Computing Nash Equilibria of Action-Graph Games

Abstract complexity of Govindan and Wilson's algorithm is open because the worst - case number of gradient - following steps is not known; however, in practice the algorithm's runtime Action - graph games (AGGs) are a fully expres - sive game representation which can compactly express both strict and context - specific indepen - dence between players' utility functions Ac - tions are represented as nodes in a graph G , and the payoff to an agent who chose the action s depends only on the numbers of other agents who chose actions connected to s We present algorithms for computing both symmetric and arbitrary equilibria of AGGs using a continua - tion method We analyze the worst - case cost of computing the Jacobian of the payoff function, the exponential - time bottleneck step, and in all cases achieve exponential speedup When the in - degree of G is bounded by a constant and the game is symmetric, the Jacobian can be com - puted in polynomial time