Optimal Strategies of the Iterated Prisoner's Dilemma Problem for Multiple Conflicting Objectives

In this paper, we present a new paradigm of searching optimal strategies in the game of iterated prisoner's dilemma (IPD) using multiple-objective evolutionary algorithms. This method is more useful than the existing approaches, because it not only produces strategies that perform better in the iterated game but also finds a family of nondominated strategies, which can be analyzed to decipher properties a strategy should have to win the game in a more satisfactory manner. We present the results obtained by this new method and discuss sub-strategies found to be common among nondominated strategies. The multiobjective treatment of the IPD problem demonstrated here can be applied to other similar game-playing tasks.

[1]  J. A. Poutré,et al.  The influence of evolutionary selection schemes on the iterated prisoner's dilemma , 2001 .

[2]  P. Jain,et al.  Multiobjective placement of electronic components using evolutionary algorithms , 2004, IEEE Transactions on Components and Packaging Technologies.

[3]  Ivo F. Sbalzariniy,et al.  Multiobjective optimization using evolutionary algorithms , 2000 .

[4]  David E. Goldberg,et al.  Genetic Algorithms with Sharing for Multimodalfunction Optimization , 1987, ICGA.

[5]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[6]  Kalyanmoy Deb,et al.  Introducing Robustness in Multi-Objective Optimization , 2006, Evolutionary Computation.

[7]  M. Nowak,et al.  A strategy of win-stay, lose-shift that outperforms tit-for-tat in the Prisoner's Dilemma game , 1993, Nature.

[8]  Jürgen Branke,et al.  Creating Robust Solutions by Means of Evolutionary Algorithms , 1998, PPSN.

[9]  Drew Fudenberg,et al.  The Folk Theorem in Repeated Games with Discounting or with Incomplete Information , 1986 .

[10]  Marcus R. Frean,et al.  A voter model of the spatial prisoner's dilemma , 2001, IEEE Trans. Evol. Comput..

[11]  Philippe Mathieu,et al.  Our Meeting with Gradual, A Good Strategy for the Iterated Prisoner's Dilemma , 1996 .

[12]  Grant Dick,et al.  On Evolving Fixed Pattern Strategies for Iterated Prisoner's Dilemma , 2004, ACSC.

[13]  Ariel Rubinstein,et al.  A Course in Game Theory , 1995 .

[14]  H. Jane Brockmann,et al.  The selfish gene (2nd edn) , 1990 .

[15]  Hisao Ishibuchi,et al.  Evolution of iterated prisoner's dilemma game strategies in structured demes under random pairing in game playing , 2005, IEEE Transactions on Evolutionary Computation.

[16]  David B. Fogel,et al.  Evolving Behaviors in the Iterated Prisoner's Dilemma , 1993, Evolutionary Computation.

[17]  Kalyanmoy Deb,et al.  Multiobjective Problem Solving from Nature: From Concepts to Applications (Natural Computing Series) , 2008 .

[18]  Kalyanmoy Deb,et al.  Multi-objective optimization using evolutionary algorithms , 2001, Wiley-Interscience series in systems and optimization.

[19]  Kalyanmoy Deb,et al.  An Investigation of Niche and Species Formation in Genetic Function Optimization , 1989, ICGA.

[20]  Kalyanmoy Deb,et al.  Multiobjective Problem Solving from Nature: From Concepts to Applications , 2008, Natural Computing Series.

[21]  Xin Yao,et al.  Behavioral diversity, choices and noise in the iterated prisoner's dilemma , 2005, IEEE Transactions on Evolutionary Computation.

[22]  Xin Yao,et al.  Co-Evolution in Iterated Prisoner's Dilemma with Intermediate Levels of Cooperation: Application to Missile Defense , 2002, Int. J. Comput. Intell. Appl..

[23]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[24]  Aravind Srinivasan,et al.  Innovization: innovating design principles through optimization , 2006, GECCO.

[25]  Robert Axelrod,et al.  The Evolution of Strategies in the Iterated Prisoner's Dilemma , 2001 .

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

[27]  J. Nash.  Equilibrium Points in N-Person Games. , 1950, Proceedings of the National Academy of Sciences of the United States of America.

[28]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems , 2002, Genetic Algorithms and Evolutionary Computation.