Methodology for Analyzing

Market Dynamics.

Adapted from three lectures given in 2014.• The Cowles Lecture: N.A.Econometric

Society, Minneapolis, June.• Keynote Address: Society for Applied

Dynamic Games, Amsterdam, July.• Keynote Address: L.A. Econometric Society

Meetings, Sao Paulo, November.

by

Ariel Pakes(Harvard University and the NBER).

1

Background: MethodologicalDevelopments in IO.

• We have been developing tools that enableus to better analyze market outcomes.

• Common thread: emphasis on incorporat-ing the institutional background needed tomake sense of the data used in analyzingthe likely causes of historical events, or thelikely responses to environmental and pol-icy changes.

• Focus. Incorporate(i) heterogeneity (in plant productivity,products demanded, bidders and/or con-sumers) and where possible,(ii) equilibrium conditions (Nash in pricesor quantities, and extensions designed toanalyze allocations in network, platform,and vertical markets).

2

We largely relied on earlier work by our gametheory colleagues for the analytic frameworks.

• Each agent’s actions a↵ect all agents’ pay-o↵s, and

• At the “equilibrium” or “rest point”(i) agents have correct perceptions, and(ii) the system is in some form of Nashequilibrium (policies such that no agent hasan incentive to deviate).

• Our contribution is the development of anability to adapt the analysis to the richnessof di↵erent real world institutions.

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Claim 1. The tools developed for the anal-ysis of market allocations conditional on the“state variables” of the problem (characteris-tics of products marketed, cost determinants,...) pass a market test for success as:(i) They have been incorporated into appliedwork in virtually all of economics that dealswith market allocations (especially where pro-ductivity and/or demand is needed),(ii) They are used by public agencies, consul-tancies and to some extent by firms and(iii) They do surprisingly well, both in fit and inproviding a deeper understanding of empiricalphenomena.

Note. There are improvements still being done,and important new work in analyzing equilib-rium allocations in markets where Nash in pricesor quantities seems inappropriate; e.g. verticalmarkets, platform markets,...

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E.g. of Fit: Pricing Behavior. Wollman’s dis-sertation (commercial trucks). Estimate BLPdemand, regress Nash markup on instrumentsto get ˆmarkup (R2=.44 or .46 with time dum-mies; sophisticated IV would do better). Lookto fit & whether coe�cient of ˆmarkup ⇡ 1?

Table 1: Fit of Pricing Equilibrium.

Price (S.E.) Price (S.E.)Gross Weight .36 (0.01) .36 (.003)Cab-over .13 (0.01) .13 (0.01)Compact front -.19 (0.04) 0.21 (0.03)long cab -.01 (0.04) 0.03 (0.03)Wage .08 (.003) 0.08 (.003)

ˆMarkup .92 (0.31) 1.12 (0.22)Time dummies? No n.r. Yes n.r.R2 0.86 n.r. 0.94 n.r.

Nobs=1,777; firms=16; t=1992-2012; Heter-cons s.e.

Note. Level shifts (time dummies) are 8% ofthe 14% of unexplained variance.

5

What About “Dynamics”? Use textbookdistinction: (i) static models solve for prof-its conditional on state variables, (ii) dynamicsanalyzes the evolution of those state variables.

The initial frameworks by our theory colleaguesmade assumptions which insurred that the

1. state variables evolve as a Markov process

2. and the equililbrium is some form of MarkovPerfection (no agent has an incentive todeviate at any value of the state variables).

E.g. Maskin and Tirole (1988) and Ericsonand Pakes (1995). We now consider each ofthese in turn.

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On (1); the Markov Assumption. Exceptin situations involving active experimentationand learning (where policies are transient), ap-plied work is likely to stick with the assump-tion that states evolve as a time homogenousMarkov process of finite order. There are atleast three reasons for this:• It is a convenient and fits the data well.• Realism suggests information access and re-tention conditions limit the memory used.• We can bound unilateral deviations (simi-lar to Weintraub, 2014), and have conditionswhich insure those deviations can be made ar-bitrarily small by letting the length of the kepthistory grow (White and Scherer, 1994).

