of pricing in more detail for undifferentiated but estab-

lished competitors. Enhancing the demand side of the diffusion process and

recognizing time-of-entry effects, Eliashberg and Jeuland (1986) derived some

normative pricing rules. Enhancing the cost dynamics in a special way,

Wernerfelt (1986) obtained optimal prices for an established duopoly with

specific demand characteristics.

Although each of these studies gives important new insights into the

peculiarities of strategic pricing in non-monopolistic markets, they all

assume the same type of competitive behavior. Specifically, competitors are

2.

assumed to maximize profits in a strictly non-cooperative environment. This

does not do justice to the reality of competitive conduct where implicit

cooperative behavior is often observed (Axelrod 1984). The objective of this

study is to investigate strategic pricing under different modes of competi-

tive behavior.

This research investigates profit maximizing price trajectories for

differentiated consumer durables in a dynamic duopoly under coalition,

competition (Nash equilibrium), price following (instantaneous and delayed),

and cost pricing (naive predation). Accordingly, both simultaneous (non-

cooperative) and sequential (reactive) pricing decisions are analyzed

(Eliashberg and Chatterjee 1985). Demand for each product is modeled as a

contagion-type diffusion process (Bass 1969). Demand functions are interre-

lated through a price mechanism and hazard rates capturing the dynamics of

adoption over time. Both primary and secondary demand effects are con-

sidered. The market has two segments defined over a heterogeneous population

in terms of reservation prices. As in Eliashberg and Jeuland (1986) the cost

structures are assumed fixed. No uncertainty is incorporated and the firms

act under full information. Price is the single decision variable considered

explicitly.

Given the complexity of the model, the price trajectories were derived

numerically over a large number of realistic scenarios (a total of 12,288

numerical optimization problems covering 256 different scenarios were

solved). Convergence of the results across scenarios served as a weak test

on uniqueness and convergence to global optima. For computational ease,

open-loop solutions over a finite time horizon were considered. Even though

feedback strategies, where firms can revise their pricing decisions in

response to sales patterns, would be more realistic, the main insights

provided by open-loop equilibria will still hold. After all, competitive

interdependencies take place largely through the price dynamics and, hence,

the mort important "gaming" aspects are captured here. However, the open-

loop results might be less aggressive than the ones obtained from closed-loop

equilibria (Wernerfelt 1985, p.932).

3.

2. DEMAND MODEL FOR DYNAMIC DUOPOLY

Unit sales of the two competing firms in the market are described by a

system of differential equations

Q1(t) = EPB1(1)1(t),P2(0) - Q1(01111[01(0,02(01

(1)

Q2(t) = EPB2(p1(t),p2(0) - 02(01h2[01(0,02(01

where

PB 1(p1(t),p2(0) and PB2(1)1(t),P2(0) denote the number of potential

buyers at time t of, respectively, Firm l's and Firm 2's product;

Q 1(t) and Q2(t) denote the accumulated sales volume by time t of,

respectively, Firm 1 and Firm 2;

h 1[Q1(t),Q2(t)] and h2[01(0,02(t)] denote the hazard rates for the

probability of purchasing, respectively, Firm l's and Firm 2's product.

Within a monopolistic formulation of (1), Bass (1969) developed a

diffusion model for consumer durables where the hazard rate is a linear

function in accumulated sales volume. This fundamental assumption found

support in empirical analyses and has been preserved in subsequent extensions

of the model (see, e.g., Bass 1980, Kalish 1983, Nascimento and Vanhonacker

1988). Since neither theoretical nor empirical reasons suggest otherwise,

linearity was adopted in the duopoly case investigated here.1

Specifically,

moi(t),Q2(01 = ao + al Q 1(t) + a2 Q2(t)

h 2[01(t),Q2(01 = bo + b1 Q 1(t) + b2 02(t)

4.

The interpretations of the parameters in the hazard functions are

identical to those in the case of monopoly. Accordingly, ao and b

o can be

referredtoas"coefficientsofinnovation,"a l , 2 ) can

be referred to as "coefficients of imitation." Note that the hazard rates

are a function of the accumulated sales volume for both competing products.

We assume, however, that "our" accumulated sales volume will have a greater

impact on the adoption of "our" product than will the competitor's accumu-

lated sales volume. Therefete, we assume ai >a, and b2>bi.

The number of potential buyers of each product is modeled as a non-

stationary variable using the. reservation price notion (Jeuland 1981).

Specifically, it is assumed that each individual in the market has a reser-

vation price for both products. These reservation prices are functions of a

large number of variables such as quality, product features, availability,

etc., which are not modeled explicitly.2

Depending on his reservation prices and the market prices for both

products, an individual can be classified at any point in time as .either a

potential buyer of Firm l's product, a potential buyer of Firm 2's product,

or not a potential buyer. Specifically, if his reservation price for product

1 is lover than product l's market price and his reservation price for

product 2 is higher than product 2's market price, the individual will be a

potential buyer of product 2. If the inequalities between the respective

reservation prices and market prices are reversed, the individual will be a

potential buyer of product 1. If both reservation prices are lover than the

respective market prices, the individual will not be a potential buyer of

either product. If, on the other hand, both reservation prices are higher

than the respective market prices, neither product is rejected a priori and

an additional assumption is needed to identify whether the individual will be

a potential buyer of either product 1 or product 2.

Two additional assumptions are homotheticity of the indifference curves

in the space of product characteristics and linear consumption technology.3

The implied choice criterion essentially states that an individual will

choose that product whose reservation price/market price ratio is the

highest. If an individual is willing to pay up to (maximally) pr, and pr2

5.

for, respectively, product 1 and product 2, this implies that the vectors

representing their consumption technologies reach exactly the same indif-

ference curve since the utility derived for each dollar spent on either

product is the same. When the prices of both products vary in the same

proportion as the reservation prices, the vectors representing consumption

technologies will again reach the same level of utility due to the

homotheticity of the indifference curves in the characteristics space.

Accordingly, when both market prices are below the respective reservation

prices at the same percentage level, the individual will be indifferennt

between both products. If the proportionality is different, the individual

will be classified according to the choice rule stated above.

Figure 1 (A) summarizes in reservation price space the classification

of each individual in the market at one point in time given market prices

(p1(t) and 1)2(0) and reservation prices (pr1(t) and pr2(0).

PB1(p1(t),p2(0) as defined above corresponds to area 1, where

FB2(p1(t),p2(0) corresponds to area 2. The border which area 1 and area 2

share is the line pr2(t) [p2(t)/p1(t)Ipr 1(t) which describes indifference

as implied by the homotheticity of indifference curves. Figure 1 (B) ii-

lustrates graphically the shifts that occur if product 1 raises its price.

Two distinct effects occur: first, there is a loss in primary demand (the

area of non-buyers expands along the x-axis); second, there is a loss in

selective demand (the number of potential buyers of product 2 expands).

Mathematically, the potential adopter populations equal (dropping time

subscripts for notational convenience)

PB1(PI ,P2) = N fm I (P2/P1)Pr1 g(pri ,pr2)dpr, dpr,

pi

and

PB2(pi ,P2) = N r

(pl/p2)pr, g(pri,pr2)dpr, dPr2

p2

Reservation Price for Product 2 (pr2(t))

A

P2(0 t) [P(0 ]pr

1 (t) 1 pr

Market Price' for Product 2

(P2 (0)

(A)

Potential Buyers of Product 2 (Area 2)

Non- cuyer.s

. Potential Buyers of Product 1

(Area 1)

Market Price for Product 1 (pi(t))

Reservation Price ) for Product 1

(prl(t))

Reservation Price for Product 2 (pr2(t+1))

A

i'lLoss of Selective Demand Potential for Product 1

(B) Market Price

for Product 2 (p2(t+1)) Loss of Primary

Demand Potential for Product 1

Reservation Price for Product 1

Market Price (pr1(t+1)) for Product 1 (pl(t+1))

Figure 1

Fopulation Breakdown at One Point in Time

6.

where g(pr,,pr2) is a bivariate distribution describing the heterogeneity in

reservation prices across the population, and N denotes the size of the

population. The numerical results reported later were derived with a

bivariate gamma distribution. The corresponding adopter populations are

derived in Appendix 1.

3. MODES OF COMPETITIVE BEHAVIOR

The various competitive environments considered in addition to monopoly

are summarized in Table 1. The monopoly case (Firm 1) was incorporated as a

benchmark. It is a simple control problem analyzed extensively by Kalish

(1983).

Under coalition, both firms cooperate by acting together as a monopoly.

Note that by changing the initial conditions (i.e., Qi(0)= Q2(0)= 0), we can

investigate the situation where one of the firms is a new entrant into an

existing market. Past cumulative sales produce higher hazard rates for the

new entrant. Accordingly, Qi(0) constitutes a barrier to entry for that

firm. The coalition case can also be interpreted as a case of one firm with

two products in a single market and, hence, can provide insights into product

line pricing and the desirability of price/product discrimination.

The competition case is one of non-cooperation where each firm vin

seek to maximize its profits taking the competitor's price as given (i.e.,

Nash equilibrium). Again, initial conditions can be altered to study the

impact on pricing strategies of a newcomer entering an existing market.

The follower case is essentially a naive competition situation: Firm 2

always matches Firm l's price. In contrant to the competition case, this

case is sot "optimal" but is very easy to implement as, apart -from Firm l's

price, no external knowledge is required. Note that by setting t different

from zero, delayed price following behavior can be analyzed.

In the cost pricing situation, Firm 2's long run objective is to

destroy Firm 1. It is willing to pursue this objective at the expense of

its own profits (by essentially pricing its product at cost). As vin

become evident from the discussion hereafter, pricing at cost over the life

Table 1

Competitive Environments Analyzed

Market Characteristics Problem Analytic Statement

Structure

1, Coalition Both firms act

together as a

monopoly

(friendly com-

petition)

Control problem Max T

with two control pl(t) p z(t) f e-rt

(p i (t) - cz ) Q z (t)

variables : t=0

p z (t) and p2(t) -rt

+e (pi (t) - c 2 1 Q 2 (t) dt

Subject to:

Qz (t)=[PBz (pz (t),p,(t))-Q i (t)) hz(Qz (t), Qz (t)).

àz(t)=IPBz (pz (t),Pz(t1)-0»t11 h 2 tO i (t), Q 2 (t)l.

2. Competition Each firm seeks Differential Firm i(i = 1,2):

profit maximiza- game problem in Max T -rt

tion given the context of non- p (t) J e (p (t) - c J Q (t) i

i Q.

competitor's Nash eguilibrium t=0

price

Subject to:

4 1 (t)=1P131 (p 1 (t),p2 (t))-Q1 (t)1 h i fQ,(t), Q 2 (t)).

ô 2 (t)=EPB,(p 1 (t),p 2 (t)1-Q 2 (t)111,(Q i (t), Q 2 (t)].

Q 1 (0) = Q,(0) = qz

Table 1 (cont'd)

Competitive Environments Analyzed

Market

Characteristics

Problem Analytic Statement

Structure

3. Follower Firm 2 matches Stackelberg Max -rt

Firm l's price game problem p (t) f e (p(t) - c2 1 Q (t)

whenever it is t=0

changed (tit-

for-tat type Subject to:

strategy

(5 i (t)=I'13(pi (t),P2 (t))-4,(t)) h i P22 (t). 02 et»1).

Q 2 (t)=[P02(p2 (t),P2(t)(-Q 2 (t)1 11 2(Q2(t), O2 tt»6-

Q(0) = 42(0) = cl,

p 2 (t) = pi (t - T)

4. Cost

pricing

Firm 2 tries to

destroy Firm 1

at the expense

of its own

profits

Control problem

with single

control

variable :

p,(t)

Firm 1

Max

p(t)

t=o

-rt e [p (t) - c i l Q i (t)

Subject to:

, 2 (t)=(1)13, (p i ft ).p, (t ) (-Q,(t)] h i lQ i (t), 42(t)'li-

(2 2 (t)=U132(pI lt),p 2(t))-Q 2 (t)1 11 2[Q 2 (t), Q2 (t)11-

Q2'" = Q2(° ) = q,

Firm 2 :

p = (t) = c,

7.

cycle is not optimal in a predatory sense. Accordingly, cost pricing can be

viewed as a "naive predation" pricing strategy.

