2008): "Comment in The Identification Power of Equilibrium in Games (original) (raw)

Comment: The Identification Power of Equilibrium in Simple Games

2008

This paper studies the identification of structural parameters in dynamic games when we replace the assumption of Markov Perfect Equilibrium (MPE) with weaker conditions such as rational behavior and rationalizability. The identification of players' time discount factors is of especial interest. I present identification results for a simple two-periods/two-players dynamic game of market entry-exit. Under the assumption of level-2 rationality (i.e., players are rational and they know that they are rational), a exclusion restriction and a large-support condition on one of the exogenous explanatory variables are sufficient for point-identification of all the structural parameters.

Comment: Identification of a Simple Dynamic Discrete Game under Rationalizability

Working Papers, 2007

This paper studies the identification power of rationalizability in a simple dynamic discrete game model. The paper extends to dynamic games some of the results in . The most commonly used equilibrium concept in empirical applications of dynamic games is Markov Perfect Equilibrium (MPE). I study the identification of structural parameters when we replace the MPE assumption with weaker conditions such as rational behavior or rationalizability. I present identification results for a simple dynamic game of market entry-exit with two players. Under the assumption of level-2 rationalizability (i.e., players are rational and they know that they are rational), exclusion restrictions and large-support conditions on the exogenous explanatory variables are sufficient for point-identification of all the structural parameters. Though the model is fully parametric, the key identifying assumptions are nonparametric in nature and it seems that these identification results might be extended to a semiparametric version of the model.

Identification of a Simple Dynamic Discrete Game under Rationalizability

2008

This paper studies the identification power of rationalizability in a simple dynamic discrete game model. The paper extends to dynamic games some of the results in Aradillas-Lopez and Tamer (2007). The most commonly used equilibrium concept in empirical applications of dynamic games is Markov Perfect Equilibrium (MPE). I study the identification of structural parameters when we replace the MPE assumption with weaker conditions such as rational behavior or rationalizability. I present identification results for a simple dynamic game of market entry-exit with two players. Under the assumption of level-2 rationalizability (i.e., players are rational and they know that they are rational), exclusion restrictions and large-support conditions on the exogenous explanatory variables are sufficient for point-identification of all the structural parameters. Though the model is fully parametric, the key identifying assumptions are nonparametric in nature and it seems that these identification r...

Identification and Estimation of Dynamic Games

This paper studies the identi¯cation problem in in¯nite horizon Markovian games and proposes a generally applicable estimation method. Every period¯rms simultaneously select an action from a¯nite set. We characterize the set of Markov equilibria. Period pro¯ts are a linear function of equilibrium choice probabilities. The question of identi¯cation of these values is then reduced to the existence of a solution to this linear equation system. We characterize the identi¯cation conditions. We propose a simple estimation procedure which follows the steps in the identi¯cation argument. The estimator is consistent, asymptotic normally distributed, and e±cient.

Equilibrium Behavior In Markets and Games: Testable Restrictions and Identification* 1

Journal of Mathematical Economics, 2004

We provide a selective survey of the recent literature on the empirical implications of individually rational behavior in markets and games. We concentrate on work that develops empirical implications while making as few parametric assumptions as possible. We focus on two major themes: 1. the testable restrictions on the equilibrium manifold and the identification of economic fundamentals from the equilibrium manifold; and 2. the implications of the revealed preference theory of individual behavior for aggregated data.

Identification and Estimation of Dynamic Games when Players' Beliefs Are Not in Equilibrium

individual.utoronto.ca

This paper deals with the identification and estimation of dynamic games when players' beliefs about other players' actions may not be in equilibrium, i.e., they do not represent the actual behavior of other players. This type of model applies naturally to competition in oligopoly industries when firms face significant strategic uncertainty such that they have imperfect knowledge about the strategies of their competitors. Our approach can be used to estimate the evolution of players' beliefs when the researcher does not have data on elicited beliefs. First, we show that a standard exclusion restriction, that is typically used to identify payoffs in empirical games, provides testable nonparametric restrictions of the null hypothesis of equilibrium beliefs. Second, we prove that an additional assumption, that we call no strategic uncertainty at two 'extreme' points, is sufficient for nonparametric point-identification of payoff functions and players' beliefs. Third, we propose a simple two-step estimation method and a sequential generalization of the method that improves its asymptotic and finite sample properties. Finally, we illustrate our model and methods with an empirical application of a dynamic game of store location by retail chains.

RECENT DEVELOPMENTS IN THE ESTIMATION OF DYNAMIC GAMES

individual.utoronto.ca

These lectures deal with recent methodological developments in the estimation of dynamic games, and on the application of these new methods to different areas of economics. The estimation of dynamic games has to deal with three main issues: the potential endogeneity of the explanatory variables that represent other players' actions; the existence of multiple equilibria; and the curse of dimensionality in the computation of expected present values. These lectures examine different approaches that have been proposed and implemented to deal with these issues.

Minimal identification of dynamic rational expectations systems

This paper presents a further view on lhe identification of rational expectations (RE) modeJs. Its main point ia lhe establishment of necessary and sufficient conditions for identification on the structural fonn of static and dynamic modeJs, which extends ~ results obtained till now; no specific asswnptions being made on lhe stochastic processes generating lhe endogenous and exogenous variables. As a consequence, a clearer view ofthe costfbenefit of further selections in lhe solution set is gained. In the RE context, the concept of identification can be enIarged, depending on the past infonnation possessed by the econometrician. The main previous results are discussed under the light of lhe proposition.

Identification and Estimation of Dynamic Games when Players' Beliefs are Not in Equilibriun

This paper deals with the identification and estimation of dynamic games when players’ beliefs about other players’ actions are biased, i.e., beliefs do not represent the probability distribution of the actual behavior of other players conditional on the information available. First, we show that a exclusion restriction, typically used to identify empirical games, provides testable nonparametric restrictions of the null hypothesis of equilibrium beliefs. Second, we prove that this exclusion restriction, together with consistent estimates of beliefs at several points in the support of the special state variable (i.e., the variable involved in the exclusion restriction), is sufficient for nonparametric point-identification of players’ payoff and belief functions. The consistent estimates of beliefs at some points of support may come either from an assumption of unbiased beliefs at these points in the state space, or from available data on elicited beliefs for some values of the state variables. Third, we propose a simple two-step estimation method and a sequential generalization of the method that improves its asymptotic and finite sample properties. We illustrate our model and methods using both Monte Carlo experiments and an empirical application of a dynamic game of store location by retail chains. The key conditions for the identification of beliefs and payoffs in our application are the following: (a) the previous year’s network of stores of the competitor does not have a direct effect on the profit of a firm, but the firm’s own network of stores at previous year does affect its profit because the existence of sunk entry costs and economies of density in these costs; and (b) firms’ beliefs are unbiased in those markets that are close, in a geographic sense, to the opponent’s network of stores, though beliefs are unrestricted, and potentially biased, for unexplored markets which are farther away from the competitors’ network. Our estimates show significant evidence of biased beliefs.