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Symmetric Nash Equilibria

In this report we study the computational problem of determining existence of pure, symmetric Nash equilibria in concurrent games as well as in symmetric concurrent game structures. Games have traditionally been used mostly in economics, but have recently received an increasing amount of attention in computer science with applications in several areas including logic, verification and multi-agent systems. Our motivation for studying symmetric Nash equilibria is to let the players in a game represent programmable devices and let strategies represent programs. Nash equilibria then correspond to a system where all devices are programmed optimally in some sense, whereas symmetric Nash equilibria correspond to systems where all devices are programmed in the same way while still preserving the optimality. The idea of modelling the interaction in distributed systems by means of games is in many cases more realistic than traditional analysis where opponents are assumed to act in the worst possible way instead of acting rationally and in their own interest. Symmetry in games has been studied to some extent in classical normal-form games and our goal is to extend the notions of symmetry to concurrent games and investigate the computational complexity of finding symmetric Nash equilibria in these games. A number of different settings and types of symmetry are introduced and analyzed. Since infinite concurrent games have not been studied thoroughly for a lot of years yet there are still many unexplored branches in the area. Some of the settings studied in the report are completely new, whereas others have a lot of resemblance with problems that have already been analyzed quite extensively. In this case we can reuse some of the same proof techniques and obtain similar results. Initially, we will study the problem of finding pure Nash equilibria in concurrent games where every player uses the same strategy. This