Identification, Estimation and Testing in Empirical Games

Open Access
Liu, Nianqing
Graduate Program:
Doctor of Philosophy
Document Type:
Date of Defense:
April 18, 2013
Committee Members:
  • Quang Vuong, Dissertation Advisor
  • Sung Jae Jun, Committee Chair
  • Paul L E Grieco, Committee Member
  • Runze Li, Committee Member
  • Isabelle Perrigne, Special Member
  • Robert Clifford Marshall, Committee Member
  • Discrete Games
  • First-price Auctions
  • Incomplete Information
  • Bayesian Nash Equilibrium
  • Monotone Strategy
This dissertation consists of three chapters. Chapter 1 studies the rationalization and identification of discrete games where players have correlated private types. Our approach is fully nonparametric. First, under monotone pure strategy Bayesian Nash Equilibrium, 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 three assumptions that have been frequently used in the empirical analysis of discrete games. Namely, we consider additive separability of the private information in the payoffs, exogeneity of the payoff shifters relative to the private information, and mutual independence of the private information conditional on the payoff shifters. Second, we study the nonparametric identification of the payoff functions and types distribution under exclusion restrictions and rank conditions. In particular, we show that our structural model is identified up to a location-scale normalization in the separable case. Third, without imposing exclusion restrictions, we characterize the sharp identification region for the payoff functions and types' distribution. Lastly, we discuss possible estimation and testing procedures. Chapter 2 studies the semiparametric identification and estimation of binary games with arbitrary finite number of players under incomplete information. Our approach allows private types to be correlated across players. By focusing on the monotone pure strategy Bayesian Nash Equilibrium (BNE), we show that, in our semiparametric model with linear payoffs, the equilibrium strategies can be represented as a single-agent binary response model. Under weak restrictions, we identify the joint distribution of private types nonparametrically, and the payoff functions in a linear-index setup. Following Klein and Spady (1993), we propose a three-stage procedure for estimating the payoff coefficients and show that our estimator is root-N-consistent, asymptotically normally distributed. A Monte Carlo experiment shows that our estimator has good properties in moderately sized samples. Chapter 3 develops nonparametric tests of monotonicity of bidding strategy in first price auctions. The monotonicity testing problem is shown to be equivalent to a convexity testing problem, and a root-N consistent test statistic, which measures a distance of integral of inverse bidding strategy from convexity, is proposed. We obtain two types of critical values: one of them is given by the asymptotic distribution, and the other one is given through bootstrap approach. We also show that our testing procedure has the correct size and is consistent.