On 2: Perfection. The type of rational-ity built into Markov Perfection is more ques-tionnable; even though it has been useful in thesimple models used by our theory colleagues toexplore possible outcomes in a structured way.We come back to this below.

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Empirical work on dynamics proceeded ina similar way to what we did in static anal-ysis; we took the Markov Perfect frameworkand tried to incorporate the institutions thatseemed necessary to analyze actual markets.

The Result. Though the MP framework wasuseful in guiding analysis of several issues (e.g.productivity) it became unweildly when con-fronted with the task of analyzing market dy-namics. This because of the complexity of theinstitutions we were trying to model. The dif-ficulties became evident when we tried to usethe Markov Perfect notions to structure

• the estimation of parameters, or to

• compute the fixed points that defined theequilibria or rest points of the system.

8

Our response. Keep the equilibrium notionand develop techniques to make it easier tocircumvent the estimation and computationalproblems. Useful contribution in this regard:

• The development of estimation techniquesthat circumvent the problem of repeatedlycomputing equilibria (that do not require anested fixed point algorithm).

• the use of approximations and functionalforms for primitives which enabled us tocompute equilibria quicker and/or with lessmemory requirements.

The underlying ideas: (i) are useful under otherequilibirum assumptions, and (ii) enabled anexpansion of computational dynamic theory.However they were not powerful enough toallow us to incorporate su�cient realism intoempirical work based on Markov Perfection.

This leads me to my second claim.

Claim 2. Empirical work on dynamic modelshave not passed beyond the hands of a fewdiligent I.O. researchers.

As a result dynamic issues are analyzed in amuch less rigorous way than static issues evenwhen dynamic computational results indicatethat they are essential to understanding theimplications of the phenomena of interest (e.g.’s:mergers or collusion). Moreover the complex-ity of Markov Perfection not only limits ourability to do dynamic analysis of market out-comes it also

• leads to a question of whether some othernotion of equilibria will better approximateagents’ behavior.

9

I want to focus on the last point. The factthat Markov Perfect framework becomes un-wieldily when confronted by the complexity ofreal world institutions, not only limits our abil-ity to do empirical analysis of market dynamics

• it also raises the question of whether someother notion of equilibria will better approx-imate agents’ behavior.

I.e. If we abandon Markov Perfection can weboth

• better approximate agents’ behavior and,

• enlarge the set of dynamic questions we areable to analyze.

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The complexity issue. When we try to incor-porate what seems to be essential institutionalbackground we find

• That the agent is required to; (i) accessa large amount of information (all statevariables), and (ii) either compute or learnan unrealistic number of strategies (one foreach information set).

How demanding is this? Consider marketswhere consumer, as well as producer, choicesare dynamic (e.g.’s; durable, experience, ornetwork goods); need the distribution of; cur-rent stocks ⇥ household characteristics, pro-duction costs, . . .. In a symmetric informationMPE an agent would have to access all statevariables, and then either compute a doublynested fixed point, or learn and retain, policiesfrom each distinct information set.

Theory Fix: Assume agents only have accessto a subset of the state variables.

• Since agents presumably know their owncharacteristics and these tend to be per-sistent, we would need to allow for assy-metric information: the “perfectness” no-tion would then lead us to a “Bayesian”Markov Perfect solution.

Problem. The burden of computing its strate-gies insures that they will not be directly com-puted by either agents or the analyst for eventhe simplest (realistic) applied problem. Theadditional burden results from the need to com-pute posteriors, as well as optimal policies; andthe requirement that they be consistent withone another.

Could agents learn these policies, or at leastpolicies which maintain some of the logical fea-tures of Bayesian Perfect policies, from com-bining data on past behavior with market out-comes? They would have to learn about;• primitives (some empirical work on this),• the likely behavior of their competitors, and• market outcomes given primitives, competi-tor behavior, and their own policies.

There is surprising little empirical evidence onhow firms formulate their perceptions abouteither other firms’ behavior, or on the impactof their own strategies given primitives and theactions of competitors.

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An ongoing study by U. Doraszelski, G. Lewisand myself of bids from the date the BritishElectric Utility market for frequency responseopened, addresses this question. The conclu-sions we are reasonably confident on to dateare (see the figures)

• The bids do eventually converge, and theyconverge to what looks like a Nash equilib-rium (in 2009), and

• In its initial stages, the learning processis complex, involves experimentation, anddi↵ers among firms.

