Cooperative fuzzy games on augmenting systems

In this paper, a generalised form of fuzzy games on augmenting systems is introduced, which can be seen as an extension of crisp case. The Shapley value for fuzzy games on augmenting systems is given. An axiomatic system of the given Shapley value is studied, and some properties are discussed. Meantime, we further research two special cases of fuzzy games on augmenting systems. The Shapley value and the core of these two kinds of fuzzy games on augmenting systems are introduced.

[1]  Jesús Mario Bilbao,et al.  Axiomatizations of the Shapley value for games on augmenting systems , 2009, Eur. J. Oper. Res..

[2]  Masahiro Inuiguchi,et al.  A Shapley function on a class of cooperative fuzzy games , 2001, Eur. J. Oper. Res..

[3]  Roger B. Myerson,et al.  Graphs and Cooperation in Games , 1977, Math. Oper. Res..

[4]  Theo S. H. Driessen,et al.  The Shapley value for games on matroids: The dynamic model , 2001, Math. Methods Oper. Res..

[5]  G. Owen.  Multilinear Extensions of Games , 1972 .

[6]  Shigeo Muto,et al.  On cores and stable sets for fuzzy games , 2004, Fuzzy Sets Syst..

[7]  Jesús Mario Bilbao,et al.  Axiomatizations of the Shapley value for cooperative games on antimatroids , 2003, Math. Methods Oper. Res..

[8]  Jesús Mario Bilbao.  Cooperative Games under Augmenting Systems , 2003, SIAM J. Discret. Math..

[9]  Qiang Zhang,et al.  The Shapley function for fuzzy cooperative games with multilinear extension form , 2010, Appl. Math. Lett..

[10]  Rodica Branzei,et al.  Convex fuzzy games and participation monotonic allocation schemes , 2003, Fuzzy Sets Syst..

[11]  Jesús Mario Bilbao,et al.  The Shapley value on convex geometries , 2000, Discret. Appl. Math..

[12]  J. Aubin.  Mathematical methods of game and economic theory , 1979 .

[13]  Jesús Mario Bilbao.  Axioms for the Shapley value on convex geometries , 1998, Eur. J. Oper. Res..

[14]  U. Faigle,et al.  The Shapley value for cooperative games under precedence constraints , 1992 .

[15]  Yan-An Hwang,et al.  Fuzzy games: A characterization of the core , 2007, Fuzzy Sets Syst..

[16]  Xiaohui Yu,et al.  The fuzzy core in games with fuzzy coalitions , 2009 .

[17]  Dan Butnariu,et al.  Enlarged cores and bargaining schemes in games with fuzzy coalitions , 2009, Fuzzy Sets Syst..

[18]  Dan Butnariu,et al.  Shapley mappings and the cumulative value for n-person games with fuzzy coalitions , 2008, Eur. J. Oper. Res..

[19]  D. Butnariu.  Stability and Shapley value for an n-persons fuzzy game , 1980 .