Bootstrap statistics for empirical games

Researchers often use normal-form games to model multi-agent interactions. When a game model is based on observational or simulated data about agent payoffs, we call it an empirical game. The payoff matrix of an empirical game can be analyzed like any normal-form game, for example, by identifying Nash equilibria or instances of other solution concepts. Given the game model's basis in sampled data, however, empirical game analysis must also consider sampling error and distributional properties of candidate solutions. Toward this end, we introduce bootstrap techniques that support statistical reasoning as part of the empirical game-theoretic analysis process. First, we show how the bootstrap can be applied to compute confidence bounds on the regret of reported approximate equilibria. Second, we experimentally demonstrate that applying bootstrapped regret confidence intervals can improve sampling decisions in simulation-based game modeling.