• The smaller changes that occured in thefirst half of 2010 (Drax signs long-termcontract with NG) seems more structurredand proceeds to an equilibrium much quicker.

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Rest of Talk.

• Unfortunately, I have little to say on “ac-tive” experimentation periods; on model-ing beliefs on the value of di↵erent experi-ments.

• For more stable environments I introduce(i) a notion of equilibrium that is less de-manding than Markov Perfect for both theagents, and the analyst, and show how to(ii) compute the equilibrium and(iii) estimate o↵ of equilibrium conditions.

• Consider restrictions that mitigate multipleequilibria.

• Provide a computed example of this equi-librium (electric utility generation).

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I start with strategies that are “rest points”to a dynamical system. Later I will considerinstitutional change, but only changes where itis reasonable to model responses to the changewith a simple reinforcement learning process (Ido not consider changes that lead to activeexperimentation). This makes my job mucheasier because:

• Strategies at the rest point likely satisfy aNash condition of some sort; else someonehas an incentive to deviate.

• However it still leaves opens the question:What is the form of the Nash Condition?

What Conditions Can We Assume for the

Rest Point at States that are Visited

Repeatedly?

We expect (and I believe should integrate intoour modelling) that

1. Agents perceive that they are doing thebest they can at each of these points, andthat

2. These perceptions are at least consistentwith what they observe.

Note. It might be reasonable to assume morethan this: that agents (i) know and/or (ii) ex-plore, properties of outcomes of states not vis-ited repeatedly. I come back to this below.

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Formalization of Assumptions.

• Denote the information set of firm i in periodt by Ji,t. Ji,t will contain both public (⇠t) andprivate (!i,t) information, so Ji,t = {⇠t,!i,t}.

• Assume Ji,t evolves as a (controlled) finitestate Markov process on J (or can be ade-quately approximated by one); and only a fi-nite number of firms are ever simultaneouslyactive.

• Policies, say mi,t 2 M, will be functions ofJi,t. For simplicity assume #M is finite, andthat it is a simple capital accumulation game,i.e. 8(mi,m�i) 2 Mn, & 8 ! 2 ⌦

P!(·|mi,m�i,!) = P!(·|mi,!).

where the public information, ⇠, is used to pre-dict competitor behavior and common demandand cost conditions which evolve as an exoge-nous Markov process.

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• So a “state” of the system, is

st = {J1,t, . . . , Jnt,t} 2 S,

#S is finite. ) any set of policies will insurethat st will wander into a recurrent subset ofS, say R ⇢ S, in finite time, and after thatst+⌧ 2 R w.p.1 forever.

• Agents do not: (i) know st, or (ii) calculatepolicies for its components.

• ) If Ji,t 2 J and #J = K, while the #firms is N , the number of states changes fromKN to either:(i) K (symmetric agents), or(ii) K ⇥N (otherwise).

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• Let the agent’s perception of the expecteddiscounted value of current and future net cashflow were it to chose m at state Ji, be

W (m|Ji), 8m 2 M & 8Ji 2 J ,

• and of expected profits be

⇡E(m|Ji).

Our assumptions imply:

• Each agent choses an action which max-imizes its perception of its expected dis-counted value, and

• For those states that are visited repeatedly(are in R) these perceptions are consistentwith observed outcomes.

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Formally

A. W (m⇤|Ji) � W (m|Ji), 8m 2 M & 8Ji 2 J ,

B. &, 8Ji which is a component of an s 2 R

W (m(Ji)|Ji) = ⇡E(m|Ji)+�X

J0i

W (m⇤(J0i)|J

0i)p

e(J0i|Ji),

where, if pe(·) provides the empirical probability(the fraction of periods the event occurs)

⇡E(m|Ji) ⌘X

J�i

E[⇡(·)|Ji, J�i]pe(J�i|Ji),

andn

pe(J�i|Ji) ⌘pe(J�i, Ji)

pe(Ji)

o

J�i,Ji,

while

n

pe(J0i|Ji) ⌘

pe(J0i, Ji)

pe(Ji)

o

J0i ,Ji

. �

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“Experience Based Equilibrium”

These are the conditions of a (restricted) EBE(Fershtman and Pakes, 2012; for related ear-lier work see Fudenberg and Levine, 1993).Bayesian Perfect satisfy them, but so do weakernotions. We now turn to its :(i) computational and estimation properties,(ii) overcoming multiplicity issues,(iii) and then to an example.

