An iterative algorithm is proposed and tested in Cournot Game models, which is based on the convergence of sequential best responses and the utilization of a genetic algorithm for determining each player-s best response to a given strategy profile of its opponents. An extra outer loop is used, to address the problem of finite accuracy, which is inherent in genetic algorithms, since the set of feasible values in such an algorithm is finite. The algorithm is tested in five Cournot models, three of which have convergent best replies sequence, one with divergent sequential best replies and one with “local NE traps"[14], where classical local search algorithms fail to identify the Nash Equilibrium. After a series of simulations, we conclude that the algorithm proposed converges to the Nash Equilibrium, with any level of accuracy needed, in all but the case where the sequential best replies process diverges.<\/p>\r\n","references":"[1] F. Alkemade, H. La Poutre and H. Amman, \"On Social Learning\r\nand Robust Evolutionary Algorithm Design in the Cournot Oligopoly\r\nGame\", Computational Intelligence, vol. 23, 2007, pp. 162-175.\r\n[2] J. Arifovic,\"Genetic Algorithm Learning and the Cobweb Model\",\r\nJournal of Economic Dynamics and Control, vol. 18, 1994, pp. 3-28.\r\n[3] R. Amir, \"Cournot oligopoly and the theory of supermodular games\",\r\nGames and Economic Behavior, vol. 15, 1996, pp. 132-148.\r\n[4] J.I. Bulow, J.D. Geanakoplos and P.D. Klemperer, \"Multimarket\r\noligopoly: strategic substitutes and complements\", Journal of Political\r\nEconomy, vol. 93, 1985, pp. 488-511.\r\n[5] A.A. Cournot, Recherches sur les principes mathematiques de la theorie\r\ndes richesses (Researches into the Mathematical Principles of the\r\nTheory of Wealth), English translation by N.T. Bacon, 1897.\r\n[6] P. Dubey,O. Haimanko and A. Zapechelnyuk, \"Strategic Complements\r\nand Substitutes and Potential Games\", Games and Economic Behavior,\r\nvol. 54, 2006, pp. 77-94.\r\n[7] D. Fundenberg and J. Tirole, Game Theory, The MIT Press, Cambridge\r\nMA, 1991.\r\n[8] D.E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine\r\nLearning, Addison-Wesley, Reading, MA, 1998.\r\n[9] B.F. Hobbs, C.F. Metzler and J.S. Pang, \"Strategic gaming analysis for\r\nelectric power systems: An MPEC approach\", IEEE Transactions on\r\nPower Systems, vol. 15, 2000, pp. 638-645.\r\n[10] N.S. Kukushkin, \"A fixed-point theorem for decreasing mappings\",\r\nEconomic Letters, vol. 46, 1994, pp. 23-26.\r\n[11] C.E. Lemke and J.T. Howson, \"Equilibrium points of bimatrix games\",\r\nJournal of the Society for Industrial and Applied Mathematics, vol. 12,\r\n1964, pp. 413-423.\r\n[12] P. Milgrom and J. Roberts, \"Rationalizability, learning, and equilibrium\r\nin games with strategic complementarities\", Econometrica, vol. 58,\r\n1990, pp. 1255-1277.\r\n[13] M. Protopapas and E. Kosmatopoulos, \"Two Genetic Algorithms yielding\r\nNash Equilibrium in Cournot Games\", Technical University of Crete\r\nWorking Paper 29-01-2008.\r\n[14] Y.S. Son and R. Baldick, \"Hybrid Coevolutionary Programming for\r\nNash Equilibrium Search in Games with Local Optima\", IEEE Transactions\r\non Evolutionary Computation, 2004, vol. 8, pp. 305-315.\r\n[15] M. Voorneveld, \"Best-response potential games, Economic Letters,\r\n2000, vol. 66, pp. 289-295.\r\n[16] N. Vriend, \"An Illustration of the Essential Difference between Individual\r\nand Social Learning, and its Consequences for Computational\r\nAnalyses\", Journal of Economic Dynamics and Control, 2000, vol. 24,\r\npp. 1-19.\r\n[17] J.D. Weber and T.J. Overbye, \"A two-level optimization problem\r\nfor analysis of market bidding strategies\",. In Proceedings of Power\r\nEngineering Society Summer Meeting, 1999, vol. 2, pp. 846-851.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 33, 2009"}