4. NUMERICAL ANALYSIS

In general, analytic modeling of optimal pricing decisions in a com-

petitive environment is difficult. To evaluate some simple pricing rules

without even establishing optimality, Clark,- and Dolan (1984) rely on a

simulation analysis. Rao and Bass (1985) and Eliashberg and Jeuland (1986)

pursue the problem analytically but finally have to resort to numerical

analyses to provide meaningful.insights into some of their analytic results.

In order not to compromise on reality to enable some analytic derivations, an

extensive numerical analysis was performed. For a set of 256 realistic

scenarios, the problems shown in Table 1 were solved numerically and cor-

responding price trajectories and cumulative profits were derived.

The parameter values are shown in Table 2. The innovation and imita-

tion parameters were derived from empirical results reported by Bass (1969)

and are similar to the values used in Nascimento and Vanhonacker (1988).

Although no empirical evidence exists on the magnitude of the imitation

impact of a competitor's cumulative sales volume on a firm's diffusion (or

hazard rate), we hypothesized it to be about 1/3 of the direct imitation

effect generated by the firm's own cumulative sales volume. Initial sales

levels were set arbitrarily at 5 and 100. The value 5 was interpreted as an

"early entry" (i.e., new firm entering the market). Because of numerical

optimization problems, the value zero could not be used. Value 100 was

interpreted as a "late entry" (i.e., firm operating in an established

market). Relative to a population size of 2000, value 100 implies 5Z

penetration given each individual buys only one unit of the product. The

absolute values are of little concern as the relative comparisons of interest

are independent of the scale adopted. In all analyzed scenarios, the con-

straint was added that sales of neither product could be negative.

Ail other parameters were fixed. The bivariate gamma distribution

describing heterogeneity in the reservation prices was relatively flat, with

a, = a, = 1 and e, e, = 40. With a, = a, = 1, the marginal densities are

Table 2

Parameter Values of Numerical Investigation

Variable

Notation

Description Values

a , b o o

a„ b2

innovation parameter for Firm 1 0.005, 0.030, 0.060, 0.100

and Firm 2

imitation parameter, own firm's 0.0003, 0.0006

cumulative sales

a2, b,' imitation parameter, competi- 0.0001, 0.0002

tor's cumulative sales

MO)

initial sales for Firm 1 5, 100

02(°)

initial sales for Firm 2 5, 100

ale 0(.2 parameters of bivariate gamma 1

( 1 (3 2 distribution (reservation price

40

distribution)

T

finite time horizon 8

C I / 2 marginal unit production cost 10

for Firm 1, Firm 2

N

size of population 2000

' With the implied constraint that a, > a2 and 1)2 > b,; all numerical

results imply scenarios with a constant ratio (3) between the corresponding parameters.

8.

exponential. Accordingly, reservation prices are concentrated towards the

axes. Furthermore, the shape of the distribution of the population remains

the same irrespective of the values of the 0 parameters.

In all, 256 scenarios were analyzed. Within each, optimal price

trajectories were derived for six different competitive environments over a

finite horizon of eight tire periods. Accordingly, 12,288 numerical optimiza-

tion problems were solved with an approach similar to the one adopted by

Pindyck (1978). GAMS (Kendrick and Meeraus 1985), a powerful optimization

program, was used to derive numericall' the optimal price trajectories.

Because of inherent checks for local versus global optima and convergence of

the results derived, we feel reasonably confident about the uniqueness of the

derived optimal trajectories.

Some of the optimization problems could not be solved satisfactorily.

For subsequent analysis and discussion, we retain the scenarios for which the

optimization could be solved over eight consecutive time periods.4 Obviously

not selected at random, subsequent analysis exhibits remarkable convergence

of results. Moreover, the scenarios are representative and provide good

overall insight into strategic pricing under the different modes of competi-

tive behavior.

5. RESULTS FOR SOME SPECIFIC SCENARIOS

A. Description of Scenaries

In order to illustrate the impact of dynamic demand characteristics,

ten scenarios were singled out for a detailed analysis. The profile of

these scenarios is described in Table 3. As can be seen there, the

scenarios differ in diffusion process parameters for both products. For the

first four scenarios, both products have symmetric diffusion processes (i.e.,

identical innovation and imitation parameters). They only differ in initial

saleslevel(i.e.,Q.(0) for i=1,2). In the first scenario, both firms can

be interpreted as early entrants. In scenario 2, the firms compete much

later in the category's life cycle. The last two scenarios have one firm

being a late entrant relative to the other. These symmetric diffusion

Table 3 Profile of Scenarios

SALES DIFFUSION PARAMETERS Firm 1 Firm 2

Description Imitation Imitation Initial Sales Stage of

Diffusion Diffusion Processes Innovation Firm 1 Firm 2 Innovation Firm 1 Firm 2 Firm 1 Firm 2 Scenario Processes Firm 1 Firm 2 (a ) (a ) (a) (b ) (b ) (b ) (Q (0) (4(0)

0 1 2 0 1 2 1 2

1. Symmetric Early Early 0.060 0.0003 0.0001 0.060 0.0001 0.0003 5 5

2. Symmetric Late Late 0.060 0.0003 0.0001 0.060 0.0001 0.0003 100 100

3. Symmetric Late Early 0.060 0.0003 0.0001 0.060 0.0001 0.0003 100 5

9. Symmetric Early Late 0.060 0.0003 0.0001 0.060 0.0001 0.0003 5 100

5. Asymmetric Late Late 0.005 0.0003 0.0001 0.005 0.0002 0.0006 100 100

6. Asymmetric Late Late 0.005 0.0006 0.0002 0.005 0.0001 0.0003 100 100

7. Asymmetric Early Early 0.100 0.0003 0.0001 0.100 0.0002 0.0006 5 5

8. Asymmetric Early Early 0.100 0.0006 0.0002 0.100 0.0001 0,0003 5 5

9. Asymmetric Late Early 0.060 0.0003 0.0001 0.030 0.0002 0.0006 100 5

10. Asymmetric Late Early 0.030 0.0006 0.0002 0.060 0.0001 0.0003 100 5

9.

scenarios will give detAdaxed insight into the effect of order of entry on

strategic pricing under iiEferent modes of competitive behavior.

The remaining six senarios consider asymmetric diffusion processes.

For scenarios 5 and 6, oth firms compete late in the category's life cycle.

In contrast, scenarios lamd 8 capture competition early in the life cycle.

In scenarios 9 and 1, Firm 2 is a late entrant relative to Firm 1. In

scenario 9, the new eatmanz has diffusion process parameters which are twice

as large as the cormlemnding parameters of the incumbent. In scenario 10,

the reverse relationshipœxists between the corresponding parameters. The

numerical results for tffieue ten scenarios are discussed next.

B. Optimal Price Traje lies

The optimal prive trzajectories for the symmetric scenarios are shown in

Figure 2. The price stiatiegies shown are those for Firm 1 under different

modes of competitive belavior. Scanning the four graphs in Figure 2, one

general result stands entr prices in a dynamic duopoly decline monotonically

over time irrespective (of the mode of competitive behavior. Given that no

cost dynamics (i.e., leuroIng/experience effects) were incorporated, this

general pattern descrAkes a strategy of dynamic price discrimination.

Specifically, no penetttinm pricing is necessary to stimulate early diffu-

sion. This is in comitiast to the optimal pricing strategy under a monopoly,

where initial penetratimo &s necessary (see scenarios 1 and 4).

More specific izastzs can be summarized as follows:

(i) Across the 6007 scenarios, optimal prices under monopoly and

competitive ante very close to one another. Monopoly prices start

out at either tehe same level (scenario 3) or a lover level but

competitive pniices drop much faster over time. Monopoly pricing

initially fonns>es on stimulating the adoption through low pricing.

Less aggresuVce. pricing is needed initially under competition as

competitor through the hazard rates provide enough of a

stimulus to tthe process. Later in the life cycle, prices will

drop fastes. Mkewever, as each company will attempt to attract

customers andt„. pence, protect its profits.

1 1 ... 1 2 3 4 5 6 7 8

T iME

Scenario 3

1 2 3 4 5 6 7

• MONOPOLY O COALITION o FOLLOWER 0 o FOLLOWER 1

O COMPETITION • COST PRICING

w u

cr 40

30

20 —

60

50

TiME

60

1 2 3

TRIE

1 5 6 7 t

50

w u cc 40

30

20

I J

1 2 3 4

TIME

5 6 7 8

• mONOPO Y

O COALITION o FOLLOWER 0 o FOLLOWER 1 • COMPETITION

✓ COST PRICING

Scenario 4

Figure 2

Price Trajectories for Firm 1 When Both Firms Have Symmetric Diffusion Processes

Scenario 2

60

50

w u

cc

- 4

0 a.

30

20 —

• MONOPOLY

O COALITION o FOLLOWER 0

o FOLLOWER 1

O COMPETITION

• COST PRICING

Scenario 1 • MONOPOLY

O COALITION o FOLLOWER 0 à FOLLOWER 1

O COMPETITION

• COST PRICING

60

50

w

cr - 40 a

30

20

10.

(ii) Cost pricing by the new entrant leads to the most aggressive

pricing by Firm 1 (see scenarios 2 and 3). Clearly, Firm 1 at-

tempts to protect its business against the "predator." When the

incumbent resorts to cost pricing at the expense of the new

entrant (Scenario 4), initial pricing is relatively high indicat-

ing profit taking when the direct threat is minimal.

(iii) Cooperative competitive behavior leads to higher prices.

Follower 0, follower 1, and coalition result in relatively high

prices for Firm 1 across the four scenarios. Follower 1 prices do

become aggressive later on to secure a large share of the expand-

ing primary demand. Coalition prices for Firm 1 are highest when

it enters a market with an established competitor. Accordingly,

some segmentation seems optimal. The price differential between

the two firms will be investigated shortly.

(iv) When both firms are early, the range of initial prices for dif-

ferent modes of competitive behavior is smallest. Except for cost

pricing, these initial prices are also the lowest among the four

scenarios. This seems to suggest that extensive price competition

is secondary to both firms attempting to stimulate the diffusion

and adoption of the category. Market growth is the dominant

objective of the players early on in the category's life cycle.

(v) Irrespective of the mode of competitive behavior, Firm l's initial

prices are highest when it is first to the market (see scenario

4). This is in contrast to the monopoly environment when early

entry would require the subsidizing of early adopters to stimulate

diffusion and adoption.

Figure 3 illustrates the price differentials under coalition and compe-

tition between both firms. The results for scenario 4 are not shown as they

are identical to the ones for scenario 3 except for switching Firm 1 and Firm

2. In scenario 1, there is no differential. Both competitors are early

entrants in the category. They are more eager to create market growth than

to differentiate on price. As one would expect, coalition pays better than

Figure 3

Price Trajectories for Both Firms Having Symmetric Diffusion Processes

Scenario 1

60 60

50 50

W u_ Q 40 o.

w u cc 4 0 Ô.

30 30

20 20

1 2 3 4 5 6 7 e

TIME

1 i t 1 t I I i

O COALITION (1. 2) 60

O COMPÉTITION (1) o COMPÉTITION (2)

50

30

20

Scenario 3

1 2 3 4 5 6 7 e

TIME

1 t ,. 1 1 1

Scenario 2 t

O COALITION (1, 2) O COMPETITION (1) o COMPETITION (2)

1 2 3

I

4

TIME

8 5 6 7

O COALITION (I ) O COALITION (2) O COMPETITION (1) O COMPETITION (2)

11.

competition. A somewhat similar pattern is observed in scenario 2. However,

prices under competition diverge somewhat over time. Whether this is a

substantively meaningful result (indicating the development of segments) or a

strictly numerical result is not clear at this point. More analysis is

needed here.

The results for scenario 3 suggest that, when both firms enter the

market sequentially, the price differential is the largest under coalition

with the new entrant having higher prices. Accordingly, segmentation is more

difficult to achieve under competition. Ove: time, however, the differential

is difficult to maintain both under cooperative and non-cooperative behavior.

