On characterization of credibilistic equilibria of fuzzypayoff twoplayer zerosum game
 Jinwu Gao,
 ZhiQiang Liu,
 Puchen Shen
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Harsanyi pointed out that “the player may lack full information about the other players’ (or even his own) payoffs, etc.” In this paper, we investigate the twoplayer zerosum game, in which the payoffs are interpreted as fuzzy variables due to incomplete information. Based on the credibility theory, we employ three decision criteria to define the behaviors of the players in different decision situations. Accordingly, three definitions of Nash equilibria, called credibilistic equilibria, are proposed. Besides the existence theorem of the three credibilistic equilibria, we also discuss their relationships to illustrate the significance of the proposed credibilistic equilibria.
 Aubin, JP (1981) Cooperative fuzzy games. Math Oper Res 6: pp. 113
 Borel E (1921) La theorie du jeu et les equations integrales a noyausymetrique[Translated as “The theory of play and integral equations with skew symmetric kernels”. Econometrica 21:97–100, 1953]. C R Hebd Seances Acad Sci 173:1304–1308
 Borel E (1924) In: Hermann J (ed) Elements de la theorie des probabilities, 3rd edn [Translated as On games that involve chance and the skill of the players. Econometrica 21:101–115, 1953]. Librairie Scientifique, Paris, pp 204–221
 Butnariu, D (1978) Fuzzy games: a description of the concept. Fuzzy Sets Syst 1: pp. 181192 CrossRef
 Campos, L, Gonzalez, A (1991) Fuzzy matrix games considering the criteria of the players. Kybernetes 20: pp. 275289 CrossRef
 Gao, J (2007) Credibilistic game with fuzzy information. J Uncertain Syst 1: pp. 7480
 Gao, J, Liu, B (2005) Fuzzy multilevel programming with a hybrid intelligent algorithm. Comp Math Appl 49: pp. 15391548 CrossRef
 Gao, J, Liu, ZQ (2007) Fuzzypayoff twoplayer nonzerosum games. Technical Report of City University of Hong Kong, Hong Kong
 Gao, J, Lu, M (2005) Fuzzy quadratic minimum spanning tree problem. Appl Math Comput 164: pp. 773788 CrossRef
 Harsanyi, JC (1966) A general theory of rational behavior in game situations. Econometrica 34: pp. 613634 CrossRef
 Harsanyi, JC (1967) Games with incomplete information played by ‘Bayesian’ player, Part I. The basic model. Manage Sci 14: pp. 159182 CrossRef
 Harsanyi, JC (1995) Games with incomplete information. Am Econ Rev 85: pp. 291303
 Kuhn, HW (1950) Extensive games. Proc Natl Acad Sci USA 36: pp. 570576 CrossRef
 Kuhn, HW (1953) Extensive form games and the problem of information. Contrib Theory Games 2: pp. 193216
 Liang R, Gao J (2008) Dependentchance programming models for capital budgeting in fuzzy environments, vol 13, No. 1. Tsinghua Univesity and Technology
 Liu, B (2002) Theory and practice of uncertain programming. PhysicaVerlag, Heidelberg
 Liu, B (2004) Uncertainty theory. Springer, Berlin
 Liu, Y (2005) Fuzzy programming with recourse. Int J Uncertain Fuzziness Knowl Based Syst 13: pp. 381413 CrossRef
 Liu, B (2006) A survey of credibility theory. Fuzzy Optim Decis Making 5: pp. 387408 CrossRef
 Liu, Y (2006) Convergent results about the use of fuzzy simulation in fuzzy optimization problems. IEEE Trans Fuzzy Syst 14: pp. 295304 CrossRef
 Liu, B (2007) Uncertainty theory. Springer, Berlin
 Liu, B (2007) A survey of entropy of fuzzy variables. J Uncertain Syst 1: pp. 110
 Liu, Y, Gao, J (2007) The independence of fuzzy variables with applications to fuzzy random optimization. Int J Uncertain Fuzziness Knowl Based Syst 15: pp. 120 CrossRef
 Liu, B, Liu, Y (2002) Expected value of fuzzy variable and fuzzy expected value models. IEEE Trans Fuzzy Syst 10: pp. 445450 CrossRef
 Liu, Y, Liu, B (2003) Expected value operator of random fuzzy variable and random fuzzy expected value models. Int J Uncertain Fuzziness Knowl Based Syst 11: pp. 195215 CrossRef
 Maeda, T (2000) Characterization of the equilibrium strategy of the bimatrix game with fuzzy payoff. J Math Anal Appl 251: pp. 885896 CrossRef
 Maeda, T (2003) Characterization of the equilibrium strategy of the twoperson zerosum game with fuzzy payoff. Fuzzy Sets Syst 139: pp. 283296 CrossRef
 Nash, J (1950) Equilibrium points in nperson games. Proc Natl Acad Sci 36: pp. 4849 CrossRef
 Nash, J (1951) Noncooperative games. Ann Math 54: pp. 286295 CrossRef
 Nishizaki, I, Sakawa, M (2000) Equilibrium solutions for multiobjective bimatrix games with fuzzy payoffs and fuzzy goals. Fuzzy Sets Syst 111: pp. 99116 CrossRef
 Nishizaki, I, Sakawa, M (2001) Fuzzy and multiobjective games for conflict resolution. PhysicaVerleg, Heidelberg
 Shapley, L (1953) A value for nperson games. Contrib Theory Games 2: pp. 307317
 Varoufakis, Y, Housego, A eds. (2001) Game theory: critical concepts in the social sciences, vol I–IV. Routledge, London
 von Neumann J (1928) Zur Theorie der Gesellschaftsspiele [Translated as On the theory of games of strategy. In: Tucker AW, Luce RD (eds) Contributions to the theory of games, vol IV. Princeton University Press, Princeton, pp 13–42, 1959]. Math Ann 100:295–320
 Neumann, J, Morgenstern, D (1944) The theory of games in economic behavior. Wiley, New York
 Zhao, R, Liu, B (2003) Renewal process with fuzzy interarrival times and costs. Int J Uncertain Fuzziness Knowl based Syst 11: pp. 573586 CrossRef
 Zhao, R, Liu, B (2004) Redundancy optimization problems with uncertainty of combining randomness and fuzziness. Eur J Oper Res 157: pp. 716735 CrossRef
 Title
 On characterization of credibilistic equilibria of fuzzypayoff twoplayer zerosum game
 Journal

Soft Computing
Volume 13, Issue 2 , pp 127132
 Cover Date
 20090101
 DOI
 10.1007/s0050000803103
 Print ISSN
 14327643
 Online ISSN
 14337479
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Game
 Fuzzy variable
 Credibility measure
 Credibilistic equilibrium
 Industry Sectors
 Authors

 Jinwu Gao ^{(1)}
 ZhiQiang Liu ^{(2)}
 Puchen Shen ^{(1)}
 Author Affiliations

 1. Uncertain Systems Lab, School of Information, Renmin University of China, Beijing, 100872, China
 2. School of Creative Media, City University of Hong Kong, Hong Kong, China