The positive core of a cooperative game

The positive core is a nonempty extension of the core of transferable utility games. If the core is nonempty, then it coincides with the core. It shares many properties with the core. Six well-known axioms that are employed in some axiomatizations of the core, the prenucleolus, or the positive prekernel, and one new intuitive axiom, characterize the positive core for any infinite universe of players. This new axiom requires that the solution of a game, whenever it is nonempty, contains an element that is invariant under any symmetry of the game.

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

[2]  Peter Sudhölter,et al.  The modified nucleolus: Properties and axiomatizations , 1997, Int. J. Game Theory.

[3]  Peter Sudhölter,et al.  A Note on an Axiomatization of the Core of Market Games , 2002, Math. Oper. Res..

[4]  B. Peleg,et al.  Nucleoli as maximizers of collective satisfaction functions , 1998 .

[5]  Peter Sudhölter,et al.  A Note on an Axiomatization of the Core of Market Games , 2002 .

[6]  E. Kohlberg.  On the Nucleolus of a Characteristic Function Game , 1971 .

[7]  Peter Sudhölter,et al.  The modified nucleolus: properties and axiomatizations , 1997 .

[8]  D. Schmeidler.  The Nucleolus of a Characteristic Function Game , 1969 .

[9]  Yan-An Hwang,et al.  Axiomatizations of the core on the universal domain and other natural domains , 2000, Int. J. Game Theory.

[10]  Peter Sudhölter.  Independence for characterizing axioms of the pre-nucleolus , 1993 .

[11]  The reactive bargaining set: structure, dynamics and extension to NTU games , 1997 .

[12]  Peter Sudhölter,et al.  Reconfirming the Prenucleolus , 2003, Math. Oper. Res..

[13]  Peter Sudhölter,et al.  The semireactive bargaining set of a cooperative game , 2001, Int. J. Game Theory.

[14]  Donald B. Gillies,et al.  3. Solutions to General Non-Zero-Sum Games , 1959 .

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

[16]  Peter Sudhölter,et al.  The positive Prekernel of a Cooperative Game , 2000, IGTR.

[17]  R. Aumann,et al.  THE BARGAINING SET FOR COOPERATIVE GAMES , 1961 .

[18]  B. Peleg,et al.  Introduction to the Theory of Cooperative Games , 1983 .

[19]  Gooni Orshan,et al.  The prenucleolus and the reduced game property: Equal treatment replaces anonymity , 1993 .

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