Uncertain Core for Coalitional Game with Uncertain Payos

Coalitional game deals with situations that involve cooperations among the players. There are dierent solution concepts such as core, Shapley value and nucleolus. This paper investigates uncertain coalitional game in which the payos are uncertain variables. Within the framework of uncertainty theory, two denitions of uncertain core are proposed. Meanwhile, a sucient and necessary condition is provided for nding the uncertain core. Finally, an example is provided for illustrating purpose.

[1]  Martin Shubik,et al.  A Method for Evaluating the Distribution of Power in a Committee System , 1954, American Political Science Review.

[2]  Donald B. Gillies,et al.  3. Solutions to General Non-Zero-Sum Games , 1959 .

[3]  R. Aumann,et al.  THE BARGAINING SET FOR COOPERATIVE GAMES , 1961 .

[4]  J. Harsanyi.  Games with Incomplete Information Played by 'Bayesian' Players, Part III. The Basic Probability Distribution of the Game , 1968 .

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

[6]  D. Schmeidler.  The Nucleolus of a Characteristic Function Game , 1969 .

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

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

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

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

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

[12]  Ariel Rubinstein,et al.  A Course in Game Theory , 1995 .

[13]  Milan Mareš.  Fuzzy Cooperative Games , 2001 .

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

[15]  Jinwu Gao,et al.  Fuzzy multilevel programming with a hybrid intelligent algorithm , 2005 .

[16]  Jinwu Gao,et al.  Credibilistic Game with Fuzzy Information , 2007 .

[17]  Baoding Liu.  Some Research Problems in Uncertainty Theory , 2009 .

[18]  Jinwu Gao,et al.  On characterization of credibilistic equilibria of fuzzy-payoff two-player zero-sum game , 2008, Soft Comput..

[19]  Jinwu Gao,et al.  N-person credibilistic strategic game , 2010, Frontiers of Computer Science in China.

[20]  Baoding Liu,et al.  Uncertainty Theory - A Branch of Mathematics for Modeling Human Uncertainty , 2011, Studies in Computational Intelligence.

[21]  Jinwu Gao,et al.  Coalitional game with fuzzy payoffs and credibilistic core , 2010, Soft Comput..

[22]  Jinwu Gao,et al.  COALITIONAL GAME WITH FUZZY PAYOFFS AND CREDIBILISTIC SHAPLEY VALUE , 2011 .

[23]  Jinwu Gao,et al.  Uncertain bimatrix game with applications , 2012, Fuzzy Optimization and Decision Making.

[24]  Jinwu Gao,et al.  CREDIBILISTIC BIMATRIX GAME WITH ASYMMETRIC INFORMATION: BAYESIAN OPTIMISTIC EQUILIBRIUM STRATEGY , 2013 .

[25]  Jinwu Gao,et al.  Credibilistic extensive game with fuzzy payoffs , 2013, Soft Comput..