A polyhedral approach to the stability of a family of coalitions

Using polyhedral combinatorics and graph theory results, we study unstable families of coalitions and analyze the effect of adding players or deleting coalitions in order to obtain a stable family. We also generalize the definitions and results to the case of fractional participation of players in coalitions.

[1]  Stef Tijs,et al.  Monotonic games are spanning network games , 1993 .

[2]  D. R. Fulkerson,et al.  Anti-blocking polyhedra , 1972 .

[3]  T. E. S. Raghavan,et al.  Shapley Value for Multichoice Cooperative Games, I , 1993 .

[4]  Mamoru Kaneko,et al.  Cores of partitioning games , 1982, Math. Soc. Sci..

[5]  Graciela L. Nasini,et al.  A Generalization of the Perfect Graph Theorem Under the Disjunctive Index , 2002, Math. Oper. Res..

[6]  Bettina Rockenbach.  Springer Lecture Notes in Economics and Mathematical Systems , 1994 .

[7]  Laurence A. Wolsey,et al.  Integer and Combinatorial Optimization , 1988 .

[8]  V. Gurvich,et al.  Stable families of coalitions and normal hypergraphs , 1997 .

[9]  P. Seymour,et al.  The Strong Perfect Graph Theorem , 2002, math/0212070.

[10]  Hans Peters,et al.  The Egalitarian Solution for Multichoice Games , 2005, Ann. Oper. Res..

[11]  Colin McDiarmid,et al.  Graph Imperfection , 2001, J. Comb. Theory, Ser. B.

[12]  Ron Holzman,et al.  Fractional Kernels in Digraphs , 1998, J. Comb. Theory, Ser. B.

[13]  V. Chvátal.  On certain polytopes associated with graphs , 1975 .

[14]  Paul D. Seymour,et al.  Recognizing Berge Graphs , 2005, Comb..

[15]  László Lovász,et al.  Normal hypergraphs and the perfect graph conjecture , 1972, Discret. Math..

[16]  Vladimir Gurvich,et al.  Perfect graphs, kernels, and cores of cooperative games , 2006, Discret. Math..

[17]  Jeroen Kuipers.  Combinatorial methods in cooperative game theory , 1994 .

[18]  Vladimir Gurvich,et al.  Perfect graphs are kernel solvable , 1996, Discret. Math..

[19]  Shlomo Weber,et al.  Strongly balanced cooperative games , 1992 .

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

[21]  H. Kunzi,et al.  Lectu re Notes in Economics and Mathematical Systems , 1975 .

[22]  Stef Tijs,et al.  Cores and related solution concepts for multi-choice games , 1995, Math. Methods Oper. Res..