Equilibrium Strategies of Two-Player Nonzero-Sum Games with Fuzzy Payoffs

This paper investigates two-player nonzero-sum games with fuzzy payoffs. According to different decision criteria, three new definitions of Nash equilibria as well as their existence theorems are proposed. An example is also provided for illustrating these new Nash equilibria.

[1]  Ichiro Nishizaki,et al.  Equilibrium Solutions for Multiobjective Bimatrix Games Incorporating Fuzzy Goals , 1994 .

[2]  Chris Field,et al.  Solution of a Satisficing Model for Random Payoff Games , 1972 .

[3]  Baoding Liu,et al.  A survey of credibility theory , 2006, Fuzzy Optim. Decis. Mak..

[4]  Takashi Maeda,et al.  On characterization of equilibrium strategy of two-person zero-sum games with fuzzy payoffs , 2003, Fuzzy Sets Syst..

[5]  Baoding Liu Uncertainty Theory: An Introduction to its Axiomatic Foundations , 2004 .

[6]  Jinwu Gao,et al.  The Independence of Fuzzy Variables with Applications to Fuzzy Random Optimization , 2007, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[7]  A. Charnes,et al.  Chance-Constrained Programming , 1959 .

[8]  T. Maeda,et al.  Characterization of the Equilibrium Strategy of the Bimatrix Game with Fuzzy Payoff , 2000 .

[9]  Ichiro Nishizaki,et al.  Equilibrium solutions in multiobjective bimatrix games with fuzzy payoffs and fuzzy goals , 2000, Fuzzy Sets Syst..

[10]  Baoding Liu,et al.  Chance constrained programming with fuzzy parameters , 1998, Fuzzy Sets Syst..

[11]  Jean-Pierre Aubin,et al.  Cooperative Fuzzy Games , 1981, Math. Oper. Res..

[12]  Ichiro Nishizaki,et al.  Fuzzy and Multiobjective Games for Conflict Resolution , 2001 .

[13]  J. Szep,et al.  Games with incomplete information , 1985 .

[14]  Abraham Charnes,et al.  Zero-Zero Chance-Constrained Games , 1968 .

[15]  Baoding Liu,et al.  Dependent-chance programming in fuzzy environments , 2000, Fuzzy Sets Syst..

[16]  Baoding Liu,et al.  Modelling stochastic decision systems using dependent-chance programming , 1997 .

[17]  Dan Butnariu,et al.  Fuzzy games: A description of the concept , 1978 .

[18]  Richard Bellman,et al.  Decision-making in fuzzy environment , 2012 .

[19]  Roger A. Blau,et al.  Random-Payoff Two-Person Zero-Sum Games , 1974, Oper. Res..

[20]  Antonio González,et al.  On the use of the ranking function approach to solve fuzzy matrix games in a direct way , 1992 .

[21]  Antonio González,et al.  Fuzzy matrix games considering the criteria of the players , 1991 .

[22]  Yian-Kui Liu,et al.  Expected Value Operator of Random Fuzzy Variable, Random Fuzzy Expected Value Models , 2003, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[23]  Yian-Kui Liu,et al.  Expected value of fuzzy variable and fuzzy expected value models , 2002, IEEE Trans. Fuzzy Syst..

[24]  John C. Harsanyi,et al.  Games with Incomplete Information Played by "Bayesian" Players, I-III: Part I. The Basic Model& , 2004, Manag. Sci..