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Linguistic Fuzzy-Logic Social Game of Cooperation

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  • Badredine Arfi

    (University of Florida, USA; barfi@polisci.ufl.edu)

Abstract

I develop a new game-theoretic approach based, not on conventional Boolean two-valued logic, but instead on linguistic fuzzy logic which admits linguistic truth values. A linguistic fuzzy game is defined with linguistic fuzzy strategies, linguistic fuzzy preferences, and the rules of reasoning and inferences of the game operate according to linguistic fuzzy logic, not Boolean logic. This leads to the introduction of a new notion of fuzzy domination and Nash equilibrium which is based not on the usual ‘greater than’ relation ordering but rather on a more general form of relation termed linguistic fuzzy relation. Each agent models others as linguistic fuzzy rational agents and tries to find a linguistic fuzzy Nash equilibrium that will achieve the highest linguistic fuzzy payoff. If the linguistic fuzzy relation is simplified into a crisp two-valued logic, the linguistic fuzzy game reduces to the conventional game. In this article I apply the new approach to situations of non-cooperative twoplayer games such as a 2 × 2 prisoner's dilemma (PD) game and a social game of cooperation with N players. I find that there is always an optimum strong Nash equilibrium which is Pareto optimal, thereby lifting many of the dilemmas that emerge in crisp game theory in two-player and social games.

Suggested Citation

  • Badredine Arfi, 2006. "Linguistic Fuzzy-Logic Social Game of Cooperation," Rationality and Society, , vol. 18(4), pages 471-537, November.
    • Handle: RePEc:sae:ratsoc:v:18:y:2006:i:4:p:471-537
    DOI: 10.1177/1043463106068811
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    References listed on IDEAS

    as
    1. Arfi, Badredine, 2005. "Fuzzy Decision Making in Politics: A Linguistic Fuzzy-Set Approach (LFSA)," Political Analysis, Cambridge University Press, vol. 13(1), pages 23-56, January.
    2. Ragin, Charles C., 2000. "Fuzzy-Set Social Science," University of Chicago Press Economics Books, University of Chicago Press, edition 1, number 9780226702773, April.
    3. repec:ucp:bkecon:9780226702766 is not listed on IDEAS
    4. Ayman M. Wasfy & Yasser A. Hosni, 1998. "Two-Party Negotiation Modeling: An Integrated Fuzzy Logic Approach," Group Decision and Negotiation, Springer, vol. 7(6), pages 491-518, November.
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    1. Svajone Bekesiene & Serhii Mashchenko, 2023. "On Nash Equilibria in a Finite Game for Fuzzy Sets of Strategies," Mathematics, MDPI, vol. 11(22), pages 1-12, November.
    2. Badredine Arfi, 2009. "Probing the Democratic Peace Argument Using Linguistic Fuzzy Logic," International Interactions, Taylor & Francis Journals, vol. 35(1), pages 30-57, March.
    3. Samuel R. Lucas, 2009. "Stratification Theory, Socioeconomic Background, and Educational Attainment," Rationality and Society, , vol. 21(4), pages 459-511, November.
    4. Anjali Singh & Anjana Gupta, 2018. "Matrix Games with Interval-Valued 2-Tuple Linguistic Information," Games, MDPI, vol. 9(3), pages 1-19, September.

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