Computational Algorithm. “Reinforcementlearning” algorithm (Pakes and McGuire, 2001).• Can be viewed as a learning process. Makesit a candidate to: (i) analyze (small) pertur-bations to the environment, as well as (ii) tocompute equilibrium.• Does not generate a curse of dimensionalityin either: (i) the number of states or (ii) thecomputation of continuation values.

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Iterative Algorithm: Iterations defined by

• A location, say Lk = (Jk1, . . . J

kn(k)) 2 S: is the

information sets of agents active.• Objects in memory (i.e. Mk):(i) perceived evaluations, Wk,(ii) No. of visits to each point, hk.

So algorithm must update (Lk,Wk, hk). Com-putational burden determined by; memory con-straint, and compute time. I use a simple (notneccesarily) optimal structure to memory.

Update Location.

• Calculate “greedy” policies for each agent

m⇤i,k = arg max

m2MWk(m|Ji,k)

• Take random draws on outcomes conditionalon m⇤

i,k: i.e. if we invest in “payo↵ relevant”

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!i,k 2 Ji,k, draw !i,k+1 conditional on (!i,k,m⇤i,k).

• Update {Ji,k}i.

Update Wk.

• “Learning” interpretation: Assume agent ob-serves b(m�i) and knows the primitives (⇡(·), p(·|!,m))conditional on (b(m�i),!,m).

• Its ex poste perception of what its valuewould have been had it chosen m is

V k+1(Ji,k,m) =

⇡(!i,k,m, b(m�i,k), dk)+maxm̃2M

�Wk(m̃|Ji,k+1(m)),

where Jk+1i (m) is what the k + 1 information

would have been given m and competitors ac-

tual play.

Treat V k+1(Ji,k) as a random draw from thepossible realizations of W (m|Ji,k), and updateWk as in stochastic integration (Robbins andMonroe,1956)

Wk+1(m|Ji,k)�Wk(m|Ji,k) =

1

hk(Ji,k)[V k+1(Ji,k,m)�Wk(m|Ji,k)].

or

Wk+1(m|Ji,k) =

1

hk(Ji,k)V k+1(Ji,k,m)+

(hk(Ji,k)� 1)

hk(Ji,k)Wk(m|Ji,k),

(other weights might be more e�cient).

Notes.

• If we have equilibrium valuations we tend tostay their, i.e. if ⇤ designates equilibrium

E[V ⇤(Ji,m⇤)|W ⇤] = W ⇤(m⇤|Ji).

• To learn equilibrium values we need to visitpoints repeatedly; only likely for states in R.

• Agents (not only the analyst) could use thealgorithm to find equilibrium policies or adjustto perturbations in the environment.

• Algorithm has no curse of dimensionality.(i) Computing continuation values: integrationis replaced by averaging two numbers.(ii) States: algorithm eventually wanders intoR and stays their, and #R #J .

•The algorithm uses the stochastic approxima-tion literature and as in that literature it canbe augmented to use functional form approxi-mations where needed (“TD learning”; Suttonand Barto,1998).

Computational Properties.

• Testing. The algorithm does not necessar-ily converge, but a test for convergence existsand does not involve a curse of dimensionality(Fershtman and Pakes, 2012).

• The test is based on simulation. It producesa consistent estimate of an L2(P (R)) norm ofthe percentage bias in the implied estimates ofV (m,Ji); where P (R) is the invariant measureon the recurrent class.

Estimation.

• Need a candidate for Ji. Either: (i) empir-ically investigate determinants of controls, or(ii) ask actual participants.

• Does not require nested fixed point algo-rithm. Use estimation advances designed forMP equilibria (POB or BBL), or a perturba-tion (or “Euler” like) condition (below).

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Euler-Like Condition.