The optimal price trajectories for Firm 1 for scenarios 5 and 6 are

shown in Figure 4. In scenario 5, Firm 1 has the slowest diffusion process;

in scenario 6, Firm 2 has the slowest process. Actually, results in scenario

5 are the optimal pricing patterns for the "slow diffusion" competitor

whereas the results in scenario 6 are the ones for the "fast diffusion"

competitor. Consistent with the symmetric scenarios discussed above, coope-

rative behavior results in high level price trajectories for both competi-

tors. In contrast to the previous four scenarios, the trajectories generally

exhibit more penetration characteristics irrespective of the mode of competi-

tive behavior. This probably is a result of the small value of the innova-

tion parameter used in scenarios 5 and 6. Because of the small innovation

effects, aggressive pricing is needed early on to stimulate diffusion. Some

specific results can be summarized as follows:

(i) Relative to the "fast diffusion" competitor (scenario 6), the

"slow diffusion" competitor (scenario 5) faces flatter price

trajectories over time irrespective of the mode of competitive

behavior. Apart from the coalition case, these trajectories start

at lover price levels than the corresponding trajectories for the

"fast diffusion" competitor. The optimal strategy for the "fast

diffusion" competitor is to price aggressively over time so as to

stimulate market growth irrespective of the pricing behavior of

its competitor.

20

Scenario 6 Scenario 5

60

• 1.40NOPOLY O COALITION o FOLLOWER 0 o FOLLOWER 1

O COMPETITION ✓ COST PRICING

• MONOPOLY O COALITION o FOLLOWER O o FOLLOWER 1

O COMPETITION • COST PRICING

60

50

cc 40

30

20

1 2 3 4 5 6 7

TIME

1 2 3 4 5 6 7

TIME

Figure 4

Price Trajectories for Firm 1 When Firms Have Asymmetric Diffusion Processes

and are Late Entrants

12.

(ii) Under coalition, the "slow diffusion" competitor prices much

higher than the "fast diffusion" competitor, The price differen- _

tial is quite large with prices showing little sign of converging

over the finite time horizon. The strategy here seems to price the

rapidly diffusing product low to stimulate diffusion and to price

the slow diffusing product high to generate profits.

Accordingly, both products seem to play a different role in the

overall maximization of discounted profits.

(iii) Follower prices are highest when Firm 1 has a relatively rapid

diffusion process (scenario 6). Accordingly, the "fast diffusion"

competitor will benefit most from reactive cooperative pricing

behavior by its competitor.

The optimal trajectories for scenarios 7 and 8 are shown in Figure 5.

In these scenarios, both firms are early entrants (see Table 3).5

The price

trajectories in scenario 7 are those of the "slow diffusion" competitor

whereas the price trajectories in scenario 8 are those of the "fast diffu-

sion" competitor. Consistent with previous results, cooperative behavior

leads to higher prices for either player. However, the price spread over the

different modes of competitive behavior is relatively small. Accordingly, a

skimming-type pricing strategy is optimal with the degree of skimming to some

extent independent of the conduct of the competitor. With their large inno-

vation parameters, the competitors focus on early profit taking. Head-on

price competition to protect their later business is evidenced by small

differences in competitors' prices for corresponding trajectories.

Figure 6 contains the results for scenarios 9 and 10. Here, Firm 1 is

the established company and Firm 2 is a new competitor entering the market.

In scenario 9, Firm 1 has a relatively slow diffusion process characterizing

the demand for its product (i.e., the new entrant's product is adopted

faster) but has a relatively large coefficient of innovation. Except for

coalition, the price trajectories are monotonically decreasing for all modes

of competitive behavior. Aggressive pricing over time is warranted to

protect the firm's position against the "fast diffusion" entrant. If the

established firm pursued a penetration strategy, the "fast diffusion" entrant

1 2 3 4 5 6 7

TIME

1 2 3 4 5

TIME

6 7

a 40

20

60

30

50

Figure 5

Price Trajectories for Firm 1 When Firms Have Asymmetric Diffusion Processes and Bath

are Early Entrants

60

50

y m 40 a

30

20

• AIONOPOLT O COALITION o FOLLOWER 0 • FOLLOWER 1

O COMPETITION • COST PRICING

Scenario 7 • MONOPOLY O COALITION o FOLLOWER o FOLLOWER 1

O COMPETITION • COST PRICING

Scenario 8

60

50

cr 40

30

20

Scenario 10 • MONOPOLY O COALITION o FOLLOWER O o FOLLOWER 1 O COMPETITION ✓ COST PRICING

T 1 6 2 3 4

TIME

5 8 1 2 3 4 5 6 7

TIME

8

• MONOPOLY O COALITION o FOLLOWER o FOLLOWER I O COMPETITIONI ✓ COST PRICING

,

Figure '6

Price Trajectories for Firm 1 When Firms Have Asymmetric Diffusion Processes

And Firm 2 is a Lane, Entrant

60

cr 40

30

20

13.

would get a disproportionate share of the market expansion irrespective of

his pricing behavior. Penetration is warranted under coalition as both would

share the expansion and, hence, the profit benefits. As is shown in Figure

7, both firms under coalition should pursue a penetration-type pricing

strategy early on to reap the full benefits of a growing market demand.

In scenario 10, Firm 1 is still the established company but also has a

relatively faster diffusion process characterizing the demand for its

product. Irrespective of the competitive behavior exhibited by the new

entrant, some penetration pricing by the ircumbent is warranted initially to

further stimulate diffusion and adoption. However, prices will decline

rapidly to prevent the new entrant from capitalizing on the expanding market

with his relatively larger innovation characteristics. Figure 7 illustrates

that under competition the price differential is small with the new entrant

charging a slight premium initially. Under coalition, there is a clear

segmentation with the new entrant charging prices much higher than the incom-

bent. In maximizing profits, the coalition capitalizes on the large

innovation parameter of the new entrant's demand and the dominant diffusion

parameters of the incumbent's demand.

As observed in previous scenarios, Figure 6 establishes that cooperative

behavior again results in higher prices. This is a general characteristic

and does not seem to be affected by either the timing of entry or the diffu-

sion processes of the competing products.

C. Cumulative Profits

The cumulative profits generated over eight periods for the selected

scenarios are summarized in Table 4.6

The table also illustrates the per-

centage of monopoly profits (Firm 1) that can be realized under different

modes of competitive behavior. From these results, it is evident that some

form of competitive behavior can have a drastic impact on prdfits. For the

selected scenarios, as much as 66% of the monopoly profits can be lost by a

competitor entering the market. The magnitude of the loss in monopoly

profits is different depending on the conduct of the competitor. The in-

sights can be summarized as follows:

O COALITION (1) o COALITION (21 • COmPETITION (1)

o COMPETITION (2)

O COALITION (1) Scenario 10

o COALITION (2)

• COmPETITION

o COMPETIT(ON (2) •

I

$0

20

50

Scenario 9

c 40 sa.

30

60

50

c 40

30

20

2 3 4 5

6 7

1 2 3

4

5 6 7

8

TIME

TIME

Figure 7

Price Trajectories for Both Firms Having Asymmetric Diffusion Processes With

Firm 2 Being a Late Entrant

Table 4

Cumulative Profits for Scenarios,

Competitive Envi ronment

Symmetric Sales Diffusion Processes Asymmetric Sales Diffusion Processes

Scenarios Scenarios Scenarios Scenarios

1 2 3 4 5 6 7 8 9 10

monopoly, 10276.3 11013.9 11013.9 10276.3 5786.8 12283.2 14156.3 18117.8 11013.9 14224.1

(1.00) (1.00) (1.00) (1.00) (1.00) (1.00) (1.00) (1.00) (1.00) (1.00)

Coalition Firm 1 8808.0 9321.1 9260.5 9227.5 5021.9 11651.6 11652.9 15890.1 8756.7 12330.8

(0.86)3 (0.85) (0.84) (0.90) (0.87) (0.95) (0.82) (0.88) (0.80) (0.87)

Firm 2 8808.0 9321.1 9227.5 9260.5 11651.6 5021.9 15890.1 11652.9 11264.2 8861.4

(0.86) (0.85) (0.84) (0.90) (2.01) (0.41) (1.12) (0.64) (1.02) (0.62)

Follower 0, 8808.0 9321.1 8791.7 9626.4 5934.9 10243.9 12262.0 14053.1 8814.4 11004.2

(0.86) (0.85) (0.80) (0.94) (1.03) (0.83) (0.87) (0.76) (0.80) (0.77)

Follower 1 2 8969.9 9615.3 9059.2 9820.9 6012.0 10716.0 12575.2 15804.0 9077.4 11540.9

(0.87) (0.87) (0.82) (0.96) (1.04) (0.87) (0.89) (0.87) (0.82) (0.81)

Competition Firm 1 8496.0 8826.9 8750.7 8941.0 5495.7 10028.3 11587.6 14670.9 8539.1 11171.0

(0.83) (0.80) (0.79) (0.87) (0.95) (0.82) (0.82) (0.81) (0.78) (0.79)

Fins 2 8550.7 8974.8 9004.8 8875.9 10172.6 5551.1 14896.1 11734.8 10561.9 9021.6

(0.83) (0.81) (0.82) (0.86) (1.76) (0.45) (1.05) (0.65) (0.96) (0.63)

Cost Pricing, 4353.7 3992.9 3727.3 4829.4 2999.8 4251.8 6017.8 7597.4 3838.6 4798.2

(0.42) (0.36) (0.34) (0.47) (0.52) (0.35) (0.43) (0.42) (0.35) (0.34)

Cumulative profits computed over eight time periods; for description of 10 scenarios, see Table 3.

Results for Firm 1. Percentage of cumulative profits for corresponding monopoly environment (i.e., 1 ne 1 in the table).

14.

(i) Cost pricing by the competitor results in a firm obtaining less

than half of its monopoly profits.

(ii) Across the scenarios, cumulative profits under Follower 0 are less

than the corresponding cumulative profits under Follower 1.

Accordingly, if the competitor opts for price following (reactive

cooperative pricing strategy), cumulative profits of a firm are

enhanced when price adjustments are delayed irrespective of demand

characteristics. One has to keen in mind, however, that to some

extent the finite horizon might explain this result. Specifical-

ly, under delayed response, the price leader makes an end move in

the last period. In order to capture a substantial share of the

market, the price leader will slash prices drastically (see, e.g.,

price trajectories for Follower 1 illustrated above). The longer

the response delay, the larger the window of opportunity to make

this move and capture the market. Even though unit margins fall,

demand might expand at a faster rate resulting in enhanced overall

profits.

(iii) Cumulative profits of a firm are generally largest when it does

not face any competition (i.e., monopoly environment). One

exception is scenario 5 where price following by the competitor

provides cumulative profits which are slightly higher than the

corresponding monopoly profits (i.e., Follower 0: 5934.9; Follower

1: 6012.0; versus Monopoly: 5786.8). Whether this is a substan-

tively meaningful result or a numerical analysis result is not

clear at this point. It indicates, however, that competitive

presence in some instances could have a positive net effect on

cumulative profits over a finite horizon. Here, the firm seems to

benefit from the dominating diffusion characteristics of the

competitor's product and his price following behavior. Further

analysis is warranted here.

(iv) In general, cooperative behavior results in larger cumulative

profits than non-cooperative behavior. There are some excep-

tions, however. In scenario 5, Firm l's cumulative profits under

15.

coalition are smaller than under competition. In this instance,

only a side payment would induce the firm into cooperative be-

havior. As seen in Figure 5 and discussed above, coalition would

require Firm 1 to price its product relatively high and, hence,

limit its market appeal. Other instances where side payments

might be needed between coalition partners are discussed in (vi)

hereafter. Other deviations from the general pattern that

cooperative behavior results in larger cumulative profits than

non-cooperative behavior are observed in scenarios 8 and 10. In

both of these scenarios, cumulative profits for Firm 1 under

competition are larger than cumulative profits under instantaneous

price following behavior (Follower 0). Accordingly, if the new

entrant is an instantaneous price follower, he will dispropor-

tionately hurt the "fast diffusion" firm irrespective of whether

or not the latter is an established firm in the market.

