Price caps as welfare-enhancing coopetition

Patrick Rey and Jean Tirole

12th CRESSE conference

Heraklion, 2 July 2017

1

INTRODUCTION (1/3)

Coopetition: agreements among potential competitors

Major antitrust concern since Sherman Act: Cartels, but also

• Mergers

• Joint marketing agreements – Patent pools

– Alliances (airlines, code-sharing)

• Platforms – Health-care (HMOs)

– Content (cable/broadband/satellite operators)

– Shopping malls

Key aspect: complements or substitutes?

2

INTRODUCTION (2/3)

Complements versus substitutes

Heterogeneous (Qantas / China Eastern)

Moving (products and usage evolve over time)

Duality for platforms

• Cooperate to attract users to the platform

• Compete for users within the platform

→ screening whether such agreements lessen competition and harm consumers is information intensive

→ authorities often (understandably) hesitant to approve

3

INTRODUCTION (3/3)

Objective: add “information-free” instrument

Firms

Agree on price caps for their products

Keep control over their products (in contrast to mergers or old-style patent pools)

Intuition

Complements: solve Cournot double marginalization pb

Substitutes: do not stifle competition

4

OUTLINE AND TAKE-AWAY POINTS

Static competition

Price-caps can only increase consumer surplus

Coopetition: when do firms agree on price caps?

Mergers vs. price caps

Repeated interaction

Could price caps facilitate undesirable collusion (e.g., by restraining deviations or by facilitating punishments)?

Answer is NO in two environments we were able to study:

• Symmetric firms, stationary equilibrium paths

• Technology adoption model (complete characterization of eq. set)

5

SETTING (1/2)

𝑛 ≥ 2 firms, indexed by 𝑖 ∈ 𝑁 = 1,… , 𝑛

Cost 𝐶𝑖(𝑞𝑖): 𝐶𝑖 0 = 0, 𝐶𝑖′ ∙ ≥ 0

Demand 𝐷𝑖 𝑝𝑖 , 𝑝𝑗

• Downward sloping (𝜕𝑖𝐷𝑖 < 0)

• Uniform price increase reduces demands ( 𝜕𝑗𝐷𝑖𝑗∈𝑁 < 0)

Substitutes or complements

(𝑆) Substitutes: 𝜕𝑗𝐷𝑖 > 0 for 𝑗 ≠ 𝑖

(𝐶) Complements: 𝜕𝑗𝐷𝑖 < 0 for𝑗 ≠ 𝑖

[Hybrid cases as well]

6

SETTING (2/2)

Assumptions

Profit function π𝑖 p = 𝑝𝑖𝐷𝑖 p − 𝐶𝑖(𝐷𝑖 p ) is strictly quasi-concave in 𝑝𝑖

Best-response 𝑅𝑖 p−𝑖 = argmax𝑝𝑖π𝑖 p satisfies 𝜕𝑗𝑅𝑖𝑗≠𝑖 < 1

Occasionally useful to further assume, under 𝑆 :

(𝑆𝐶) Strategic Complements: 𝜕𝑗𝑅𝑖 > 0 for 𝑗 ≠ 𝑖

[often the case under (𝑆)]

Industry profit Π p = π𝑖 p𝑗∈𝑁 is strictly quasi-concave and

achieves its maximum for pM

7

NON-REPEATED INTERACTION: PRELIMINARIES

Lemma

There exists a unique Nash equilibrium

Under (𝑆), all monopoly prices lie above the best-responses

Under (𝐶), at least one monopoly price lies below the best-response

Proposition 1: Price caps

Price-cap implementable prices are those below the best-responses

Intuition: strict quasi-concavity

If 𝑝𝑖 > 𝑅𝑖 𝑝𝑗 , firm 𝑖 lowers its price to its best-response (doable)

Conversely, if p = 𝑝1, 𝑝2 satisfies 𝑝𝑖 ≤ 𝑅𝑖 𝑝𝑗 for 𝑖 = 1,2, then price caps p = p implement p: firms want to raise their prices, but cannot.

