1 Motivation • Game theory is fundamental in industrial organi- zation • Agents are not anonymous, they interact often in small numbers • Game theory starts with a specification of strate- gies, payoffs and information • From these objects, predictions of behavior are derived • Economic theory: Model Parameters= ⇒Predictions
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1 Motivation - faculty.washington.edu · 1 Motivation • Game theory is fundamental in industrial organi-zation • Agents are not anonymous, they interact often in small numbers
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1 Motivation
• Game theory is fundamental in industrial organi-zation
• Agents are not anonymous, they interact often insmall numbers
• Game theory starts with a specification of strate-gies, payoffs and information
• From these objects, predictions of behavior are
derived
• Economic theory: Model Parameters=⇒Predictions
• Some problems with using game theoretic modelsfor ”real” economic problems:
1. Predictions can depend delicately on the specifi-
cation of the model
2. Little evidence to guide us on how to make these
choices
3. Difficult to derive the predictions for all but the
simplest games
4. Multiplicity of outcomes
5. Unwillingness of theorists to confront dynamics
• Next, we will study how to use a game as an
econometric model
• Econometrics: Data=⇒Payoffs and other modelparameters
• The flexibility of game theory is an advantageeconometrically
• It allows the researcher to fit a broad class ofbehaviors
• Models that are trivially rejected are not very use-ful empirically
• Estimation involves two steps:
1. Flexibly estimate reduced form decision rules
• ”Solution” to the multiple equilibrium problem is
to condition on the one that is in the data
2. Find structural parameters that make these deci-
sion rules optimal
• Computationally simple and accurate methods
• Emphasis on implimentation, substantive empiri-cal applications.
2 Static Games
• A game is a generalization of a standard discretechoice model (e.g. logit or probit)
• Payoffs depend on exogenous covariates and pref-erence shocks
• In a game, payoffs also depend on actions of otherplayers
• Observed behavior is assumed to be an equilib-rium to the game
• Objective: Estimate agents utilities and equilib-rium selection mechanism
• Early work:Vuong and Bjorn (1984), Bresnahanand Reis (1990,1991) and Berry (1992).
• More recent work: Mazzeo (2002), Tamer (2003),Sweeting (2004), Ackerberg and Gowrisankaran
(2006), Aradillas-Lopez (2005), Ryan and Tucker
(2006), Pakes, Porter, Ho and Ishii (2005), Ho(2005),
Ishii (2005), Ciliberto and Tamer (2007)
• Dynamic Games: Aguirregabiria and Mira (2007),Pesendorfer and Schmidt-Dengler (2007),Pakes,
Ovtrovsky and Berry (2007) and Bajari, Benkard
and Levin (2007).
3 Outline
1. Simple entry example
2. Static Games
3. Nonparametric identification
4. Nonparametric/semiparametric estimator
3.1 Entry Example.
• Data on a cross section of markets.
• Entry by Walmart and/or Target.
• Markets = 1 and firms = 1 2
• Let = 1 denote entry and = 0 denote noentry.
• Economic theory suggests that profits depends ondemand, costs and number of competitors
• is population of market (demand)
• is distance from headquarters (costs)
• − indicates entry by competitors
• The profit of firm is:
= ·+ ·+ ·−+ if = 1
= 0 if = 0
• is private information
• ( = 1) is probability that enters market .
• In a Bayes-Nash equilibrium, agent makes bestresponse to −(− = 1)
• Therefore, ’s decision rule is:
= 1⇐⇒ · + · + · −(−= 1) + 0
• If error terms are extreme value, then
(= 1) =exp(·+·+·−(−=1))1+exp(·+·+·−(−=1))
• Equilibrium- two equations in two unknowns (1(1 =1) and 2(2 = 1)):
1(1= 1) =exp(·+·1+·2(2=1))1+exp(·+·1+·2(2=1))
2(2= 1) =exp(·+·2+·1(1=1))1+exp(·+·2+·1(1=1))
Two-Step Estimator
• First, estimate b( = 1|12)
using a “flexible” method.
• This is the frequency that entry is observed em-pirically.
• Standard problem.
• We are recovering an agent’s equilibrium beliefs
by using the sample analogue.
• Given this first stage estimate, agent ’s decisionrule is estimated as :
= 1⇐⇒ · + · +·b−(−= 1) + 0
• The probability that choose to enter is
(= 1) =exp(·+·+·b−(−=1))1+exp(·+·+·b−(−=1))
• This is the familiar conditional logit model!
• In second step, let ( ) denote the pseudolikelihood function defined as:
( ) =
Y=1
2Y=1
³exp(·+·+b−(−=1)·)1+exp(·+·+b−(−=1)·)´1{=1}
³1− exp(·+·+b−(−=1)·)
1+exp(·+·+b−(−=1)·)´1{=0}
• Maximize psuedo-likelihood to estimate .
• Bottom line: this is the logit model with b( =1|12) as an additional in-
dependent variable.
• Simple generalization of widely used model.
• Computationally simple and accurate
• Easy to include unobserved heterogeneity.
• Generalize to richer models, including dynamicmodels.