(v) Irrespective of demand characteristics, total cumulative profits

for the coalition partners are larger than their combined profits

under competition. Accordingly, coalition pays. This result is

also interesting when interpreting it in the framework of product

line pricing decisions. Stated simply, product proliferation may

lead to a reduction in overall profits when individual products

are allowed to compete directly with one another.

(vi) As discussed in (iv) above, coalition in scenario 5 would be

achieved if Firm 1 received a side payment to cover the differen-

tial between its cumulative profits under coalition and its

cumulative profits under competition. Similarly, Firm 2 is likely

to request a side payment in scenarios 6, 8, and- 10. Although

further analysis is warranted here, these results suggest that

side payments generally will be necessary to achieve coalition in

cases of asymmetric diffusion, with the "fast diffusion" partner

paying the "slow diffusion" partner.

16.

6. SUMMARY OF NUMERICAL RESULTS

A. Optimal Price Trajectories

A convenient way to summarize all numerical results is to use a set of

linear regression equations (see, e.g., Nascimento and Vanhonacker 1987a).

The equations reported here relate the parameters of the diffusion processes

and their pairwise interactions to a number -f dependent measures describing

aspects of either the optimal price trajectories (i.e., initial price, price

range over time, period in which price peaked, mean price level, and dif-

ference in mean price level over different modes of competitive behavior) or

cumulative profits over a finite time horizon (i.e., absolute cumulative

profits, and differences in cumulative profits over different modes of com-

petitive behavior). Higher-order interactions were not considered so that

adequate degrees of freedom were assured for estimation and testing. The

linearity assumption is restrictive and might be a crude approximation for

some dependent measures, but highly significant fits were established in- _

dicating that in general the approximation was adequate. The results are

reported in the form of significant standardized regression coefficients

(e.g., Beta coefficients).

The main independent variables in each of the estimated equations are

the six characteristics of the diffusion processes: initial cumulative sales

for both firms (i.e., Q,(0) and 02(0)), the innovation parameters for both

firms (i.e., ao

and bo), and the imitation parameters (i.e., ai and bi for

i=1,2). Because of the constant relationship between both imitation

parameters within each diffusion process (i.e., a,/a2= b2/b,= 3; see Table

2), the imitation parameters were incorporated as a single variable.

The regression results for the optimal price trajectories are sum-

marized in Table 5. The primary results for the four selected aspects can

be described as follows:

(i) Initial Price Level: Consistent with the monopoly case, when the

diffusion processes of both firms are less dependent on imitation

effects than on innovation effects and both firms are established

1.12

-0.65 0.92 -0.65 -0.74 -0.43

0.49 (0.37) 0.50 0.41 0.67

-0.10 -0.17 -0.19 (-0.13)

-0.52 (0.08) -0.20 -0.46 0.42

0.62 0.77 0.41

0.32 0.27 (0.37)

0.43 0.56

(0.16)

(0.69)

-0.35 0.47 0.34 0.27

-0.22

0.95

(0.16)

0.28

-0.31

0.95

-0.16 0.32

(-0.10)

(-0.47)

(0.29)

-0.28 (-0.23)

(0.13)

(0.15) -0.25

(0.31)

-0.29 (0.32)

1.1

-0.51

(0.16) -0.15 -0.18 (-0.12)

-0.49 (0.08) -0.17

(0.47) (0.25)

(0.12) 0.19 (0.16)

(0.15)

-0.46 -0.27

-0.24

Table 5

Summary of Numerical Results on Price Trajectories for Firm 1 1

Initial Price Price Range Over Fixed Time Horizon

Follower Cost Follower Cost

Mono- Coali- Compe- Pricing Mono- Coali- 0 1 Compe- Pricing

poly tion 0 1 tition poly tion tition

Main Effects (Sales Diffusion

Parameters)

(1) Initial Cumulative

Sales

(2) Firm 1 Innovation

(3) Imitation

0.44 (-0.58) 0.92 0.68

1.16 -0.92 1.28 1.49 0.92

-0.23 (-0.18) (-0.20) (-0.32)

-0.81 -1.34 -1.52 -1.04 -0.94 (-0.39)

1.37 0.92 (0.30)

(0.96) (0.30)

(4) Initial Cumulative

Sales

0.71 (0.17) (0.29) 0.78

(-0.57) (-0.53) (0.38)

(5) Firm 2 Innovation

1.56 0.51

(6) Imitation

(0.13) -0.34 -0.58 -0.51

Pairwise Interactions

Àdjusted 0.96

0.65 0.94

0.91 0.94

0.82

0.49 0.52

0.52 0.58

0.92 0.83

)Table entries are the standardized estimates (Beta coefficients) significant at 0.01; entries in parentheses are significant at

0.05.

Summary of Numerical

Table 5 (cont'd)

Results on Price Trajectories for Firm 11

Period in Which Maximum Price was Reached Mean Price

Follower Cost Follower Cost

Mono- Coali- Compe- Pricing Mono- Coali- Compe- Pricing

poly tion 0 1 tition poly tion 0 1 tition

Main Effects (Sales Diffusion Parameters)

(1) Initial Cumulative

Sales -0.69 -0.79 -0.84 -0.82 (0.22) -1.05 (0.29) (0.41) -0.76 -1.19

(2) Firm 1 Innovation -1.67 -1.30 -1.68 -1.59 -1.35 (-0.56) 1.03 -1.68 1.50 1.59 -0.42

(3) Imitation -0.36 (-0.37) (-0.26) -0.46 -0.86 (-0.31) -0.65

(4) Initial Cumulative

Sales -1.05 (-0.38) (-0.72) -0.99 (0.33) (0.25) (0.37) 0.98

(5) Firm 2 Innovation (-0.37) -0.91 0.86 0.67

(6) Imitation -0.63 0.27 (0.26) -0.34 -0.38

Pairwise Interactions

(1) x (2) 0.47 (-0.20) 0.52 0.53 0.69 (0.17) -0.82 0.42 -0.77 -0.86 -0.32 0.12

(1) x (3) (-0.27) 0.61 0.34 0.93 0.44 0.53

(1) x (4) (-0.57) (0.10) 0.32 -0.17 -0.23 -0.32 (-0.08)

(1) x (5) 0.28 (0.09) 0.45 -0.31 -0.28 -0.25 (1) x (6) (0.38) (-0.24) (0.32) 0.41

(2) x (3) 0.63 0.56 0.24 0.74 0.31 (0.10)

(2) x (4) 0.25 0.19 (0.13) 0.39 0.38 (0.14) -0.23 -0.25 -0.18

(2) x (5) 0.76 0.60 (0.11) 0.19 (0.24) 0.49 -0.25 -0.17 (-0.07)

(2) x (6) 0.62 0.59 (0.21)

(3) x (4) (0.17) 0.21

(3) x (5) (0. 29) (0.15) 0.28 0.20

(3) x (6) (-0.26) (-0.19)

(4) x (5) (0.16) 0.51 -0.32 -0.39 -0.20

(4) x (6) (0.20)

(5) x (6) 0.53

Adjusted 0.88 0.65 0.85 0.84 0.81 0.43 0.90 0.82 0.86 0.85 0.91 0.93

'Table entries are the standardized estimates (Geta coefficients) significant at 0.01; entries in parentheses are significant

at 0.05.

17.

in the market, initial prices for Firm 1 will be high under com-

petition and price following behavior. Under coalition, initial

prices for Firm 1 will be high when, relative to Firm 2, its

innovation effects are small and it entered the market later. If

Firm 2 as a new entrant resorts to cost pricing, incumbent Firm 1

will price high initially when the entrant's sales are driven

primarily by innovation rather than imitation.

(ii) Price Range Over Fixed Time Ho!izon: For established firms exer-.

cising cooperative behavior (i.e., coalition or price following),

the range of Firm l's prices over time will be narrow when its

sales diffusion is driven primarily by innovation effects where

that of the other firm is driven by imitation effects. Under

competition, the range of Firm l's prices will be narrow when it

is established and has a rapid sales diffusion process relative to

a new entrant. When Firm 2 opts for cost pricing, the range of

established Firm l's prices will be narrow when its sales diffu-

sion process is driven by innovation rather than imitation, the

reverse of the competitor's sales diffusion process.

(iii) Time Period in which Prices Will Peak: Prices for Firm 1 viii

peak early and decline monotonically afterwards when both firms

are established competitors and Firm 1 sales diffuse relatively

fast over time. This result generally holds irrespective of the

conduct of the competitor. In the case of cost pricing, this

result is strengthened when Firm 2's sales diffusion has a strong

innovation effect.

(iv) Mean Price Level: consistent with the monopoly case, the average

of Firm l's prices will be high when both established competitors

have sales diffusion processes with strong innovation and weak

imitation effects and Firm 2 exhibits price following behavior.

Under coalition and non-cooperative behavior (i.e., competition

and cost pricing) in a market with an established competitor whose

sales diffusion process is driven primarily by innovation effects,

18.

Firm 1, as a new entrant, will have a high average price level

when its sales diffuse slowly over time.

The regression results on the pairwise differences in mean price level

are shown in Appendix 2. The main effects are summarized in Table 6. That

table specifically describes the instances in which the difference in mean

price level for Firm 1 will be large. For example, the top cell describes

the instance where for Firm 1 the average price level under monopoly will be

higher than the average price level under coalition. As indicated, this will

be the case when Firm 1, as an incumbent, has a sales diffusion process with

both strong innovation and strong imitation characteristics but its competi-

tor's sales diffusion process is primarily driven by imitation effects.

Moreover, the three key characteristics (i.e., time of entry, innovation, and

imitation) which give rise to large price differentials between modes of

competitive behavior are tabulated in Table 6. In general, the results

indicate that at least one difference in the firms' profile along the three

characteristics gives rise to average price level differences. The parti-

cular characteristic which drives the result varies depending on the mode of

competitive behavior.

Table 7 shows the regression results for the difference between the

average price level of both firms under coalition and competition. Interes-

tingly enough, what drives the price difference is not all that different in

the cooperative and non-cooperative situations. Specifically, mean price

level between both firms will be large when Firm 1 is a new entrant with the

sales diffusion process of both firms being slow. This is consistent with

the analysis of scenario 3 discussed above. In other words, this result

seems to suggest that identical factors will lead to price segmentation

irrespective of cooperative or non-cooperative conduct. The payoff in terms

of cumulative profits will, of course, be different as vin. be discussed

shortly.

B. Cumulative Profits

Regression results on the cumulative profits for Firm 1 are shown in

Table 8. The very high adjusted R2's indicate that the assumed linear model

adequately captures the characteristics of the relationships. Although there

is some variance in magnitude and in level of significance, the direction of

Monopoly Coalition Follower 0 Follower 1 Competition Firm 1 Firm 2 Firm 1 Firm 2 Firm 1 Firm 2 Firm 1 Firm 2 Firm 1 Firm 2

Table 6 1 Profile of Instances Where Difference in Firm l's Average Price Level Will Be Large

Established 2 -- Strong Weak

Coalition Innovation Innovation Strong Strong Imitation Imitation

-- New Entrant -- Weak Weak Strong

Follower 0 Innovation Innovation Innovation Weak Weak Weak Weak Imitation Imitation Imitation Imitation

New Entrant New Entrant -- -- Strong Weak Strong Strong

Follower 1 Innovation Innovation Innovation Innovation Weak Weak Weak Weak Strong -- Imitation Imitation Imitation Imitation Imitation

Established New Entrant New Entrant Established New Entrant -- New Entrant Strong -- Weak -- Strong Weak Strong Weak

Competition Innovation Innovation Innovation Innovation Innovation Innovation -- Weak Weak -- Strong -- --

Imitation Imitation Imitation

Cost Pricing

-- New Entrant Established -- Established -- Established Established Strong Weak Strong -- Strong -- Strong Strong

Innovation Innovation Innovation Innovation Innovation Innovation Weak Weak Weak Strong -- Strong Imitation Imitation Imitation Imitation Imitation

,Difference is measured as the column mean minus the row mean; results are based on the main effects significant at 0.05 or better (sec Appendix 21. ,"Established" and "strong" refer to significant positive effects of, respectively, initial cumulative sales and either innovation or imitation parameters. "New Entrant" and "weak" refer to significant negative effects of the identical variables.

