Strategy Analysis and Creation by Simulation in the General Game

Authors: Gábor Szűcs, Gábor Neszveda, Xin Fang

Abstract:

In this paper the General Game problem is described. In this problem the competition or cooperation dilemma occurs as the two basic types of strategies. The strategy possibilities have been analyzed for finding winning strategy in uncertain situations (no information about the number of players and their strategy types). The winning strategy is missing, but a good solution can be found by simulation by varying the ratio of the two types of strategies. This new method has been used in a real contest with human players, where the created strategies by simulation have reached very good ranks. This construction can be applied in other real social games as well.

Keywords: competition, cooperation, finding good strategy, General Game

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1332358

References:

[1] J. Merolla, M. Munger, and M. Tofias, "Lotto, Blotto, or Frontrunner: An Analysis of Spending Patterns by the National Party Committees in the 2000 Presidential Election" (http://www.socsci.duke.edu/ssri/ federalism/papers/tofiasmunger.pdf)
[2] J. Partington: "Colonel Blotto-s Game" (http://www.geocities.com/ j_r_partington/blotto.html), 2009.
[3] L. Mérő: Presentation slides about "Game Theory" (2009.07.23) on Corvinus Egyetem Budapest, (in Hungarian) (http://mkt.unicorvinus. hu/download.php?view.120)
[4] R. Axelrod, "Effective choice in the prisoner-s dilemma" J. Conflict Resolution, 24, 1980, pp. 3-25.
[5] R. Axelrod, "The Evolution of Cooperation" (Revised edition) Perseus Books Group, 2006.
[6] J. Szép. and F. Forg├│, Introduction to the Theory of Games, Akadémiai Kiad├│, Budapest, 1985.
[7] Gy. Szabó, G. Fáth, "Evolutionary games on graphs", Physics Reports 446, 2007, pp. 97-216.
[8] N. J. van Eck, M. van Wezel, "Application of reinforcement learning to the game of Othello", Computers & Operations Research, Volume 35, Issue 6, June 2008, Pages 1999-2017.
[9] I. Erev, E. Haruvy, "Generality, repetition, and the role of descriptive learning models", Journal of Mathematical Psychology, Volume 49, Issue 5, October 2005, Pages 357-371.
[10] G. Cai, P. R. Wurman, "Monte Carlo approximation in incomplete information, sequential auction games", Decision Support Systems, Volume 39, Issue 2, April 2005, Pages 153-168
[11] O. Toivanen, M. Waterson, "Empirical research on discrete choice game theory models of entry: An illustration", European Economic Review, Volume 44, Issues 4-6, May 2000, Pages 985-992.
[12] S. Azhar, A. McLennan, J.H. Reif, "Computation of equilibriain noncooperative games", Computers & Mathematics with Applications, Volume 50, Issues 5-6, September 2005, Pages 823-854.
[13] G. Szűcs, "Solutions of Cooperative and Non-cooperative problems by Intelligent Agents in Simulation", International Mediterranean Modelling Multiconference, MAS2004, October 28-30, 2004, Bergeggi, Italy. pp. 365-369.
[14] J. Baron, "Thinking and Deciding", (Third Edition), Cambridge University Press, 2000.