Computing the Nash equilibria of large non-cooperative games using single-processor computers is not feasible due to the exponential time required by the existing algorithms. In this thesis, we consider the use of parallel computing in solving large games. We design and implement three parallel algorithms for computing Nash equilibria in non-cooperative games.
First, we design and implement a parallel algorithm for computing all Nash Equilibria in bimatrix games. The algorithm computes all Nash equilibria by searching all possible supports of mixed strategies. Second, we design and implement a parallel vertex enumeration algorithm that computes all Nash equilibria of large bimatrix games in reasonable amount of time using parallel systems with few number of processors. By using a balancing mechanism we were able to efficiently achieve good speedup despite the sequential nature of the depth-first search type algorithm. Finally, we design and implement a parallel algorithm that computes all totally mixed Nash equilibria in an n -player game by enumerating all totally mixed strategy supports.
The performance of the parallel algorithms is analyzed for games with different number of pure strategies for each player and, in the case of n-player games, for different number of players. The analysis shows that the algorithms scale very well and could potentially be used for much larger games if run on large parallel systems.
