Identification and Estimation of Dynamic Games when Players' Beliefs Are Not in Equilibrium
AbstractThis paper deals with the identification and estimation of dynamic games when playersâ€™ beliefs about other playersâ€™ 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 playersâ€™ 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 yearâ€™s network of stores of the competitor does not have a direct effect on the profit of a firm, but the firmâ€™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) firmsâ€™ beliefs are unbiased in those markets that are close, in a geographic sense, to the opponentâ€™s network of stores, though beliefs are unrestricted, and potentially biased, for unexplored markets which are farther away from the competitorsâ€™ network. Our estimates show significant evidence of biased beliefs.
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Bibliographic InfoPaper provided by Department of Economics, University of Calgary in its series Working Papers with number 2012-03.
Date of creation: 16 Jul 2012
Date of revision:
Other versions of this item:
- Victor Aguirregabiria & Arvind Magesan, 2012. "Identification and estimation of dynamic games when players' beliefs are not in equilibrium," Working Papers tecipa-449, University of Toronto, Department of Economics.
- C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
- C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
- L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
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