Factoring Games to Isolate Strategic Interactions

Game theoretic reasoning about multi-agent systems has been made more tractable by algorithms that exploit various types of independence in agents’ utilities. However, previous work has assumed that a game’s precise independence structure is given in advance. This paper addresses the problem of finding independence structure in a general form game when it is not known ahead of time, or of finding an approximation when full independence does not exist. We give an expected polynomial time algorithm to divide a bounded-payout normal form game into factor games that isolate independent strategic interactions. We also show that the best approximate factoring can be found in polynomial time for a specific interaction that is not fully independent. Once known, factors aide computation of game theoretic solution concepts, including Nash equilibria (or ǫequilibria for approximate factors), in some cases guaranteeing polynomial complexity where previous bounds were exponential.