A fingerprint comparison of different Prisoner's Dilemma payoff matrices

The Iterated Prisoner's Dilemma is a simultaneous two-player game. The actual values of payoffs take on different values in different research projects. In this study we perform an affine normalization of the payoff matrix and compare the agents that evolve when each of five different payoff matrices is used. Four of the matrices are chosen to lie near extremes of the normalized space, while the other lies in its center. The probability of cooperative behavior evolving is strongly influenced by the choice of payoff matrix. Fingerprinting of the evolved agents demonstrates a significant shift in the distribution of strategies that arise. A significant difference in pairwise competitive ability is also found between agents evolved with different payoff matrices. Placed into tournaments with agents evolved using all five payoff matrices, the players evolved with the central payoff matrix were found to have significantly better average tournament ranking. We conclude that the choice of payoff values is not a neutral choice and must be controlled for in any design of experiments.

[1]  Michael Kirley,et al.  The effects of time-varying rewards on the evolution of cooperation , 2009, Evol. Intell..

[2]  Daniel A. Ashlock,et al.  The effect of tag recognition on non-local adaptation , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[3]  Julian Francis Miller,et al.  Redundancy and computational efficiency in Cartesian genetic programming , 2006, IEEE Transactions on Evolutionary Computation.

[4]  Daniel A. Ashlock,et al.  Techniques for analysis of evolved prisoner's dilemma strategies with fingerprints , 2005, 2005 IEEE Congress on Evolutionary Computation.

[5]  W. Ashlock.  Evolving diverse populations of Prisoner’s Dilemma strategies , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[6]  D. Ashlock,et al.  Analysis of game playing agents with fingerprints , 2005 .

[7]  Sung-Bae Cho,et al.  The Impact of Payoff Function and Local Interaction on the N-Player Iterated Prisoner's Dilemma , 2000, Knowledge and Information Systems.

[8]  M. Nowak,et al.  Evolutionary game theory , 1995, Current Biology.

[9]  D. Roy.  Learning and the theory of games. , 2000, Journal of theoretical biology.

[10]  W. Hamilton,et al.  The Evolution of Cooperation , 1984 .

[11]  K. Lindgren,et al.  Evolutionary dynamics of spatial games , 1994 .

[12]  Daniel A. Ashlock,et al.  An Updated Taxonomy of Evolutionary Computation Problems using Graph-based Evolutionary Algorithms , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[13]  Daniel A. Ashlock,et al.  Fingerprints: enabling visualization and automatic analysis of strategies for two player games , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[14]  M. Hemesath.  Cooperate or Defect? Russian and American Students in a Prisoner's Dilemma , 1994 .

[15]  Daniel A. Ashlock,et al.  Fingerprint Analysis of the Noisy Prisoner's Dilemma Using a Finite-State Representation , 2007, IEEE Transactions on Computational Intelligence and AI in Games.

[16]  Daniel A. Ashlock,et al.  Fingerprinting: Visualization and Automatic Analysis of Prisoner's Dilemma Strategies , 2008, IEEE Transactions on Evolutionary Computation.

[17]  L. Tesfatsion,et al.  Preferential partner selection in an evolutionary study of Prisoner's Dilemma. , 1994, Bio Systems.

[18]  Eun-Youn Kim,et al.  Understanding representational sensitivity in the iterated prisoner's dilemma with fingerprints , 2006, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[19]  Xin Yao,et al.  Self-Adapting Payoff Matrices in Repeated Interactions , 2006, 2006 IEEE Symposium on Computational Intelligence and Games.

[20]  C. Terry,et al.  Competitiveness and Conflict Behavior in Simulation of a Social Dilemma , 2000, Psychological reports.

[21]  Daniel A. Ashlock,et al.  Changes in Prisoner’s Dilemma Strategies Over Evolutionary Time With Different Population Sizes , 2006, 2006 IEEE International Conference on Evolutionary Computation.