Partnership formation and binomial semivalues

Partnership formation in cooperative games is studied, and binomial semivalues are used to measure the effects of such a type of coalition arising from an agreement between (a group of) players. The joint effect on the set of involved players is also compared with that of the alternative alliance formation. The simple game case is especially considered, and the application to a real life example illustrates the use of coalitional values closely related to the binomial semivalues when dealing with partnership formation and coalitional bargaining simultaneously.

[1]  Rudolf Henn,et al.  Mathematical Economics and Game Theory , 1977 .

[2]  Pradeep Dubey,et al.  Value Theory Without Efficiency , 1981, Math. Oper. Res..

[3]  Robert J. Weber,et al.  Probabilistic Values for Games , 1977 .

[4]  Josep Freixas,et al.  Reliability Importance Measures of the Components in a System Based on Semivalues and Probabilistic Values , 2002, Ann. Oper. Res..

[5]  L. Shapley,et al.  The Shapley Value , 1994 .

[6]  Josep Freixas,et al.  Semivalues as power indices , 2003, Eur. J. Oper. Res..

[7]  P. Hall.  On Representatives of Subsets , 1935 .

[8]  Guillermo Owen,et al.  Characterization of the Banzhaf–Coleman Index , 1978 .

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

[10]  Antonio Magaña,et al.  Alliances, partnerships and the Banzhaf semivalue , 2008, Ann. Oper. Res..

[11]  Josep Freixas,et al.  Semivalue Versatility and Applications , 2002, Ann. Oper. Res..

[12]  María Albina Puente,et al.  A Parametric Family of Mixed Coalitional Values , 2006 .

[13]  L. Shapley.  A Value for n-person Games , 1988 .

[14]  Francesc Carreras,et al.  A comparative axiomatic characterization of the Banzhaf-Owen coalitional value , 2007, Decis. Support Syst..

[15]  E. Kalai,et al.  On weighted Shapley values , 1983 .

[16]  Josep Freixas,et al.  Complete simple games , 1996 .

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

[18]  G. Owen.  VALUES OF GAMES WITH A PRIORI UNIONS , 1977 .

[19]  G. Owen.  Multilinear extensions and the banzhaf value , 1975 .

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

[21]  Francesc Carreras,et al.  Axiomatic characterizations of the symmetric coalitional binomial semivalues , 2007, Discret. Appl. Math..