• With assymetric information the equilibriumcondition

W (m⇤|Ji) � W (m|Ji)

is an inequality which can generate (set) esti-mators of parameters.

• Ji contains both public and private informa-tion. Let J1 have the same public, but di↵erntprivate, information then J2. If a firm is at J1

it knows it could have played m⇤(J2) and itscompetitors would respond by playing on the

equilbrium path from J2.

• If m⇤(J2) results in outcomes in R, we cansimulate a sample path from J2 using only ob-served equilibrium play. The Markov propertyinsures it would intersect the sample path from

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the DGP at a random stopping time with prob-ability one and from that time forward the twopaths would generate the same profits.

• The conditional (on Ji) expectation of thedi↵erence in discounted profits between thesimulated and actual path from the period ofthe deviation to the random stopping time,should, when evaluated at the true parame-ter vector, be positive. This yields momentinequalities for estimation as in Pakes, Porter,Ho and Ishii (forthcoming), Pakes, (2010).

Multiplicity.

• R contains both “interior” and “boundary”points. Points at which there are feasible strate-gies which can lead outside of R are boundarypoints. Interior points are points that can onlytransit to other points in R no matter which(feasible) policy is chosen.

• Our conditions only insure that perceptionsof outcomes are consistent with the resultsfrom actual play at interior points. Perceptionsof outcomes for some feasible (but inoptimal)policy at boundary points are not tied down byactual outcomes.

• MPBE are a special case of (restricted) EBEand they have multiplicity. Here di↵ering per-ceptions at boundary points can support a (pos-sibly much) wider range of equilibria.

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Narrowing the Set of Equilibria.

• In any empirical appliction the data will ruleout equilibria. m⇤ is observable, at least forstates in R, and this implies inequalities onW (m|·). With enough data W (m⇤|·) will alsobe observable up to a mean zero error.

• Use external information to constrain percep-tions of the value of outcomes outside of R.If available use it.

• Allow firms to experiment with mi 6= m⇤i at

boundary points (as in Asker, Fershtman, Ji-hye, and Pakes, 2014). Leads to a strongernotion of, and test for, equilibrium. We insurethat perceptions are consistent with the resultsfrom actual play for each feasible action atboundary points (and hence on R).

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Boundary Consistency.

Let B(Ji|W) be the set of actions at Ji 2 s 2R which could generate outcomes which arenot in the recurrent class (so Ji is a bound-ary point) and B(W) = [Ji2RB(Ji|W). Thenthe extra condition needed to insure “Bound-ary Consistency” is:

Extra Condition. Let ⌧ index future periods,then 8(m,Ji) 2 B(W)

Eh

1X

⌧=0�⌧⇡(m(Ji,⌧),m(J�i,⌧))|Ji = Ji,0,W

i

W (m⇤|Ji),

where E[·|Ji,W] takes expectations over futurestates starting at Ji using the policies gener-ated by W. �

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Testing for Boundary Consistency.

From each (m,Ji) 2 B(W) simulate indepen-dent sample paths. Index the periods of a pathby ⌧ & terminate it the first time Ji 2 s 2 R (orif that does not occur at some large number),say ⌧⇤. The path’s estimate of W (m|Ji) is

W̃ (m|Ji) ⌘⌧⇤X

⌧=0�⌧⇡(m(Ji,⌧),m(J�i,⌧))+�⌧

⇤W (m⇤|Ji,⌧⇤),

with mean and variance; W (m|Ji), V ar[W (m|Ji)].

Let f(x)+ = max[0, f(x)], and

T (m|Ji) ⌘[W (m|Ji)�W (m⇤|Ji)]+

W (m⇤|Ji)

Now use a one-sided test of

H0 :

P

(m,Ji)2B(W) T (m|Ji)q

P

(m,Ji)2B(W) V ar[T (m|Ji)]= 0,

where V ar[T (m|Ji)] is the variance of T (m|Ji).26

Simple Electric Utility Eg.

Two firms: each has a vector of generators.Firm’s decisions: bid or not each generator. Ifnot bid, do maintenance or not.ISO: sum bid functions, intersect with demand(varies by day of the week), pay a uniform priceto accepted electricity.

