Nash equilibria in random games
We consider Nash equilibria in 2-player random games and analyze a simple Vegas algorithm for finding an equilibrium. The algorithm is combinatorial and always finds a equilibrium; on m x n payoff matrices, it runs in time O(m(2)n log log n + n(2)m log log m) with probability. Our result follows from showing that a 2-player random game has a Nash with supports of size two with high probability, at least 1 - O(1/ log n). Our main tool is a formulation of equilibria. (C) 2007 Wiley Periodicals, Inc.
nash equilibria random games polynomial time algorithmic game theory