The Myerson value for complete coalition structures

In order to describe partial cooperation structures, this paper introduces complete coalition structures as sets of feasible coalitions. A complete coalition structure has a property that, for any coalition, if each pair of players in the coalition belongs to some feasible coalition contained in the coalition then the coalition itself is also feasible. The union stable structures, which constitute the domain of the Myerson value, are a special class of the complete coalition structures. As an allocation rule on complete coalition structures, this paper proposes an extension of the Myerson value for complete coalition structures and provides an axiomatization.

[1]  P. Borm,et al.  Allocation rules for hypergraph communication situations , 1992 .

[2]  Jesús Mario Bilbao,et al.  Cooperative games on antimatroids , 2004, Discret. Math..

[3]  Gerard Hamiache,et al.  A Value with Incomplete Communication , 1997 .

[4]  Jesús Mario Bilbao,et al.  The position value for union stable systems , 2000, Math. Methods Oper. Res..

[5]  G. Owen,et al.  Games with permission structures: The conjunctive approach , 1992 .

[6]  Atsushi Kajii,et al.  Cominimum Additive Operators , 2007 .

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

[8]  J. M. Bilbao,et al.  Cooperative Games on Combinatorial Structures , 2000 .

[9]  F. Carreras,et al.  Games and cooperation indices , 1995 .

[10]  Philip Wolfe,et al.  Contributions to the theory of games , 1953 .

[11]  S. Hart,et al.  Potential, value, and consistency , 1989 .

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

[13]  Atsushi Kajii,et al.  Coextrema Additive Operators , 2007 .

[14]  Peter Borm,et al.  On the Position Value for Communication Situations , 1992, SIAM J. Discret. Math..

[15]  R. Myerson.  Conference structures and fair allocation rules , 1978 .

[16]  Guillermo Owen,et al.  Cooperative Games and Disjunctive Permission Structures , 1999 .

[17]  Jesús Mario Bilbao,et al.  The Myerson value for union stable structures , 2001, Math. Methods Oper. Res..

[18]  L. S. Shapley,et al.  17. A Value for n-Person Games , 1953 .

[19]  Jesús Mario Bilbao,et al.  A note on a value with incomplete communication , 2006, Games Econ. Behav..

[20]  S. K. Neogy,et al.  Modeling, computation and optimization , 2009 .