• ! 2 ⌦. Cost of producing electricy on eachfirm’s generators. Cost increases stochas-tically with use, but reverts to a startingvalue if the firm goes down for mainte-nance.

• mi 2 Mi. Vector of mi,r 2 {0,1,2}; 0 )shutdown without maintenance, 1 ) shut-down with maintenance, 2 ) bid into mar-ket.

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• b(mi) : mi ! {0, bi}ni where bi is the fixedbid schedule of firm i. b observed. m notobserved.

• d is demand on that day,f is maintenancecost (“ investment”), p = p(b(mi), b(m�i), d)is price, q = q(b(mi), b(m�i), d) is allocatedquantity vector, so realized profits are

⇡i,t =X

rptqi,r,t�

X

rci(!i,r,t, qi,r,t)�fi

X

r{mi,r,t = 1}

⌘ ⇡i(!i,mi, b(m�i), d)

mi,r,t = 0 ) !i,r,t+1 = !i,r,t,mi,r,t = 1 ) !i,r,t+1 = !i,r (!=restart state),mi,r,t = 2 ) !i,r,t+1 = !i,r,t � ⌘i,r,twith P (⌘) > 0 for ⌘ 2 {0,1}.

Note b(m) is the only signal sent in each pe-riod. b(m�i,t�1) is a signal on !�i,t�1 whichis unobserved to i and is a determinant ofb(m�i,t) (and so ⇡i,t).

State of the game. si,t = (J1,t, . . . Jnt,t) 2 S,and

Ji,t = (⇠t,!i,t) 2 (⌦(⇠),⌦)

where

• !i,t represents private information

• and ⇠t is public information (shared by all).Example ⇠t = {b(m1,⌧), b(m2,⌧), d⌧}⌧t, andknowledge of !�i,t the last period of reve-lation (happens every T periods).

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Model Details.

Parameter Firm B Firm SNumber of Generators 2 3Range of ! 0-4 0-4MC @ ! = (0,1,2,3)⇤ (20,60,80,100) (50,100,130,170)Capacity at Const MC 25 15Costs of Maintenance 5,000 2,000

⇤MC is constant at this cost until capacity and then goesup linearly. At ! = 4 the generator shuts down.

Firm S: small (gas fired) generators with highMC but low start up costs.Firm B: large (coal fired) generators lower MCand higher start up costs.Constant, small, elasticity of demand.

Computational Details.• High initial conditions “insures” we try allstrategies (induces a lot of experimentation).• Convergence test is in terms of L2(P(R))norm of percentage bias in estimates of W .300 million iterations L2(P(R)) ⇡ .00005.

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The Economics of Alternative

Environments: Planner vs AsI.

Base Case: Planner Strategy. Constrainplanner to use the same bid function (comparejust investment strategies). Never shuts downwithout doing maintenance. Weekdays: oper-ates at almost full capacity. Maintenance doneon weekend. Maintenance done about 15% ofthe periods for both B and S generators.

Base Case: AsI Equilibrium. Shuts downabout 20% of the periods. However about halfthe time generators are shutdown they are notdoing maintenance. Only does maintenance inabout 10% of the periods. ) 25-30% more

shutdown but 30% less maintenance than thesocial planner. Most (but not all) shutdownon weekends (just as social planner).

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Base Case: Costs. Planner does more main-tenance and can optimize maintenance jointlyover large and small generators. ) much lowerproduction costs and lower total costs per unitquantity.• I.e. the planner produces more and has loweraverage total costs in a model in which marginalcosts increase in quantity. E↵ect of increasedmaintenance.

Base Case: Prices and Quantities. Plan-ners 2% more output on weekdays, with in-elastic demand ) price fall of ⇡ 10%.• Planner’s extra maintenance makes it opti-mal for it to bid in more and therefore keepprice down, and it internalizes the extra CS.AsI firms do not.• Even the social planner has weekday pricesthat are 20% higher than weekend prices (theAsI di↵erence is larger). With these primi-tives large weekend/weekday price di↵erencesare “optimal”.

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Base CaseSP AsI FI

Panel A: Strategies.

