Approximate Strategic Reasoning through Hierarchical Reduction of Large Symmetric Games

To deal with exponential growth in the size of a game with the number of agents, we propose an approximation based on a hierarchy of reduced games. The reduced game achieves savings by restricting the number of agents playing any strategy to fixed multiples. We validate the idea through experiments on randomly generated local-effect games. An extended application to strategic reasoning about a complex trading scenario motivates the approach, and demonstrates methods for game-theoretic reasoning over incompletely-specified games at multiple levels of granularity. Motivation Consider the task of selecting among a large set of strategies to play in an 8-player game. Through careful judgment you manage to narrow down the candidates to a reasonable number of strategies (say 35). Because the performance of a strategy for one agent depends on the strategies of the other seven, you wish to undertake a game-theoretic analysis of the situation. Determining the payoff for a particular strategy profile is expensive, however, as your observations of prior game instances are quite limited, and the only operational description of the game is in the form of a simulator that takes a non-negligible time (say 10 minutes) to produce one outcome. Moreover, since the environment is stochastic, numerous samples (say 12) are required to produce a reliable estimate for even one profile. At two hours per profile, ex