Selecting strategies using empirical game models: an experimental analysis of meta-strategies

In many complex multi-agent domains it is impractical to compute exact analytic solutions. An alternate means of analysis applies computational tools to derive and analyze empirical game models. These models are noisy approximations, which raises questions about how to account for uncertainty when analyzing the model. We develop a novel experimental framework and apply it to benchmark meta-strategies -- general algorithms for selecting strategies based on empirical game models. We demonstrate that modeling noise is important; a naive approach that disregards noise and plays according to Nash equilibrium yields poor choices. We introduce three parameterized algorithms that factor noise into the analysis by predicting distributions of opponent play. As observation noise increases, rational players generally make less specific outcome predictions. Our comparison of the algorithms identifies logit equilibrium as the best method for making these predictions. Logit equilibrium incorporates a form of noisy decision-making by players. Our evidence shows that this is a robust method for approximating the effects of uncertainty in many contexts. This result has practical relevance for guiding analysis of empirical game models. It also offers an intriguing rationale for behavioral findings that logit equilibrium is a better predictor of human behavior than Nash equilibrium.