The paper considers the computation of Nash equilibria for noncooperative bi-matrix games. The standard method for finding a Nash equilibrium in such a game is the Lemke-Howson method. That method operates by solving a related linear complementarity problem (LCP). However, the method may fail to reach certain equilibria because it can only start from a limited number of strategy vectors. The method proposed here finds an equilibrium by solving a related stationary point problem (SPP). Contrary to the Lemke-Howson method it can start from any strategy vector. Besides, the path of vectors along which the equilibrium is reached has an appealing game-theoretic interpretation. An important feature of the algorithm is that it finds a perfect equilibrium when at the start all actions are played with positive probability. Furthermore all Nash equilibria can be found in principle by repeated application of the algorithm starting from different strategy vectors.
展开▼
