Axiomatizing the Harsanyi solution, the symmetric egalitarian solution and the consistent solution for NTU-games

Abstract.The validity of the axiomatization of the Harsanyi solution for NTU-games by Hart (1985) is shown to depend on the regularity conditions imposed on games. Following this observation, we propose two related axiomatic characterizations, one of the symmetric egalitarian solution (Kalai and Samet, 1985) and one of the consistent solution (Maschler and Owen, 1992). The three axiomatic results are studied, evaluated and compared in detail.

[1]  Lloyd S. Shapley,et al.  Utility comparisons and the theory of games , 1988 .

[2]  Independence of irrelevant expansions , 1981 .

[3]  Guillermo Owen,et al.  Values of games without side payments , 1971 .

[4]  J. Nash.  THE BARGAINING PROBLEM , 1950, Classics in Game Theory.

[5]  E. Kalai,et al.  Monotonic Solutions to General Cooperative Games , 1985 .

[6]  Sergiu Hart.  A comparison of non-transferable utility values , 2004 .

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

[8]  Robert J. Aumann,et al.  AN AXIOMATIZATION OF THE NON-TRANSFERABLE UTILITY VALUE , 1985 .

[9]  S. Hart,et al.  Bargaining and Value , 1996 .

[10]  G. Owen,et al.  The consistent Shapley value for hyperplane games , 1989 .

[11]  John C. Harsanyi,et al.  A Simplified Bargaining Model for the n-Person Cooperative Game , 1963 .

[12]  Gustavo Bergantiños,et al.  A focal-point solution for bargaining problems with coalition structure , 2005 .

[13]  Sergiu Hart,et al.  An axiomatization of Harsanyi's nontransferable utility solution , 1985 .

[14]  E. Kalai.  Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons , 1977 .

[15]  Sergiu Hart,et al.  An axiomatization of the consistent non-transferable utility value , 2005, Int. J. Game Theory.

[16]  Yan-An Hwang,et al.  The Harsanyi-Shapley solution and independence of irrelevant expansions , 2003, Int. J. Game Theory.

[17]  G. Owen,et al.  The Consistent Shapley Value for Games without Side Payments , 1992 .

[18]  R. Myerson,et al.  Monotonicity and independence axioms , 1980 .

[19]  Lloyd S. Shapley,et al.  The Shapley value: Utility comparison and the theory of games , 1967 .

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