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Fuzzy Nash-Pareto Equilibrium: Concepts and Evolutionary Detection

  • Dumitru Dumitrescu
  • Rodica Ioana Lung
  • Tudor Dan Mihoc
  • Reka Nagy
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6024)

Abstract

Standard game theory relies on the assumption that players are rational agents that try to maximize their payoff. Experiments with human players indicate that Nash equilibrium is seldom played. The goal of proposed approach is to explore more nuance equilibria by allowing a player to be biased towards different equilibria in a fuzzy manner. Several classes of equilibria (Nash, Pareto, Nash-Pareto) are defined by using appropriate generative relations. An evolutionary technique for detecting fuzzy equilibria is considered. Experimental results on Cournot’ duopoly game illustrate evolutionary detection of proposed fuzzy equilibria.

Keywords

Nash Equilibrium Pareto Front Membership Degree Fuzzy Class Fuzzy Game 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Bade, S., Haeringer, G., Renou, L.: More strategies, more Nash equilibria, Working Paper 2004-15, School of Economics University of Adelaide University (2004)Google Scholar
  2. 2.
    Deb, K., Agrawal, S., Pratab, A., Meyarivan, T.: A Fast and Elitist Multi-Objective Genetic Algorithm: NSGA-II KanGAL Report No. 200001, Indian Institute of Tehnology Kanpur (2000)Google Scholar
  3. 3.
    Deb, K.: Multi-objective optimization using evolutionary algorithms. Wiley, Chichester (2001)zbMATHGoogle Scholar
  4. 4.
    Dumitrescu, D., Lung, R.I., Mihoc, T.D.: Evolutionary Equilibria Detection in Non-cooperative Games. In: Giacobini, M., Brabazon, A., Cagnoni, S., Di Caro, G.A., Ekárt, A., Esparcia-Alcázar, A.I., Farooq, M., Fink, A., Machado, P. (eds.) EvoStar 2009. LNCS, vol. 5484, pp. 253–262. Springer, Heidelberg (2009)Google Scholar
  5. 5.
    Lung, R.I., Dumitrescu, D.: Computing Nash Equilibria by Means of Evolutionary Computation. Int. J. of Computers, Communications & Control, 364–368 (2008)Google Scholar
  6. 6.
    Maskin, E.: The theory of implementation in Nash equilibrium: A survey. In: Hurwicz, L., Schmeidler, D., Sonnenschein, H. (eds.) Social Goals and Social Organization, pp. 173–204. Cambridge University Press, Cambridge (1985)Google Scholar
  7. 7.
    McKelvey, R.D., McLennan, A.: Computation of equilibria in finite games. In: Amman, H.M., Kendrick, D.A., Rust, J. (eds.) Handbook of Computational Economics. Elsevier, Amsterdam (1996)Google Scholar
  8. 8.
    Nash, J.F.: Non-cooperative games. Annals of Mathematics 54, 286–295 (1951)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Osborne, M.J.: An Introduction to Game Theory. Oxford University Press, New-York (2004)Google Scholar
  10. 10.
    Wu, S.H., Soo, V.W.: A Fuzzy Game Theoretic Approach to Multi-Agent Coordination. In: Ishida, T. (ed.) PRIMA 1998. LNCS (LNAI), vol. 1599, pp. 76–87. Springer, Heidelberg (1999)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Dumitru Dumitrescu
    • 1
  • Rodica Ioana Lung
    • 1
  • Tudor Dan Mihoc
    • 1
  • Reka Nagy
    • 1
  1. 1.Babeş Bolyai UniversityCluj NapocaRomania

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