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Entropy-Norm space for geometric selection of strict Nash equilibria in n-person games

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  • A. B. Leoneti
  • G. A. Prataviera

Abstract

Motivated by empirical evidence that individuals within group decision making simultaneously aspire to maximize utility and avoid inequality we propose a criterion based on the entropy-norm pair for geometric selection of strict Nash equilibria in n-person games. For this, we introduce a mapping of an n-person set of Nash equilibrium utilities in an Entropy-Norm space. We suggest that the most suitable group choice is the equilibrium closest to the largest entropy-norm pair of a rescaled Entropy-Norm space. Successive application of this criterion permits an ordering of the possible Nash equilibria in an n-person game accounting simultaneously equality and utility of players payoffs. Limitations of this approach for certain exceptional cases are discussed. In addition, the criterion proposed is applied and compared with the results of a group decision making experiment.

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  • A. B. Leoneti & G. A. Prataviera, 2020. "Entropy-Norm space for geometric selection of strict Nash equilibria in n-person games," Papers 2003.09225, arXiv.org.
    • Handle: RePEc:arx:papers:2003.09225
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    1. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, April.
    2. Wu, Te & Fu, Feng & Dou, Puxuan & Wang, Long, 2014. "Social influence promotes cooperation in the public goods game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 413(C), pages 86-93.
    3. George J. Mailath, 1998. "Corrigenda [Do People Play Nash Equilibrium? Lessons from Evolutionary Game Theory]," Journal of Economic Literature, American Economic Association, vol. 36(4), pages 1941-1941, December.
    4. Matsui Akihiko & Matsuyama Kiminori, 1995. "An Approach to Equilibrium Selection," Journal of Economic Theory, Elsevier, vol. 65(2), pages 415-434, April.
    5. Robert Aumann & Adam Brandenburger, 2014. "Epistemic Conditions for Nash Equilibrium," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 5, pages 113-136, World Scientific Publishing Co. Pte. Ltd..
    6. Binmore, Ken & Shaked, Avner, 2010. "Experimental Economics: Where Next? Rejoinder," Journal of Economic Behavior & Organization, Elsevier, vol. 73(1), pages 120-121, January.
    7. George J. Mailath, 1998. "Do People Play Nash Equilibrium? Lessons from Evolutionary Game Theory," Journal of Economic Literature, American Economic Association, vol. 36(3), pages 1347-1374, September.
    8. E. M. S. Ribeiro & G. A. Prataviera, 2014. "Information theoretic approach for accounting classification," Papers 1401.2954, arXiv.org, revised Sep 2014.
    9. Leoneti, Alexandre Bevilacqua, 2016. "Utility Function for modeling Group Multicriteria Decision Making problems as games," Operations Research Perspectives, Elsevier, vol. 3(C), pages 21-26.
    10. Li, Ming & Jia, Chun-Xiao & Liu, Run-Ran & Wang, Bing-Hong, 2013. "Emergence of cooperation in spatial public goods game with conditional participation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(8), pages 1840-1847.
    11. Li, Zhaofeng & Shen, Bi & Jiang, Yichuan, 2017. "The maintenance of cooperation in multiplex networks with limited and partible resources of agents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 499-507.
    12. Dionisio, Andreia & Reis, A. Heitor & Coelho, Luis, 2008. "Utility function estimation: The entropy approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3862-3867.
    13. Binmore, Ken & Shaked, Avner, 2010. "Experimental economics: Where next?," Journal of Economic Behavior & Organization, Elsevier, vol. 73(1), pages 87-100, January.
    14. Wang, Yongjie & Chen, Tong & Chen, Qiao & Si, Guangrun, 2017. "Emotional decisions in structured populations for the evolution of public cooperation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 475-481.
    15. Presbitero, Alva & Monterola, Christopher, 2018. "Challenging the evolution of social cooperation in a community governed by central control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 511(C), pages 378-388.
    16. Ribeiro, E.M.S. & Prataviera, G.A., 2014. "Information theoretic approach for accounting classification," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 651-660.
    17. Binmore, Ken, 2007. "Playing for Real: A Text on Game Theory," OUP Catalogue, Oxford University Press, number 9780195300574.
    18. Bault, Nadège & Fahrenfort, Johannes J. & Pelloux, Benjamin & Ridderinkhof, K. Richard & van Winden, Frans, 2017. "An affective social tie mechanism: Theory, evidence, and implications," Journal of Economic Psychology, Elsevier, vol. 61(C), pages 152-175.
    19. Golan, Amos & Judge, George G. & Miller, Douglas, 1996. "Maximum Entropy Econometrics," Staff General Research Papers Archive 1488, Iowa State University, Department of Economics.
    20. Ali E. Abbas, 2006. "Maximum Entropy Utility," Operations Research, INFORMS, vol. 54(2), pages 277-290, April.
    21. Wang, Le & Chen, Tong & You, Xinshang & Wang, Yongjie, 2018. "The effect of wealth-based anti-expectation behaviors on public cooperation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 493(C), pages 84-93.
    22. Guth, Werner & Schmittberger, Rolf & Schwarze, Bernd, 1982. "An experimental analysis of ultimatum bargaining," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 367-388, December.
    23. Bergh, Andreas, 2008. "A critical note on the theory of inequity aversion," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 37(5), pages 1789-1796, October.
    24. Kim, Youngse, 1996. "Equilibrium Selection inn-Person Coordination Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 203-227, August.
    25. Ernst Fehr & Helen Bernhard & Bettina Rockenbach, 2008. "Egalitarianism in young children," Nature, Nature, vol. 454(7208), pages 1079-1083, August.
    26. Colin Camerer, 2003. "Behavioural studies of strategic thinking," Levine's Bibliography 506439000000000490, UCLA Department of Economics.
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