Table 7

Summary of Numerical Results on Differences in Mean Price Level Between Both Firms

Under Coalition and Competition

Coalition Competition

Main Effects (Sales Diffusion Parameters)

(1) Initial Cumulative Sales (2) Firm 1 Innovation

(3) Imitation

(4) Initial Cumulative Sales (5) Firm 2 Innovation (6) Imitation

-0.78 -1.43 -0.56

-0.71

-0.87 -0.98 -1.20

(-0.60) -0.75

Pairwise Interactions

(1) (1)

x x (2) (3)

0.40 0.50

(1) x (4) (-0.16) (1) x (5) -0.21 (-0.16) (1) x (6) (0.29) (0.30) (2) x (3) 0.50 0.45 (2) x (4) 0.25 (0.14-) (2) x (5) (0.12) (2) x (6) 0.57 (3) x (4) 0.52 (3) x (5) 0.48 (3) x (6) (4) x (5) -0.38 -0.28 (4) x (6) (0.28) (0.40) (5) x (6) 0.86 0.56

Adjusted R2

0.85 0.88

' Mean price level for Firm 1 minus mean price level for Firm 2. Table entries are the standardized estimates (Beta coefficients) significant at 0.01; entries in parentheses are significant at 0.05.

Table 8

Summary of Numerical Results on Cumulative Profits for Firm 1 2

Competitive Environment

Monopoly Coalition

Follower

Competition

Cost

Pricing 0 1

Main Effects (Sales Diffusion Parameters)

(1) Initial Cumulative Sales 0.32 0.24 0.31 0.35 0.29 (2) Firm 1 Innovation 1.14 1.07 1.17 1.14 0.13 0.90 (3) Imitation 0.52 0.46 0.62 0.61 0.68 0.62

(4) Initial Cumulative Sales 0.14 0.27 0.23 0.26 0.35 (5) Firm 2 Innovation 0,16 0.21 0.17 (0.14) (0.10) (6) Imitation (-0.07) (-0.07) -0.37

Pairwise Interactions

(1) x (2) -0.42 -0.34 -0.35 -0.37 -0.37 -0.33 (1) x (3) 0.23 0.18 0.11 0.11 0.12 -0.09 (1) x (4) -0.09 -0.09 -0.10 -0.11 -0.17 (1) x (5) (-0.04) -0.10 -0.08 -0.23 (1) x (6) 0.29 (2) x (3) -0.16 -0.18 -0.25 -0.19 -0.23 -0.24 (2) x (4) -0.13 -0.11 -0.08 -0.14 -0.10

(2) x (5) -0.10 -0.11 -0.09 (-0.04) -0.14 (2) x (6) (0.11) (0.10) (0.06) 0.18 0.21 (3) x (4) 0.09 0.12 0.16 0.12 (3) x (5) 0.07 (-0.06) 0.13

(3) x (6) (0.13)

(4) x (5) -0.07 -0.07 -0.19 (4) x (6) (5) x (6) (-0.11) 0.38

Adjusted R 2 0.98 0.99 0.98 0.99 0.99 0.98

2 Table entries are the standardized estimates (Beta coefficients) significant at 0.01; entries in parentheses are significant at 0.05.

19.

the effects are quite similar across the modes of competitive behavior.

Accordingly, the selected diffusion process parameters enhance cumulative

profits of Firm 1 identically irrespective of the conduct of the competitor.

Specifically, rapid diffusion and early entry enhance profits for Firm 1

particularly when its competitor's sales diffusion process is characterized

by weak imitation effects. Innovation is the dominating factor in determin-

ing cumulative profits over a fixed time horizon across all modes of

competitive behavior except competition. Under competition (i.e., Nash

equilibrium), imitation is the dominating fa-_tor.

The regression results on pairwise differences in cumulative profits

obtained under each mode of competitive behavior are shown in Appendix 3.

The significant main results are summarized in Table 9. That table is

structured in much the same way as Table 6. Specifically, the entries

describe the profile of both competitors on the three demand characteristics

for which Firm l's cumulative profits under the column mode of behavior are

larger than the cumulative profits under the row mode of behavior. Comparing

monopoly profits to profits accumulated in a dynamic duopoly (first column in

Table 9), a pattern emerges which is independent of the conduct of the com-

petitor. Specifically, for an incumbent with rapidly diffusing sales, its

cumulative profits in a duopoly will be drastically below its monopoly

profits when the new entrant's sales diffusion process has weak innovation

characteristics irrespective of his conduct. This result is consistent with

the profit patterns for scenarios 3, 9, and 10 shown in Table 4. The profit

differential is accentuated in some instances when the new entrant's sales

diffusion process has strong imitation effects (see the Follower 0 and Cost

Pricing case).

The results in the bottom row of Table 9 indicate that, generally, cost

pricing by the competitor is devastating when both competitors have rapidly

diffusing sales. Here, sharply decreasing prices over time lead to cumula-

tive profits for Firm 1 significantly below cumulative profits which could be

obtained if the competitor resorted to a different pricing strategy (even a

non-cooperative one).

Some specific differences are highlighted in Table 10. The first

column contains the regression results on the difference in cumulative

profits between the two firms under competition. The findings suggest that

the profit difference will be large when one firm's sales diffusion process

Table 9

1 Profile of Instances Where Difference in Firm l's Cumulative Profits Will Be Large

Monopoly Coalition Follower 0 Follower 1 Competition Firm 1 Firm 2 Firm 1 Firm 2 Firm 1 Firm 2 Firm 1 Firm 2 Firm 1 Firm 2

Coalition

Established 2 New Entrant Strong Weak Innovation Innovation

Follower 0

Established New Entrant -- Strong Weak Strong Innovation Innovation Innovation

Strong Strong Strong Imitation Imitation Imitation

Follower 1

Established New Entrant -- New Entrant -- Strong Weak Strong Strong -- Innovation Innovation Innovation Innovation

Strong -- -- Strong Imitation Imitation

Competition

Established New Entrant -- New Entrant -- Established New Entrant Strong -- Strong -- Strong Strong Weak Innovation Innovation Innovation Innovation Innovation

Strong -- Strong Strong -- Strong Weak Imitation Imitation Imitation Imitation Imitation

Cost Pricing Innovation

-- New Entrant Established -- -- New Entrant Established Established Established Established Strong Weak Strong Strong Strong Weak Strong Stclng Strong Strong Innovation Innovation Innovation Innovation Innovation Innovation Innovation Innovation Innovation

Strong Strong Imitation Imitation

Strong Strong Imitation Imitation

Strong Strong Imitation Imitation

Strong Strong Imitation Imitation

Strong Strong Imitation Imitation

Difference is measured as the column profits minus the row profits; results are based on the main effects significant at 0.05 or better (see Appendix 3).

2 "Established" and "strong" refer to significant positive effects of, respectively, initial cumulative sales and either innovation or imitation parameters. "New Entrant" and "weak" refer to significant negative effects of the identical variables.

Table 10

Results orlDifferences in Cumulative Profits

Both Firms Between Both Under Firms Under Coalition and

2

Competition Competition

Main Effects (Sales Diffusinu Parameters)

(1) Initial Connelwtive Sales (2) Firm 1 Innovation 0.81 1.60

(3) Imitation 1.55

(4) Initial ConeUnive Sales -0.38 (5) Firm 2 Innovation -0.51 -2.25 (6) Imitation 0.50 (0.81) Pairwise Interactions

(1) x (2) -0.25 (1) x (3) (1) x (4) (1) x (5) 0.07 (1) x (6) (2) x (3) -0.17 (-0.68) (2) x (4) (-0.06) (2) x (5) (2) x (6) -1.36 (3) x (4) (3) x (5) 1.21 (3) x (6) -2.09 (4) x (5) 0.30 (4) x (6) (0.16) (5) x (6) -0.27 1.15

Adjusted R2 0.99 0.48

' Table entries are the !slamdardized estimates (Beta coefficients) significant at 0.01; entries in parenükeses are significant at 0.05.

2 Measure of incéntive Uo meperate for both firms, defined as [Profits (Firm 1,Coalition)-ProfitstF•i:rn I, Competition)] x [Profits(Firm 2, Coalition)- Profits(Firm 2,Competivional.

20.

has strong innovation characteristics whereas the new entrant's process has

weak innovation but strong imitation characteristics.

The second set of regression results shown in Table 10 provide some

insight into instances where cooperative behavior (i.e., coalition) would be

mutually beneficial. The dependent measure vas constructed as the difference

in cumulative profits for one firm under coalition and competition times the

same difference for the other firm. A large positive value would imply that

both competitors would benefit tremendously from coalition. Keeping in mind

that the linear model captured only 48% of .he variance in the dependent

measure, the results suggest that order of entry does not impact the

desirability of cooperation. Strong imitation effects and asymmetries in

innovation effects should drive both competitors from competition to coali-

tion. These diffusion process characteristics also identify instances where

competition should be avoided in product line pricing.

7. SUMMARY AND DISCUSSION

The optimal price trajectories derived for a dynamic duopoly are of

three types: (a) pure penetration (i.e., monotonically increasing), (b) pure

skimming (i.e., monotonically decreasing), and (c) an initial phase of

penetration followed by a period of skimming. These shapes also characterize

profit maximizing price trajectories in a monopoly situation (Kalish 1983).

In light of these results, it is insightful to discuss the major results

obtained in this research in contrast to the monopoly situation. As such,

the impact of a different mode of competitive pricing behavior on the shape

of optimal price trajectories can be better understood.

Under monopoly, the price trajectories are primarily of type (a) and

type (b). One striking result obtained here is that across various

scenarios, initial penetration pricing is much more prevalent in a monopoly

ahan in a duopoly irrespective of the conduct of the competitor. Relative to

a duopoly, one product cannot span the market as well as two products can

(sold at the same price). The hazard rate in the sales diffusion process

tends to be lower since there are no cross product effects. Therefore, the

firm has to execute the penetration effort alone and more intensively.

21.

Under coalition, the shape of the optimal price trajectories varies the

mort across scenarios. Except for price following behavior, prices

generally tend to be higher under coalition than under different modes of

competitive pricing behavior. Basically, the two-product coalition strategy

consists of price segmentation: the dominant (high hazard rate) product is

mass-marketed through relatively low pricing and the weaker product is tar-

geted with a higher price tag at a market niche comprised of potential buyers

with high reservation prices. The segmentation is entirely dependent on the

asymmetry in diffusion process characteristi.ls, with the price differential

being dictated by the degree of asymmetry. Under symmetric diffusion, the

price trajectories for both firms coincide. Cumulative profits were

generally larger for the "fast diffusion" partner as the niche strategy

tended to weaken the profit position of the other firm.

Across scenarios, the optimal price trajectories under price following

behavior are similar in shape to the monopoly price trajectories and are

generally the highest among all modes of competitive pricing behavior. An

intelligent price leader viii recognize the passive pricing behavior of his

competitor and an implicit form of coalition will be established. These

results are to some extent consistent with Axelrod's (1984) assertion that a

tit-for-tat strategy leads to cooperation. Instantaneous and delayed price

following lead to very similar trajectories until the last period. There,

under delayed following behavior, the price leader will take advantage of the

response delay by slashing his price drastically (i.e., an endgame move).

Delayed response also enhances cumulative profits for the price leader.

Under instantaneous price following, optimal price trajectories for the price

leader coincide exactly with his coalition price when both firms have per-

fectly symmetric diffusion processes.

When the competitor resorts to cost pricing, the optimal price trajec-

tories are generally of type (b). The degree of skimming is largely

dependent on whether this naive predation strategy characterizes competitive

conduct early or late in thé product life cycle. Early on, the predator

takes upon himself the burden of developing the market by charging low

prices. The optimal pricing strategy of the other firm is skimming with very

high initial prices. Interestingly, cumulative profits for this firm are not

the lowest among those obtained under various modes of competitive pricing

22.

behavior. If predation begins later in the life cycle, the skimming trajec-

tories are more defensive with lower initial prices and narrower ranges over

the fixed time horizon. It should also be noted that cost pricing (or any

strategy where the price is purposely kept at a low but constant level) is

not an optimal predatory strategy. Altho'igh not explicitly analyzed here,

the results suggest that such an optimal strategy would likely be of the

skimming type with high initial prices in an attempt to slow down or halt the

diffusion process (and, hence, market development) followed by low prices to

grab market share.

