Approximate Analysis of Large Simulation-Based Games.

Abstract

Game theory offers powerful tools for reasoning about agent behavior and incentives in multi-agent systems. Traditional approaches to game-theoretic analysis require enumeration of all possible strategies and outcomes. This often constrains game models to small numbers of agents and strategies or simple closed-form payoff descriptions. Simulation-based game theory extends the reach of game-theoretic analysis through the use of agent-based modeling. In the simulation-based approach, the analyst describes an environment procedurally and then computes payoffs by simulation of agent interactions in that environment.

I use simulation-based game theory to study a model of credit network formation. Credit networks represent trust relationships in a directed graph and have been proposed as a mechanism for distributed transactions without a central currency. I explore what information is important when agents make initial decisions of whom to trust, and what sorts of networks can result from their decisions. This setting demonstrates both the value of simulation-based game theory—extending game-theoretic analysis beyond analytically tractable models—and its limitations—simulations produce prodigious amounts of data, and the number of simulations grows exponentially in the number of agents and strategies.

I propose several techniques for approximate analysis of simulation-based games with large numbers of agents and large amounts of simulation data. First, I show how bootstrap-based statistics can be used to estimate confidence bounds on the results of simulation-based game analysis. I show that bootstrap confidence intervals for regret of approximate equilibria are well-calibrated. Next, I describe deviation-preserving reduction, which approximates an environment with a large number of agents using a game model with a small number of players, and demonstrate that it outperforms previous player reductions on several measures. Finally, I employ machine learning to construct game models from sparse data sets, and provide evidence that learned game models can produce even better approximate equilibria in large games than deviation-preserving reduction.