Identification of a Simple Dynamic Discrete Game under Rationalizability (original) (raw)

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.

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.

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

2015

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.

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

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.

Some rationalizability results for dynamic games

International Journal of Economic Theory, 2012

We study the relation between dynamical systems describing the equilibrium behavior in dynamic games and those resulting from (single-player) dynamic optimization problems. More specifically, we derive conditions under which the dynamics generated by a model in one of these two classes can be rationalized by a model from the other class. We study this question under different assumptions about which fundamentals (e.g. technology, utility functions and time-preference) should be preserved by the rationalization. One interesting result is that rationalizing the equilibrium dynamics of a symmetric dynamic game by a dynamic optimization problem that preserves the technology and the utility function requires a higher degree of impatience compared to that of the players in the game.

Rationalization and Identification of Binary Games with Correlated Types

SSRN Electronic Journal, 2016

This paper studies the rationalization and identification of binary games where players have correlated private types. Allowing for correlation is crucial in global games and in models with social interactions as it represents correlated information and homophily, respectively. Our approach is fully nonparametric in the joint distribution of types and the strategic effects in the payoffs. First, under monotone pure Bayesian Nash Equilibrium strategy, we characterize all the restrictions if any on the distribution of players' choices imposed by the game-theoretic model as well as restrictions associated with two assumptions frequently made in the empirical analysis of discrete games. Namely, we consider exogeneity of payoff shifters relative to private information, and mutual independence of private information given payoff shifters. Second, we study the nonparametric identification of the payoff functions and types distribution. We show that the model with exogenous payoff shifters is fully identified up to a single location-scale normalization under some exclusion restrictions and rank conditions. Third, we discuss partial identification under weaker conditions and multiple equilibria. Lastly, we briefly point out the implications of our results for model testing and estimation.

Identification and Counterfactuals in Dynamic Models of Market Entry and Exit

2012

Abstract: This paper deals with a fundamental identification problem in the structural estimation of dynamic oligopoly models of market entry and exit. Using the standard datasets in existing empirical applications, there are three key components of a firm's profit function that are not separately identified: the fixed cost of an incumbent firm, the entry cost of a new entrant, and the scrap-value of an exiting firm.