Under competition (Nash equilibrium), the optimal price trajectories

tend to be similar in shape to the corresponding optimal monopoly trajec-

tories (except in early stages where monopoly trajectories exhibit penetra-

tion characteristics). As one would expect, however, they manifest

themselves at much lower levels.

Recognizing that competitive conduct can differ, these results supple-

ment the established insights on strategic pricing in non-monopolistic

markets. They were, however, derived in a specific framework. Relaxing the

constraints of the current study constitutes a fruitful avenue for future

research. Another avenue for future research would be some empirical work to

validate the normative results in real environments. Empirical research is

lacking in this general research area.

23.

FOOTNOTES

1. Eliashberg and Jeuland (1986) assume the hazard functions to be linear

in price and price differential.

2. A different approach is taken by Clarke and Dolan (1984). They relate

the reservation prices for both products directly and confine the diffu-

sion dynamics to non-stationary reservation prices.

3. In characterizing a choice rule, Hauser and Shugan (1983) also rely on

homotheticity which in the DEFENDER model is implied by the strict

assumption of parallel linear indifference curves.

4. Of the 256 scenarios, the percentage successfully solved over eight

consecutive time periods per mode of competitive behavior was: monopoly

(100%), coalition (70%), Follower 0 (78%), Follower 1 (88%), competition

(45%), and cost pricing (91%).

5. The price increase in the last period of scenario 8 for Follower 0 is a

numerical result and should not be interpreted substantively.

6. Note that under competition, the Firm 1 and Firm 2 results for

scenarios 5 and 6 and scenarios 7 and 8 should be mirror images.

However, some differences are observed which are a result of solving the

differential game problems numerically.

24.

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Books, Inc.

Bass, F. M. 1969. A New Product Growth Model for Consumer Durables.

Management Science 15, 215-227.

Bass, F. M. 1980. The Relationship Between Diffusion Rates, Experience

Curves, and Demand Elasticities for Consumer Durable Technical

Innovations. Journal of Business 53: 551-567.

Clarke, D. G. and R. J. Dolan. 1984. A Simulation Analysis of Alternative

Pricing Strategies for Dynamic Environments. Journal of Business 57:

S179-S200.

Eliashberg, J. and R. Chatterjee. 1985. Analytical Models of Competition

with Implications for Marketing: Issues, Findings, and Outlook. Journal

of Marketing Research 22: 237-261.

Eliashberg, J. and A. P. Jeuland. 1986. The Impact of Competitive Entry in a

Developing Market Upon Dynamic Pricing Strategies. Marketing Science 5:

20-36.

Hauser, J. R. and S. M. Shugan. 1983. Defensive Marketing Strategies.

Marketing Science 2: 319-360.

Jeuland, A. P. 1981. Parsimonious Models of Diffusion and Innovation. Part

B. Incorporating the Variable Price. Working Paper, Center for Research

in Marketing, University of Chicago.

Kalish, S. 1983. Monopolistic Pricing with Dynamic Demand and Production

Costs. Marketing Science 2: 135-159.

25.

Kendrick, D. and A. Meeraus. 1985. GAMS. Washington, D.C.: The World Bank.

Nascimento, F. and W. R. Vanhonacker. 1988. Optimal Strategic Pricing of

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Pindyck, R. S. 1978. Gains to Producers from the Cartelization of

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Rao, R. C. and F. M. Bass. 1985. Competitpn, Strategy, and Price Dynamics:

A Theoretical and Empirical Investigation. Journal of Marketing Research

22: 283-296.

Spence, A. M. 1981. Learning Curve and Competition. The Bell Journal of

Economics 12: 49-70.

Thompson, G. L. and J. T. Teng. 1984. Optimal Pricing and Advertising

Policies for New Product Oligopoly Models. Marketing Science 3: 148-169.

Wernerfelt, B. 1985. The Dynamics of Prices and Market Shares Over the

Product Life Cycle. Management Science 31: 928-939.

Wernerfelt, B. 1986. A Special Case of Dynamic Pricing Policy. Management

Science 32: 1562-1566.

26.

Appendix 1: Determination of Number of Potential Buyers (PB1(t) and

PB,(0).

For notational simplicity, we will drop all time subscripts in this

appendix.

By definition,

PB,(p„p,) = N J f(P2/101)Pri g(pr„Pr2)dPr2 dpr1

PI 13

where g(prl,pr2) is a bivariate gamma with parameters a1 / a 2 (integers) and

0,, S2• Since the bivariate distribution we consider is the product of two

independent univariate gammas,

PB1(P1,P2) = N (P /P )Pr S 2 1 I

o

pr eΠ-1 pr

' /0' Pr a2-1 epr2/0.2

i' , dpr,dpri.

Qat oc 2' r(Œt) P-• 2 F(a2)

Applying the known integral

m , mt xm-i f x

m eax

= E (-1)". eax

i=0 (m-1)! a

putting m = a, -1 and a = -1/0, , we obtain

pr, a

2-1-i OC 2-1

02

e-pr,/e,

i=0 02 x2-1 (Œ2-1-0!

or

PB1(PI,P2) =

pr i a,-1

epri C,

N

PI 131 œ1 r(<11)

(P2/P1)Pr, dpr i (1-2)

0

PB,(P 1 ,P 2 )

27.

pria,-1e

N f

Pl 01 1 r(al)

a2-1 (cc -1)! pr 2 (OE2 1 1) e-pr 2/02

E(-1) '

02a2(Œ2-1)! i=0 (a2-1-i)! (-1702)1+1

(P2/P1)Pri dpr i

0

CC2 - 1 - i = (X 2 - 1

az - 1 - i = a2 - 2

a,

az

- 1

- 1

i

- i

=

=

a,

0

- 1

Since

for i = 0

for i = 1

for i = a2 - 2

and for i = a, - 1

- (x2 + 2 = 1,

we can replace a, - 1 - i by i. Accordingly, expression (1-2) becomes

pr a,-1 aa,-1 pr i ,

, P13 1(131 /P2) = N f a

(1 -

P1 01 r(al)

a2-1 PrIP2 (3- E e 2 p 1

i=0

Pr,

1 - }dpri . i!

13

a2 -1

E

i=0

al -l+i

E (-1) j j=0 (a1 -1+i-j)! (1 + 1

13; 737

(a1-1+i)! pria,-144-i

P2

pi

1

28.

Again applying integral

part, and rearranging

PB1(p1,p2) = N

Ce 2-1 co

- ( E f e-pr

i=0 PI

Again applying

the

-pr,

(1-1) setting

second part,

- - cx1 -1

E

m = Π2

i 1

i!

m =

we obtain:

- 1 and

œ

Pi

0.--2 5- 13'c'

al -1 + i

a

--!

P2

Pi

and

i

a =

= -1/02 to

1

the first

dpr,).(1-3)

P2

PI

e (31

1

'(-- +

°2

integral

[pr,

i=0 si

1

-- 12±) pri a,+i-1

°1 PI

(1-1) putting

(a1 -1)!

1 1 -- +

°I 02

PB 1(pip2) becomes

-p, al -1

PB,(p1,p2) = N e t31 E

i=0

i Pr: 1

5, i!

-KI( 1.4- -4- 1-z-) P2 PI P1 al

+i-1 +i-1

e Pr: -i ΠI

P a

2 PI

P2

P 1

i 1 CO

P1 (a, -1)!

pi

ei i!

P2 PI )

- e f32 P131(p„p2) = Ne -'

a,

) •

oi

a2 -1 E

i=0 (1-4)

p, pfli,1

f7:

1 axe I' i (al+i-1)!

1=0 (al+i-1-j)!

This expression can be gic.Dwn to equal

29.

For F13 2(PI /P2), a simigl , erivation leads to

) 114,- PB 2 (pi , p 2 ) = Ne Pz E

PI P2

- T 73-2 1 )

i! P2

ai -1 E

i=0

P2 «2

P, (a2+i-1)! L.

j'mC (a2+i-1-j)!

1 . (1-5)

02

[pi: J+1

Appendix 2: Table 2-1

Summarv of Numerical Recuits on Differences in Mean Price Level for Firm 1 1

Monopoly Versus Coalition Versus

Follower Cost Follower Cost

Coalition 0 1 Competi- Pricing 0 1 Competi- Pricing

tion tion

Main Effects (Sales Diffusion

Parameters)

(1) Initial Cumulative Sales 0.96. 0.76 -1.00 -1.05 (-1.29) -0.55

(2) Firm 1 Innovation 1.87 -0.67 1.03 -1.95 -2.14 (-1.54) -1.86

(3) Imitation (0.42) -0.91 (-0.43) -0.62 (-0.49) (-1.66) -1.14

(4) Initial Cumulative Sales -0.58 -0.82 (0.49)

(5) Firm 2 Innovation -0.72 (0.36) (1.28) 0.74 1.07 1.29

(6) Imitation 0.49 -0.53 -0.37 -0.60 0.59 (-0.89) -0.55

Pairwise Interactions

(1) x (2) -0.70 -0.34 -0.37 -0.72 -0.66 0.71 0.59 0.49

(1) x (3) 0.59 0.48 (0.28) (0.47) 0.42

(1) x (4) 0.30 0.40 0.28

(1) x (5) 0.27 0.20 (-0.31) -0.28 -0.37 (-0.17)

(1) x (6) (-0.37) (0.33) (-0.79) (0.37) (0.44)

(2) x (3) -0.55 0.77 0.44 0.66 0.74 (0.72) 0.90

(2) x (4) (-0.14) 0.37 0.44 (0.14) 0.20 (0.22)

(2) x (5) (0.16) (-0.14) (-0.20) -0.27 -0.27

(2) x (6) -0.50 (0.32) (0.33) (0.51) 0.63 0.66

(3) x (4) -0.34 -0.33

(3) x (5) -0.31 -0.34 (-0.21) (-0.28) -0.44

(3) x (6) (0.46) -0.26

(4) x (5) 0.28 0.35 -0.28 -0.34

(4) x (6) (-0.33) (-0.99)

(5) x (6)

Adjusted R 0.83 0.72 0.80 0.88 0.34 0.79 0.75 0.29 0.81

1 Table entries are the standardized estimates (Beta coefficients) significant at 0.01: entries in parentheses are

significant at 0.05.

Table 2-1 (cont'd)

Summary of Numerical Results on Differences in Mean Price Level for Firm 1 1

Follower O Versus Follower 1 Versus

Follower 1 Competition

Cost

Pricing Competition Cost

Pricing

Competition Versus

Cost Pricing

Main Effects (Sales Diffusion

Parameters)

(1) Initial Cumulative Sales (0.80) 1.31 0.99

(2) Firm 1 Innovation (1.55) 1.49 1.27 (0.40)

(3) Imitation (0.73) (-1.06)

(4) Initial Cumulative Sales (-0.94) (-0.89) (0.50)

(5) Firm 2 Innovation (0.69) (-0.62) (-1.02) 0.86

(6) Imitation (0.48) 0.50 (0.30)

Pairwise Interactions (1) x (2) (-0.58) (-0.62) 0.57 -0.41

(1) x (3) (0.48) (0.21) 0.32

(1) x (4) (0.23) (0.16)

(1) x (5) (-0.23) (0.28) (0.40) 0.30 (0.13)

(1) x (6) (-0.41) 0.57

(2) x (3) (-0.36) (-0.44) (-0.43) (-0.16)

(2) x (4) -0.15 -0.17

(2) x (5) (-0.26) (0.24) (0.32) (0.30) (0.14)

(2) x (6) (-0.35)

(3) x (4) (0.60)

(3) x (5) (-0.39) -0.41

(3) x (6) (4) x (5) (0.41) (0.50) 0.19 (0.14)

(4) x (6) -0.27 -0.32

(5) x (6) (-0.77) -0.45 -0.70

Adjusted R 0.26 0.78 0.31 0.61 0.86 0.93

1 Table entries are the standaudized estimates (Beta coefficients) significant at 0.01; entries in parentheses are significant

at 0.05.

