Potential games with continuous player sets

We study potential games with continuous player jets, a class of games char acterized by an externality symmetry condition. Examples of these games inc lude random matching games with common payoffs and congestion games. We off er a simple description of equilibria which are locally stable under a broa d class of evolutionary dynamics, and prove that behavior converges to Nash equilibrium from all initial conditions. We consider a subclass of potenti al games in which evolution leads to efficient play, Finally, we show that the games studied here are the limits of convergent sequences of the finite player potential games studied by Monderer and Shapiey [22]. (C) 2001 Acad emic Press.