Probabilistic Analysis of Simulation-Based Games YEVGENIY VOROBEYCHIK Computer and Information Science University of Pennsylvania
[email protected] The field of Game Theory has proved to be of great importance in modeling interactions between self-interested parties in a variety of settings. Traditionally, game theoretic analysis relied on highly stylized models to provide interesting insights about problems at hand. The shortcom- ing of such models is that they often do not capture vital detail. On the other hand, many real strategic settings, such as sponsored search auctions and supply-chains, can be modeled in high resolution using simulations. Recently, a number of approaches have been introduced to perform analysis of game-theoretic scenarios via simulation-based models. The first contribution of this work is the asymptotic analysis of Nash equilibria obtained from simulation-based mod- els. The second contribution is to derive expressions for probabilistic bounds on the quality of Nash equilibrium solutions obtained using simulation data. In this vein, we derive very general distribution-free bounds, as well as bounds which rely on the standard normality assumptions, and extend the bounds to infinite games via Lipschitz continuity. Finally, we introduce a new maximum-a-posteriori estimator of Nash equilibria based on game-theoretic simulation data and show that it is consistent and almost surely unique. Categories and Subject Descriptors: I.6.6 [Simulation and Modeling]: Simulation Output Analysis; J.4 [Social and Behavioral Sciences]: Economics General Terms: Game theory, Simulation and Modeling Additional Key Words and Phrases: Game theory, simulation, Nash equilibrium 1. INTRODUCTION In analyzing economic systems, especially those composed primarily of autonomous computational agents, the complexities must typically be distilled into a stylized model, with the hope that the resulting model captures the key components of the system and is nevertheless amenable to analytics.