Reinterpreting the Kernel

The reduced game relevant for the consistency of the prekernel is used to reinterpret this solution concept in a way that makes it independent of interpersonal utility comparisons. Based on this reinterpretation, a non-cooperative model is presented that yields in stationary equilibria the prekernel (kernel) for the class of monotonic transferable utility games. Next, we apply the same non-cooperative model to more general coalitional games. For pure bargaining problems, the model yields the Nash solution. For general non-transferable utility games, a natural extension of the prekernel arises. Thus, the prekernel is obtained as the set of payoffs where the relevant bargaining range between every pair of players is split in half.Journal of Economic LiteratureClassification Numbers: C71, C72, C78.

[1]  A. Roth.  Values for Games without Sidepayments: Some Difficulties with Current Concepts , 1980 .

[2]  R. Stearns.  Convergent transfer schemes for $N$-person games , 1968 .

[3]  L. Shapley,et al.  The kernel and bargaining set for convex games , 1971 .

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

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

[6]  By B. Moldovanu.  Stable bargained equilibria for assignment games without side payments , 1990 .

[7]  L. S. Shapley,et al.  Geometric Properties of the Kernel, Nucleolus, and Related Solution Concepts , 1979, Math. Oper. Res..

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

[9]  Alvin E. Roth,et al.  ON THE NON-TRANSFERABLE UTILITY VALUE: A REPLY TO AUMANN' , 1986 .

[10]  Faruk Gul.  Bargaining Foundations of Shapley Value , 1989 .

[11]  Morton D. Davis,et al.  The kernel of a cooperative game , 1965 .

[12]  Roberto Serrano.  Strategic bargaining, surplus sharing problems and the nucleolus , 1995 .

[13]  Douglas Gale,et al.  Bargaining and Competition Part I: Characterization , 1986 .

[14]  Louis J. Billera,et al.  Games in Support Function Form: An Approach to the Kernel of NTU Games , 1994, Essays in Game Theory.

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

[16]  R. Aumann.  On the Non-transferable Utility Value: A Comment on the Roth-Shafer Examples [Values for Games without Side Payments: Some Difficulties with Current Concepts] [On the Existence and Interpretation of Value Allocations] , 1985 .

[17]  J. Nash.  Two-Person Cooperative Games , 1953 .

[18]  Terje Lensberg,et al.  Stability and the Nash solution , 1988 .

[19]  Roberto Serrano.  Non-cooperative implementation of the nucleolus: The 3-player case , 1993 .

[20]  R. Serrano,et al.  An axiomatization of the prekernel of nontransferable utility games , 1996 .

[21]  Robert J. Aumann,et al.  Rejoinder [Values for Games without Sidepayments: Some Difficulties with Current Concepts] , 1986 .

[22]  A. Mas-Colell.  An equivalence theorem for a bargaining set , 1989 .

[23]  Douglas Gale,et al.  Bargaining and Competition Part II: Existence , 1986 .

[24]  A. Rubinstein,et al.  Equilibrium in a market with sequential bargaining , 1985 .

[25]  V. Krishna,et al.  Perfect equilibria of a model of n-person noncooperative bargaining , 1995 .

[26]  A. Rubinstein,et al.  The Nash bargaining solution in economic modelling , 1985 .

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

[28]  Roberto Serrano,et al.  A Market to Implement the Core , 1995 .

[29]  Sharon C. Rochford,et al.  Symmetrically pairwise-bargained allocations in an assignment market , 1984 .

[30]  S. Hart,et al.  Handbook of game theory with economic applications: volume 3 , 1993 .

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

[32]  A. W. Tucker,et al.  Advances in game theory , 1964 .

[33]  B. Peleg.  On the reduced game property and its converse , 1987 .

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

[35]  W. Thomson.  Consistent Allocation Rules , 1996 .

[36]  Ehud Kalai.  EXCESS FUNCTIONS FOR COOPERATIVE GAMES WITHOUT SIDEPAYMENTS. , 1975 .

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

[38]  M. Maschler.  The bargaining set, kernel, and nucleolus , 1992 .

[39]  M. Herrero.  The nash program: Non-convex bargaining problems , 1989 .