8

NON-REPEATED INTERACTION: DUOPOLY (1/3)

Assumption A

For any 𝑗 ≠ 𝑖 ∈ 1,2 and any price 𝑝𝑖 ≤ 𝑝𝑖𝑁, if 𝑅𝑗 𝑝𝑖 > 𝑝𝑗

𝑁 then

𝑅𝑗′ 𝑝𝑖 > −

𝐷𝑖 𝑝𝑖,𝑅𝑗 𝑝𝑖

𝐷𝑗 𝑅𝑗 𝑝𝑖 ,𝑝𝑖

Holds for instance under 𝑆𝐶 (𝑅𝑗′ ⋅ > 0) or when demand is

quasi-symmetric

Proposition 2: Price caps benefit consumers

Any other prices than Nash that can be sustained with price caps yield strictly more consumer surplus than Nash

9

NON-REPEATED INTERACTION: DUOPOLY (2/3)

Intuition

Implementable prices lie below best-responses

At worst on a best-response

Moving from pM toward p:

𝑑𝑆 = − 𝐷1 + 𝐷2𝑅2

′ 𝑑𝑝1 > 0

(+) (−)

Np

Price-cap implementable

prices

0

2R

2p

1p

1R

p

10

NON-REPEATED INTERACTION: DUOPOLY (3/3)

Proposition 3: Will firms use price caps?

Under 𝑆 :

• Price caps cannot increase both firms’ profits (hence, not used in the absence of side payments)

• Under 𝑆𝐶 , cannot even raise industry profit

Under (𝐶), price caps can raise both firms’ profits

Proposition 4: Price caps versus mergers

If 𝑝𝑖𝑀 ≥ 𝑝𝑖

𝑁 for 𝑖 = 1,2, with at least one strict inequality, then a merger harms consumers; price caps can only benefit them.

If 𝑝𝑖𝑀 ≤ 𝑝𝑖

𝑁 for 𝑖 = 1,2, and 𝑝𝑖𝑀 ≤ 𝑅𝑖 𝑝𝑗

𝑀 for 𝑗 ≠ 𝑖 ∈ 1,2 , then a merger and price caps yield the same outcome.

11

NON-REPEATED INTERACTION: SYMMETRIC OLIGOPOLY

Assumptions

Symmetric costs and demands

Reaction curve when others charge same 𝑝 has slope < 1

Results

Proposition 5: Price caps benefit consumers

Proposition 6: Firms’ incentives

• Under 𝑆 , firms cannot gain from price caps

• Under 𝐶 , can sustain monopoly outcome

(uniquely so if non deceasing returns to scale)

12

REPEATED INTERACTION: SYMMETRIC OLIGOPOLY (1/4)

Setting

At date 0, firms agree on price caps.

At date 𝑡 = 1,2,…, firms set prices

Profit: 𝛿𝑡π𝑖 p𝑡𝑡≥1

Assumptions

Symmetric costs and demands

Symmetric, stationary equilibrium paths [no restriction off the equilibrium path.]

If price caps: 𝑝 𝑖 = 𝑝

13

REPEATED INTERACTION: SYMMETRIC OLIGOPOLY (2/4)

Let 𝑃+ (resp., 𝑃𝑐+) denote the set of equilibrium prices p that are

(weakly) more profitable than the static Nash equilibrium and can be sustained in the absence of price caps (resp., with price caps).

Lemma: 𝑝𝑁 ∈ 𝑃+ ⊆ 𝑃𝑐+

Proposition 7: Price caps and tacit coordination

Under 𝑆 and 𝑆𝐶 , price caps have no impact on the scope for tacit coordination

Under 𝐶 , price caps enable perfect coordination, which benefits consumers

(uniquely so if non deceasing returns to scale)

14

REPEATED INTERACTION: SYMMETRIC OLIGOPOLY (3/4)

Intuition: 𝑆 and 𝑆𝐶

Let 𝑝 be sustained by cap 𝑝 ≥ 𝑝

optimal punishment: lowest cont. value 𝑉𝑖

best deviation (on/off-eq): on reaction curve

0 < 𝑅′ ⋅ < 1: price cap never constrains deviations

1p

2R

1R

Np

p̂

p

Mp

0

15

REPEATED INTERACTION: SYMMETRIC OLIGOPOLY (4/4)