Firm B: Shutdown and Maintenance.Shutdown % 14.52 19.96 12.31Maintenance % 14.52 10.1 10.9Firm S: Shutdown and Maintenance.Shutdown % 16.85 21.48 20.74Maintenance % 16.85 9.83 9.91Firm B: Operating Generators (by day).Saturday 1,41 1.08 1.72Sunday .88 1.21 1.65Weekday Ave. 1.93 1.78 1.78Firm S: Operating Generators (by day).Saturday 1.55 1,56 2.03Sunday 1.89 1.75 1.86Weekday Ave. 2.80 2.64 2.55

Panel B: Costs ( ⇥10�3).Maint. B 29 20.2 21.95Maint. S 20.2 11.8 11.9Var. B 211.1 235.1 240.4Var. S 174.8 228.1 215.9Total/Quantity 0.389 0.452 0.444Panel C: Quantities and Prices.Ave. Q Wkend 93.5 92.0 98.6Ave. P Wkend 303 325 260Ave. Q Wkday 185.7 181.8 181.2Ave. P Wkday 374 401 411

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Base Case vs Excess Capacity: AsI & FI

• Maintenance and Shutown.Base case: the FI equlibrium generates lessshutdown and more maintenance.“Excess” Capacity (more capacity relative todemand) the AsI equilibrium generates less shut-down and more maintenance.

• Weekday vs Weekend.Base case: AsI vs FI strategies: weekends theAsI equilibrium shuts down more genrators. Thisenables the firms to signal that their genera-tors will be bid in on the high-priced weekdays.Excess Capacity: Now the ASI firm no longerdistinguishes much between weekend and week-day.

• Prices.With excess capacity the di↵erence betweenweekday and weekend prices drops dramati-cally (to 5.4% in the AsI and 1% in the FI equi-librium) and AsI operation increases on week-end.

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• Costs.Increasing capacity relative to demand the av-erage cost is over 30% lower. Raises questionsof what are the capital costs and incentives forprivate generator construction?

• Total Surplus:

Increase in capacity/demand ratio generatesa large increase in consumer surplus, and asomewhat smaller total surplus increases. Doesincreased surplus cover social cost of genera-tor construction? And if so how do we inducethe investment?

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Base Case Excess CapacityAsI FI AsI FI

Panel A: Strategies.

Firm B: Shutdown and Maintenance.Shutdown % 19.96 12.31 41.97 43.75Maintenance % 10.1 10.9 6.47 6.25Firm S: Shutdwon and Maintenance.Shutdown % 21.48 20.74 53.1 56.4Maintenance % 9.83 9.91 5.22 4.84Firm B: Operating Generators (by day).Saturday 1.08 1.72 1.03 1.0Sunday 1.21 1.65 1.03 1.0Weekday Ave. 1.78 1.78 1.03 1.0Firm S: Operating Generators (by day).Saturday 1,56 2.03 1.21 0.48Sunday 1.75 1.86 1.20 0.44Weekday Ave. 2.64 2.55 1.25 1.44Panel B: Quantities and Prices.Ave. Q Wkend 92.0 98.6 33.6 33.1Ave. P Wkend 325 260 168 175.6Ave. Q Wkday 181.8 181.2 42.50 42.43Ave. P Wkday 401 411 177 177

Costs, Consumer Surplus and TotalSurplus (⇥10�3) .

Base Case Excess CapacityAsI FI AsI FI

Average Cost .452 .444 .290 .282CS⇤ 581.5 595.0 1,316 1,311Total Surplus 288.9 301.4 1,374 1,373

⇤ CS= these numbers plus 58,000.⇤⇤ Total Surplus = these numbers plus 59,000.

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Conclusions.

• There is a need for increased research on thedynamics of market outcomes.

• The framework used for this analysis oughtprobably to require less of both the agent andthe analyst then does “Bayesian Perfect” no-tions of equilibria.

• Ultimately, that framework will have to inte-grate the analysis of the reactions to changesin institutions with an analysis of policies forstates that are observed repeatedly. “Adap-tation” processes, like reinforcement learning,might be adequate for reactions to changesthat do not induce calculated experimentation.

• A start for equilibirum conditions at situa-tions that are observed repeatedly are those of“Experience Based Equilibrium”. If more strin-gent equilibrium conditions are justified theyshould be imposed as they will result in a moreprecise analysis.

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