On the econometric estimation of simultaneous games

This dissertation addresses the problem of estimating the payoff-parameter vector of game-theoretic models. We focus on methodologies that rely solely on the assumption that observed actions are the result of a Nash equilibrium, avoiding the introduction of explicit or implicit equilibrium selection rules. Chapter 2 focuses on a 2 x 2 simultaneous game which has been the focus of previous econometric work. Assuming players have complete information, it is shown that if the only assumption is that players play a Nash equilibrium; a well-defined likelihood function for each of the four outcomes exists if and only if mixed-strategies are allowed. However, it is also shown that if players have complete information it is impossible to obtain a likelihood function that relies only on Nash equilibrium for an entire family of versions of the game which we call "symmetric".;Chapter 3 re-examines the properties of this 2 x 2 game assuming that players play with incomplete information about the realization of some of the payoff relevant variables of their opponent. We allow players to condition their beliefs on a vector of publicly observed signals Z, which may include continuous and/or discrete random variables. These signals are observed by the researcher, but their exact distribution is known only to the players. The resulting Bayesian-Nash equilibrium (BNE) involves a vector of conditional moment restrictions. First, we compare the stochastic properties of the game with complete and incomplete information. We show that if the support of the privately observed variables is rich enough, conditions for existence of a well-defined likelihood function derived solely from Nash equilibrium assumptions are generically weaker if players have incomplete information. Specifically, a well-defined likelihood function which does not rely on equilibrium selection rules exists for symmetric versions of the game only if players have incomplete information.;The remainder of Chapter 3 focuses on the incomplete information case and presents a two-step iterative estimation procedure. The first step estimates players' unobserved BNE beliefs using semiparametric restrictions analog to the population BNE conditions. The second step maximizes a trimmed log-likelihood function that uses the first step estimates as substitutes for the unknown BNE beliefs. Each realization of Z inside the trimming set has a unique BNE. The resulting estimator is N -consistent. Its efficiency depends on the predictive power of the signals Z for the privately observed variables. We discuss extensions to more complicated incomplete-information games. Chapter 4 presents an empirical application of the methodology examined in Chapter 3. We estimate a simple game of investment under uncertainty in industries with only two publicly traded firms. Results are consistent with a model in which the smaller firm has a comparatively greater incentive to predict the actions of the larger one, which bases its actions mainly on its private information and measures of industry uncertainty. Detailed proofs of all results and claims are included in a Mathematical Appendix.