Intuition: 𝐶

Suppose 𝑝 = 𝑝𝑀:

If prices ≠ 𝑝𝑀, 𝑝𝑀 in one period, one firm must get less than π 𝑝𝑀, 𝑝𝑀 / 1 − 𝛿

But can guarantee itself π 𝑝𝑀, 𝑝𝑀 / 1 − 𝛿 by playing repeatedly 𝑝𝑀 because 𝐶 and non-decreasing returns to scale

1p

2p

2 (if SC)R

1 (if SC)R

Np

Mp

0

2 (if SS)R

1 (if SS)R

Mp p

Mp p

16

REPEATED INTERACTION: TECHNOLOGY MODEL (1/5)

Setting (special case of Lerner-Tirole AER 2004)

Two symmetric firms 1 and 2 (extension to n > 2, asymmetry)

Users’ value

• 𝑉 − 𝑃 − with both products (patents) at total price 𝑃

• 𝑉 − 𝑒 − 𝑝 − with one product (either one) at price 𝑝

𝑒: essentiality parameter

: adoption cost, distributed according to 𝐹 on [0, 𝑉]

17

REPEATED INTERACTION: TECHNOLOGY MODEL (2/5)

Simple set-up

All users pick the same basket if they adopt the technology

Menus do not increase profit under joint marketing

→ avoids discussing (mixed) bundling & price discrimination

Hybrid demand

From perfect substitutes to perfect complements as 𝑒 increases

• Complements for low prices (users favour full technology)

• Substitutes for high prices (users favour partial technology)

Pool is socially desirable if 𝑒 > 𝑝𝑚 = argmax𝑝 𝑝𝐹 𝑉 − 2𝑝

18

REPEATED INTERACTION: TECHNOLOGY MODEL (3/5)

Repeated interaction without price caps Coordination easiest when lack thereof is very costly Substitutes: collusion involves loss of efficiency/demand

No collusion

or cooperation

1

1

2

0Mp

e

Rivalry Complementors

Perfect cooperation

0V

( )C e

( )C

e

Inefficientcollusion

( )R e

at Mpat Mp

Limited

cooperation

19

REPEATED INTERACTION: TECHNOLOGY MODEL (4/5)

Repeated interaction with price caps No impact of price caps for substitutes Higher consumer surplus and profit for complements

No collusion

1

1

2

0Mp

e

Rivalry Complementors

0V

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

Inefficientcollusion

at Mp

Perfect cooperation

at Mp

perfect cooperation and

Price caps enable

lower price to Mp

20

REPEATED INTERACTION: TECHNOLOGY MODEL (5/5)

Does “independent licensing” suffice?

Independent licencing

• Guidelines (US, Europe, Japan,. . . ): Patent pools must allow independent licensing

• Lerner – Tirole 2004: Perfectly screens in good pools and out bad pools in absence of tacit coordination (Boutin 2016)

Price cap = independent licensing + unbundling

With tacit coordination, independent licensing still useful, but no longer a perfect screen

21

CONCLUDING REMARKS (1/3)

When is commercial cooperation is desirable?

(complements vs. substitutes)

Relevant for IP rights, but also in many other industries

content carried by cable operators

payment systems used by merchants

airline alliances and code-sharing agreements

providers included in health insurance networks (Katz 2011)

music performance rights licensed by Pandora

22

CONCLUDING REMARKS (2/3)

Review of mergers and joint marketing agreements (JMAs) plagued by limited information price/demand data patchy or non-existent

evolving patterns of complementarity/substitutability

price-dependent patterns of complementarity/substitutability

→ Calls for information-light rules

Here: price caps as an alternative to mergers and JMAs enable firms to solve Cournot’s problem in case of complements,

but not to raise prices in case of substitutes

if used by firms, raise consumer welfare

• non-repeated interaction

• repeated interactions (in environments studied in this paper)

23

CONCLUDING REMARKS (3/3)

Alleys for future research

Theory of repeated interaction for general cost and demand

Market transparency and focal points

Non-linear pricing and price discrimination

Cooperation on other dimensions

• Cross licensing

• R&D

• Production capacity