Appendix 3: Table 3-1

Summarv of Numerical Results on Differences in Cumulative Profits for Firm 1 1

Monopoly Versus Coalition Versus Follower Cost Follower Cost

Coalition 0 1 Competi- Pricing 0 1 Competi- Pricing tion tion

Main Effects (Sales Diffusion

Parameters)

(1) Initial Cumulative Sales 0.52 (0.21) (0.21) 0.43 0.26

(2) Firm 1 Innovation 1.21 0.76 0.81 1.00 0.81 (0.28) 0.30 0.63 0.94

(3) Imitation 0.28 (0.24) (0.33) 0.58 0.60 0.43

(4) Initial Cumulative Sales -0.58 -0.38 -0.53 -0.69 -0.38 (-0.16) -0.38

(5) Firm 2 Innovation -0.67 (-0.29) -0.32 -0.51 (0.16) 0.13

(6) Imitation (0.14) 0.50 (0.19) 0.31 0.36 0.17

Pairwise Interactions

(1) x (2) -0.62 -0.43 -0.39 -0.53 -0.25 (-0.10) -0.15 -0.30

(1) x (3) 0.43 0.40 0.34 0.37 0.30 0.17 (0.10) (0.27)

(1) x (4) 0.32 0.14 0.26 0.29 (-0.03)

(1) x (5) 0.18 0.16 0.18 (0.08) 0.07 0.10 0.10 0.07

(1) x (6) -0.37

(2) x (3) (-0.16) -0.17 (-0.09) -0.17 -0.17

(2) x (4) 0.34 0.16 0.22 0.30 (-0.06) -0.19 -0.16 -0.12

(2) x (5) 0.16 0.15 0.16

(2) x (6) -0.39 (0.19) 0.20 (0.13)

(3) x (4) -0.25 -0.22 -0.35 -0.27' 0.13

(3) x (5) (0.13) (-0.12) (-0.16) -0.34 -0 11 -0.12

(3) x (6) 0.67 0.74 (0.13)

(4) x (5) 0.14 0.14 0.15 0.30 0.24 0.26 0.24 0.12

(4) x (6) (0.16)

(5) x (6) 0.40 -0.20 -0.27 -0.46 -0.59 -0.50 -0.28

Adjusted R 0.90 0.92 0.93 0.95 0.99 0.94 0.97 0.99 0.99

-4

1 Table entries are the standardized estimates (Beta coefficients) significant at 0.01; entries in parentheses are

significant at 0.05.

Table 3-1 (cont'd)

Summary of Numerical Results on Differences in Cumulative Profits for Firm 1 1

Main Effects (Sales Diffusion

Follower 0 Versus Follower 1 Versus

Follower 1 Competition

Cost

Pricing Competition

Cost

Pricing

Compétition Versus

Cost Pricing

Parameters)

(1) Initial Cumulative Sales (0.28) (0.45) 0.45

(2) Firm 1 Innovation (0.76) 0.81 0.42 1.15 1.16

(3) Imitation 0.58 (0.21) 0.58 0.60

(4) Initial Cumulative Sales -0.38 (-0.30) 0.13 (0.20)

(5) Firm 2 Innovation -0.51 (-0.27 0.17 0.33

(6) Imitation 0.50 0.14 0.18

Pairwise Interactions

(1) x (2) 0.35 -0.25 -0.32 -0.36 -0.38

(1) x (3) 0.22 0.23

(1) x (4) (0.17) (-0.03)

(1) x (5) (-0.25) 0.07 -0.07 0.03 (0.06)

(1) x (6) -0.13

(2) x (3) -0.36 -0.62 -0.17 -0.19 -0.20

(2) x (4) (0.34) (-0.06) 0.27 -0.06 -0.17

(2) x (5) -0.37 (-0.03)

(2) x (6) (3) x (4) -0.41 (0.42) 0.76 0.13

(3) x (5) 0.57 -0.24

(3) x (6) -0.52 (-0.08)

(4) x (5) 0.30 -0.14 0.14

(4) x (6) (0.16) (0.15) (-0.09)

(5) x (6) -0.27 (0.23) -0.17 -0.33

Adjusted R 0.68 0.58 0.99 0.97 0.99 0.98

1 Table entries are the standardized estimates (Beta coefficients) significant at 0.01; entries in parentheses are significant

at 0.05.

Arnoud DE MEYER

Philippe A. NAERT Marcel WEVERBERGH and Guido VERSWIJVEL

86/03 Michael BRIMM

86/04 Spyros MAKRIDAKIS and Michèle HIBON

86/05 Charles A. VYPLOSZ

86/06 Francesco CIAVA22I, Jeff R. SBEEN and Charles A. VYPLOSZ

86/07 Douglas L. MacLACHLAN and Spyros HAKRIDAKIS

86/08 José de la TORRE and David H. NECKAR

86/09 Philippe C. BASPESLAGH

86/10 R. MOENART, Arnoud DR MEYER, J. BARBE and D. DESCHOOLMEESTER.

86/11 Philippe A. NAERT and Alain BULTE2

86/12 Roger BETANCOURT and David CAUTSCHI

86/13 S.P. ANDERSON and Damien J. NEVEU

86/14 Charles VALDMAN

86/15 Mihkel TOMRAg and Arnoud DE MEYER

1986

86/01

86/02

86/26 Barry EICHENGREEN "The econoeic conséquences of the Franc and Charles VYPLOSZ Poincare", September 1986.

86/28 Manfred KETS DE VRIES and Danny MILLER

"Interpreting organizational tees.

"Flexibility: the next competitive hattle,

86/29 Manfred KETS DE VRIES 'Why follov the leader?".

86/30 Manfred KETS DE VRIES 'The succession gamet the real story.

86/31 Arnoud DE MEYER

"The R & D/Production interface".

"Subjective estimation in Integrating communication budget and allocation decisions: e case study", January 1986.

"Sponsorship and the diffusion of organizational innovations a preliminary viev".

"Confidence intervals: an empirical investigation for the series in the H-Competition" .

"A note on the reduction of the vorkveek", July 1985.

"The real exchange rate and the fiscal aspects of e naturel resource discovery", Revised version: February 1986.

"Judgmental bisses in sales forecasting", February 1986.

"Forecasting political risks for international operations", Second Draft: March 3, 1986.

"Conceptualixing the strategic process in diversified firas: the role and nature of the corporate influence process", February 1986.

"Antlysing the issues concerning technological de-maturity".

'From "Lydiametry" to "Pinkhamization": ■isspecifying advertising dynamics rarely affects profitability".

"The economics of recel' firme, Revised April 1986.

"Spatial coepetition à la Cournot".

comparaison internationale des marges brutes du commerce', June 1985.

"Boy the manageriel attitudes of firas vith FMS differ from other manufacturing fins: survey results". June 1986.

86/16 B. Espen ECKBO and Hervig M. LANGOHR

86/17 David B. JEMISON

86/18 James TEBOUL and V. HALLERET

86/19 Rob R. VEITZ

86/20 Albert CORHAY, Gabriel HAVAWINI and Pierre A. MICHEL

86/21 Albert CORHAY, Gabriel A. flAWAVINI and Pierre A. MICHEL

86/22 Albert CORHAY, Gabriel A. HAVAWINI and Pierre A. MICHEL

86/23 Arnoud DE MEYER

86/24 David GAUTSCHI and Vithala R. RAO

86/25 H. Peter GRAY and Ingo WALTER

86/27 Karel COOL and Ingemar DIERIGKX

86/31 Arnoud DE MEYER, Jinichiro NAKANE, Jeffrey G. MILLER and Kasra FERDOVS

86/32 Karel COOL and Dan SCHENDEL

"Les primes des offres publiques, la note d'information et le *arche des transferts de contrôle des sociétés".

'Strategic capability transfer in acquisition intégration", May 1986.

"Tovards an operational definition of services", 1986.

"Nostradamus: a knovledge-based forecasting advisor".

"The pricing of equity on the London stock exchange: seasonolity and size preeium", June 1986.

"Risk-premla aeasonality in U.S. and European equity markets", February 1986.

"Stasonality in the risk-return relationships some international evidence", July 1986.

"An exploratory study on the integration of information systeas in nanufacturine, July 1986.

"A oethodology for specification and aggregation in product concept testing", Juiy 1986.

'Protection', August 1986.

"Negative risk-return relationships in business strategy: paradox or truism?", October 1986.

"Flexibility: the next coopetitive hattle, Revised Version: March 1987

Performance differences &sang strategic group me■bers", October 1986.

IMSEAD VORT.INC PAPERS SUIES

October 1986.

86/33 Ernst BALTENSPERGER and Jean DERMINE

86/34 Philippe HASPESLACH and David JEMISON

'The role of public policy in insuring financial stability: e cross-country, comparative perspective", August 1986, Revised

November 1986.

"Acquisitions: wyths and reality", July 1986.

87/06 Arun K, JAIN, Christian PINSON and Naresh K. KALHOTRA

87/07 Rolf BANZ and Gabriel HAVAWINI

*Customer loyalty as e construct in the aarketing of banking services", July 1986.

"Equity pricing and stock market anomalies", February 1987.

87/08 Manfred KETS DE VRIES 'Leaders vho can't manage", February 1987. 86/35 Jean DERMINE

86/36 Albert CORHAY and Gabriel HAVAVINI

86/37 David GAUTSCAI and

Roger BETANCOURT

86/38 Gabriel CAVAWINI

86/39 Gabriel HAVAVINI

Pierre MICHEL and Albert COREAY

86/40 Charles WYPLOSZ

86/41 Kasra FERDOVS and Vickham SKINNER

86/42 Kasra PERDONS and Per LINDBERG

86/43 Damien NEVEN

86/44 Ingemar DIERICKX Carmen MATUTES and Damien NEVEN

1987

87/01 Manfred KETS DE VRIES

87/02 Claude VIALLET

87/03 David GAUTSCHI and Vithala RAO

87/04 Sumantra CHOSHAL and Christopher BARTLETT

87/05 Arnoud DE MEYER and Kasra. PERDUS

"Measuring the market value of a bank, e primer', November 1986.

"Seasonality in the risk-return relationshipt some international evidence", July 1986.

'The evolution of retailing: e suggested

economic interpretation".

'Financial innovation and recent developments in the French capital markets', Updated: September 1986.

'The pricing of cannon stocks on the Brussela stock exchanget e re-examination of the evidence", November 1986.

'Capital flovs liberalization and the EMS, a French perspective", December 1986.

"Manufacturing in a nev perspective", July 1986.

"FMS as indicator of aanufacturing strategy", December 1986.

"On the existence of equilibriui in hotelling's sodel", November 1986.

"Value added tax and coapetition", December 1986.

'Prisoners of leadership".

"An eapirical investigation of international asset pricing", November 1986.

'A sethodology for specification and aggregation in product concept testing", Revised Version: January 1987.

"Organizing for innovations: case of the multinational corporation", February 1987.

"Kanagerial focal points in manufacturing strategy", February 1987.

"Entrepreneurial activities of European KBAs",

March 1987.

"A cultural viev of organizational change", March 1987

"Forecasting and loss functions", March 1987.

"The Janus Head: learning from the superior and subordinate faces of the manager's job", April 1987.

"Multinational corporations as diffcrentiated netvorks", April 1987.

"Product Standards and Competitive Strategy: An Analysis of the Principles", May 1987.

"KETAFORECASTING: Vays of improving Porecasting. Accuracy and Usefulness", May 1987.

"Tak_over attempts: vhat does the language tell

us?, June 1987.

"Managers' cognitive caps for upvard and dovnvard relationships", June 1987.

"Vhy the EMS? Dynamic games and the equilibrlum

policy regime, May 1987.

"A nev approach to statistIcal forccasting", June 1987.

"Strategy formulation: the impact of national

culture", Revised: July 1987.

