Abstract
The problem of equilibria detection in many-player games is computationally untractable by standard techniques. Generative relations represent an useful tool for equilibria characterization and evolutionary equilibria detection. The generative relation for k-Berge-Zhukovskii equilibrium is introduced. An evolutionary technique based on differential evolution capable to cope with hundred players is proposed. Experimental results performed on a multi-player version of Prisoner’s Dilemma indicate the effectiveness of the approach.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Aumann, R.: Acceptable Points in General Cooperative n Person Games. In: Contributions to the Theory of Games. Annals of Mathematics Studies 40, vol. IV, pp. 287–324 (1959)
Aumann, R., Hart, S. (eds.): Handbook of Game Theory. Handbooks in Economics (11), vol. 1. North-Holland, Amsterdam (1992)
Deb, K., Agrawal, S., Pratab, A., Meyarivan, T.: A Fast Elitist Non-Dominated Sorting Genetic Algorithm for Multi-Objective Optimization: NSGA-II. In: Schoenauer, M., Deb, K., Rudolph, G., Yao, X., Lutton, E., Merelo, J.J., Schwefel, H.-P. (eds.) Proceedings of the Parallel Problem Solving from Nature VI Conference, Paris, France (2000)
Deb, K., Beyer, H.: Self-adaptive genetic algorithms with simulated binary crossover. Complex Systems 9, 431–454 (1995)
Lung, R.I., Dumitrescu, D.: Computing Nash Equilibria by Means of Evolutionary Computation. Int. J. of Computers, Communications & Control, 364–368 (2008)
Nash, J.F.: Non-cooperative games. Annals of Mathematics 54, 286–295 (1951)
Nessah, R., Larbani, M., Tazdait, T.: A note on Berge equilibrium. Applied Mathematics Letters 20, 926–932 (2007)
Osborne, M.: An Introduction to Game Theory. Oxford University Press, New York (2004)
Thomsen, R.: Multimodal optimization using crowding-based differential evolution. In: Proceedings of the 2004 IEEE Congress on Evolutionary Computation, June 20-23, pp. 1382–1389. IEEE Press, Portland (2004)
Zhukovskii, V.I.: Linear Quadratic Differential Games. Naukova Doumka, Kiev (1994)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Gaskó, N., Dumitrescu, D., Lung, R.I. (2011). Evolutionary Detection of Berge and Nash Equilibria. In: Pelta, D.A., Krasnogor, N., Dumitrescu, D., Chira, C., Lung, R. (eds) Nature Inspired Cooperative Strategies for Optimization (NICSO 2011). Studies in Computational Intelligence, vol 387. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24094-2_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-24094-2_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-24093-5
Online ISBN: 978-3-642-24094-2
eBook Packages: EngineeringEngineering (R0)