Identification and Estimation of Dynamic Games When Players' Beliefs are Not in Equilibrium

70 Pages Posted: 13 Oct 2015

See all articles by Victor Aguirregabiria

Victor Aguirregabiria

University of Toronto - Department of Economics

Arvind Magesan

University of Calgary

Date Written: October 2015

Abstract

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. Furthermore, imposing the restriction of unbiased beliefs generates a substantial attenuation bias in the estimate of competition effects.

Keywords: dynamic games, estimation, identification, market entry-exit, rational behavior, rationalizability

JEL Classification: C57, C73, L13

Suggested Citation

Aguirregabiria, Victor and Magesan, Arvind, Identification and Estimation of Dynamic Games When Players' Beliefs are Not in Equilibrium (October 2015). Available at SSRN: https://ssrn.com/abstract=2673624

Victor Aguirregabiria (Contact Author)

University of Toronto - Department of Economics ( email )

150 St. George Street
Toronto, Ontario M5S 3G7
Canada
4169784358 (Phone)

HOME PAGE: http://https://app.scholarsite.io/victor-aguirregabiria?reload=true

Arvind Magesan

University of Calgary ( email )

2500 University DR NW
Calgary, AB
Canada

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