"Conflicting Ideologics: structural and motivational conséquences", August 1987.

"The deaand for retail products and the household production atodel: nev vievs on complementarity and substitutabillty".

87/18 Reinhard ANGELMAR and "Patents and the European biotechnology lag: a Christoph LIEBSCHER study of large European phareaceutical firas",

June 1987.

87/09 Lister VICKERY, Mark PILKINCTON and Paul READ

87/10 André LAURENT

87/11 Robert FILDES and Spyros MAKRIDAKIS

87/12 Fernando BARTOLOME and André LAURENT

87/13 Sumantra CHOSHAL and Nitin NOURIA

87/14 candis LABEL

87/15 Spyros HAKRIDAKIS

87/16 Susan SCHNEIDER

and Roger DUNBAR

87/17 André LAURENT and Fernando BARTOLOME

87/19 David BEGG and Charles WYPLOSZ

87/20 Spyros MAKRIDAYIS

87/21 Susan SCHNEIDER

87/22 Susan SCUNEIDER

87/23 Roger BETANCOURT David GAUTSCHI

87/29 Susan SCHNEIDER and "Interpreting strategic behavior: basic Paul SHRIVASTAVA assumptions theres in organizations", September

1987

87/26 Roger BETANCOURT "Demand complementarities, household production and David GAUTSCHI and retail assortments", July 1987.

88/10 Bernard SINCLAIR- DESGAGNé

80/11 Dernard SINCLAIR. DESGACNé

"The robustness of some standard auction galle fonts", February 1988.

"nen atitionary atrategiee nr@ Pqm111brluu bidding strategyt The single-ergeginî property", February 19$8.

87/39 Manfred KETS DE VRIES "The dark side of CEO succession", November 1987

87/40 Carmen KATUTES and "Product compatibility and the scope of entry", Pierre RECIBEAU November 1987

"The internai and externat careers: a theoretical and cross-cultural perspective", Spring 1987.

"The robustness of KDS configurations in the face of incomplete data", March 1987, Revised: July 1987.

"Is there a capital shortage in Europe?", August 1987.

"Controlling the interest-rate risk of bonds: an introduction to duration analysis and immunization strategies", September 1987.

"Privatization: its motives and likely consequences", October 1987.

"Strategy formulation: the impact of national culture", October 1987.

87/41 Gabriel HAVAVINI and Claude VIALLET

87/42 Damien NEVEN and Jacques-F. TRISSE

87/43 Jean GABSZEVICZ and Jacques-F. TRISSE

87/44 Jonathan HAK/LTON, Jacques-F. TRISSE and Anita VESKAMP

87/45 Karel COOL, David JEMISON and Ingemar DIERICKX

87/46 Ingemar DIERICKX and Karel COOL

88/01 Michael LAVRENCE and Spyros MAKRIDAKIS

88/02 Spyros MAKRIDAKIS

88/03 James TEBOUL

88/04 Susan SCHNEIDER

88/05 Charles VYPLOSZ

88/06 Reinhacd ANGELMAR

88/07 Ingemar DIERICKX and Karel COOL

88/08 Reinhard ANGELMAR and Susan SCHNEIDER

88/09 Bernard SINCLAIR- DESGAGNé

"Seasonality, size premium and the relationship betveen the risk and the return of French coamon stocks", November 1987

"Coabining horizontal and vertical differentiation: the principle of max-min differentiation", December 1987

"Location", December 1987

"Spatial discrimination: Bertrand vs. Cournot in a Bodel of location choice", December 1987

"Business strategy, market structure and risk-return relationships: e causal interpretation", December 1987.

"Asset stock accumulation and sustainability of coapetitive advantage", December 1987.

"Factors affecting judgemental forecasts and confidence Intervale, January 1988.

"Predicting recessions and other turning points", January 1988.

"De-industrialise service for quality", January 1988.

'National vs. corporate culture: implications for huaan resource management", January 1988.

"The svinging dollar: is Europe out of step?", January 1988.

"Les conflits dans les canaux de distribution", January 1988.

"Competitive advantage: a resource based perspective", January 1988.

"Issues in the study of organizational cognition", February 1988.

"Price formation and product design through bidding", February 1988.

87/30 Jonathan HAMILTON V. Rentley MACLEOD and J. F. TRISSE

87/24 C.B. DERR and André LAURENT

87/25 A. K. JAIN, N. K. MALHOTRA and Christian PINSON

87/27 Michael BUROA

87/28 Gabriel HAVAVINI

87/31 Martine QUINZII and "On the optimality of central places", J. F. l'HISSE September 1987.

"German, French and British aanufacturing strategies less different than one thinks", September 1987.

"A process framevork for analyzing cooperation betveen firme, September 1987.

'European manufacturers: the dangers of couplacency. Insights fro■ the 1987 European aanufocturing futures survey, October 1987.

87/32 Arnoud DE MEYER

87/35 P. J. LEDERER and "Co■petitive location on netvorks under J. P. TRISSE discriminatory pricing", September 1987.

87/36 Manfred KETS DE VRIES "Prisoners of leadership", Revised version October 1987.

87/37 Landis LABEL

87/38 Susan SCHNEIDER

"Spatial competition and the Core", August 1987.

87/33 Yves DOZ and Amy SHEN

87/34 Kasra FERDOVS and Arnoud DE MEYER

1988

*The multinational corporation as a netvork: perspectives from interorganizational theory', May 1988.

88/28 Sumantra GHOSHAL and C. A. BARTLETT

88/12 Spyros MAKRIDAKIS

88/13 Manfred KETS DE VRIES

88/14 Alain NOEL

88/15 Anil DEOLALIKAR and Lars-Rendrik ROLLER

88/16 Gabriel RAVAVINI

88/17 Michael BURDA

88/18 Michael BURDA

88/19 M.J. LAVRENCE and Spyros MAKRIDAKIS

88/20 Jean DERMINE, Damien NEVEN and J.F. TRISSE

88/21 James TEBOUL

88/22 Lars-Hendrik RÔLLER

88/23 Sjur Didrik FLAM and Georges ZACCOUR

88/24 B. Espen ECKBO and Hervig LANGOHR

88/25 Everette S. GARDNER and Spyros MAKRIDAKIS

88/26 Sjur Didrik FLAN and Georges ZACCOUR

88/27 Murugappa KRISRNAN Lars-Rendrik RÔLLER

"Business firas and managers in the 21st century*, February 1988

"Alexithynia in organizational life: the organization man revisited", February 1988.

"The interpretation of strategies: a study of the impact of CEOs on the corporation", March 1988.

"The production of and returna from industrial innovation: an econoeetric analysis for a developing country", December 1987.

"Market efficiency and equity pricing: international evidence and implications for global investine, March 1988.

"Monopolistic coepetition, costs of adjustvent and the behavior of European esploysent", September 1987.

"Reflections on ',voit Unemployment" in Europe", November 1987, revised February 1988.

"Individual blas in judgements of confidence", March 1988.

"Portfolio selection by ■utual funds, an eguilibrium model", March 1988.

"De-industrialize service for guality", March 1988 (88/03 Revised).

"Proper Ouadratic Punctions vith an Application to AT&T", May 1987 (Revised March 1988).

"Equilibres de Nash-Cournot dams le marché européen du gaz: un cas où les solutions en boucle ouverte et en feedback coIncident", Mars 1988

"Information disclosure, ■eans of paysent, and takeover premia. Public and Private tender offers in France", July 1985, Sixth revision, April 1988.

"The future of forecasting", April 1988.

"Seri-coepetitive Cournot equilibrium in multistage oligopolies", April 1988.

"Entry rame vith resalable capacity", April 1988.

88/29 Naresh K. MALROTRA, Christian PINSON and Arun K. JAIN

88/30 Catherine C. ECKEL and Theo VERMAELEN

88/31 Sumantra GHOSRAL and Christopher BARTLETT

88/32 Kasra FERDOVS and David SACKRIDER

88/33 Mihkel M. TOMBAK

88/34 Mihkel M. TOMBAK

88/35 Mihkel M. TOMBAK

88/36 Vikas TIBREVALA and Bruce BUCHANAN

88/37 Murugappa KRISRNAN Lars-Rendrik ROLLER

88/38 Manfred KETS DE VRIES

88/39 Manfred KETS DE VRIES

88/40 Josef LAKON/SROK and Theo VERMAELEN

88/41 Charles VYPLOSZ

88/42 Paul EVANS

88/43 B. SINCLAIR-DDSGAGNE

88/44 Essam MAHMOUD and Spyros MAKRIDAKIS

88/45 Robert KORAJCZYK and Claude VIALLET

88/46 Yves DOl and Amy SHUEN

"Consumer cognitive eomplexity and the dimensionality of multidimensional scaling configurations", May 1988.

"The financial fellout from Chernobyl: risk perceptions and regulatory response", May 1988.

*Creation, adoption, and diffusion of innovations by subsidiaries of multinational corporations", June 1988.

"International manufacturing: positioning plants for success", June 1988.

"The importance of flexibility in aanufacturing", June 1988.

"Flexibility: an important dimension in manufacturing", June 1988.

'A strategic analysis of investeent in flexible eanufacturing systems*, July 1988.

"A Predictive Test of the no Modal that Contrôle for Non.,starionerlty". June 1188.

"Regulating Price-Liability Competition To Isprove Velfare", July 1988.

"The Motivating Role of Envy : A Forgotten Factor in Management, April 88.

"The Leader as Mirror : Clinical Reflections", July 1988.

"Anoaalous price behavlor around repurchase tender offers", August 1988.

"Assymetry in the EMS: intentional or systemic?", August 1988.

"Organizational development in the transnational enterprise", June 1988.

"Group decision support systems implement Rayesian rationality*, September 1988.

"The state of the art and future directions in combining forccasts", September 1988.

"An empirical investigation of international asset pricing", November 1986, reyised August 1988.

"From lntent to outcome: e process frasevork for partncrships", August 1988.

88/4/

Alain BULTEZ, "Asymmetric cannibalism between substitute

Els GIJSBRECHTS, items listed by retailers", Septernber 1988.

Philippe NAERT and Pie VANDEN ABEELE

88/48

Michael BORDA

"Reflections on 'Vait ttnemployment' in

Europe, II", April 1988 revised Septernber 1988.

"Information asymmetry and equity issues",

Septernber 1988.

"Managing expert systems: from inception

through updating", October 1987.

"Technology, vork, and the organization: the

impact of expert systems", July 1988.

"Cognition and organizational analysis: who's

minding the store?", Septernber 1988.

88/49 Nathalie DIERKENS

88/50

Rob VEITZ and

Arnoud DE MEYER

88/51 Rob VEITZ

88/52

Susan SCHNEIDER and

Reinhard ANGELMAR

88/53 Manfred KETS DE VRIES "Vhatever happened to the philosopher-king: the

leader's addiction to power, Septernber 1988.

88/54 Lars-ilendrik RÔLLER "Strategic choice of flexible production

and Mihkel M. TOMBAK technologies and velfare implications",

October 1988

88/55 Peter BOSSAERTS

and Pierre MILLION

88/56 Pierre MILLION

88/57 Wilfried VANHONACKER

and Lydia PRICE

88/58 B. SINCLAIR-DESGAGNE

and Mihkel M. TOMBAK

88/59 Martin KILDUFF

88/60 Michael BURDA

88/61 Lars-Hendrik RÔLLER

88/62 Cynthia VAN NULLE, Thco VERMAELEN and

Paul DE VOUTERS

"Method of moments tests of contingent clairon

asset pricing models", October 1988.

"Site-sorted portfolios and the violation of

the random walk hypothesis: Additional

empirical evidence and implication for tests

of asset plicing models", June 1988.

"Data transferability: entimeting the recponne

effect of future events based on historical

analogy", October 1988.

"Assessing economic inequality", November 1988.

"The interpersonal structure of decision

making: a social comparison approach to

organizational choice", November 1988.

"Is mismatch really the problem? Some estimates

of the Chelvood Gate II model with US data",

Septernber 1988.

"Modelling cost structure: the Bell System

revisited", November 1988.

"Régulation, taxes and the market for corporate control in Belgium", Septernber 1988.