IDENTIFICATION OF INCOMPLETE INFORMATION GAMES WITH MULTIPLE EQUILIBRIA AND UNOBSERVED HETEROGENEITY
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This dissertation mainly studies identification of finite action games with incomplete information. The essential contribution of this dissertation is to allow for the presence of multiple equilibria and/or unobserved market-level heterogeneity. Chapter 2 provides a novel methodology to nonparametrically identify static games with multiple equilibria. Exploiting the results in mis-classification error models, I show that the number of equilibria, the equilibrium selection mechanism and individual equilibrium strategies associated with all positively employed equilibria can be nonparametrically identified from the distributions of the game outcomes. Provide the equilibrium conditional choice probabilities, payoffs then can be identified nonparametrically with exclusion restrictions. A natural estimator is also proposed following the constructive identification procedure. The empirical application investigates the strategic interaction among radio stations when they choose commercial timings, which provides evidence that two equilibria exist. Chapter 3 extends chapter 2 to incorporate unobserved market-level heterogeneity. This chapter assumes that the market-level latent type is discrete and has a finite support. With the discrete feature, the presence of unobserved heterogeneity generates similar finite mixture feature as the presence of multiple equilibria. The combination of both payoff-relevant and payoff un-relevant latent factor complicates the identification because of lacking information to disentangle the two. Consequently, instead of providing point identification, I provide set identification for the payoff parameters in chapter 3. To understand the trade-off between point identification and extra assumptions, I also provide conditions under which the identified set shrinks to a point. Chapter 4 considers identification in dynamic settings. If only Markov Perfect Equilibria being considered, observables including actions and payoff relevant covariates in period $t$ follow a first-order Markov process in time series by a market. This Markov property is a key condition under which dynamic games can be nonparametric identified with four periods of data. In particular, the law of motion associated with every possible combination of equilibria and the unobserved market-types can be nonparametrically identified. Additionally, payoffs can be identified nonparametrically with exclusion restrictions. More importantly, multiple equilibria and unobserved heterogeneity can be distinguished from the test with the null that payoffs associated with two levels of latent factor are the same. Specifically, if two payoffs are the same, then they should belong to the same latent market type but different equilibria. On the other hand, if two payoffs are different, they should be driven by the heterogeneity. Chapter 5 concludes and proposes possible avenues for future research based on this dissertation.