The partnered core of a game with side payments

An outcome of a game is partnered if there are no asymmetric dependencies between any two players. For a cooperative game, a payoff is in the partnered core of the game if it is partnered, feasible and cannot be improved upon by any coalition of players. We show that the relative interior of the core of a game with side payments is contained in the partnered core. For quasi-strictly convex games the partnered core coincides with the relative interior of the core. When there are no more than three partnerships, the sums of the payoffs to partnerships are constant across all core payoffs. When there are no more than three players, the partnered core satisfies additional properties. We also illustrate our main result for coalition structure games.

[1]  E. Bennett.  The aspiration approach to predicting coalition formation and payoff distribution in sidepayment games , 1983 .

[2]  Debraj Ray.  Credible coalitions and the core , 1989 .

[3]  R. Selten.  A Noncooperative Model of Characteristic-Function Bargaining , 1988 .

[4]  M. Wooders.  Large Games and Economies with Effective Small Groups , 1994 .

[5]  M. Jackson,et al.  Strongly Stable Networks , 2002 .

[6]  The Partnered Core of a Game without Side Payments , 1996 .

[7]  M. Dufwenberg.  Game theory. , 2011, Wiley interdisciplinary reviews. Cognitive science.

[8]  On minimal separating collections , 1968 .

[9]  William R. Zame,et al.  Bargaining in cooperative games , 1988 .

[10]  H. P. Williams.  THEORY OF LINEAR AND INTEGER PROGRAMMING (Wiley-Interscience Series in Discrete Mathematics and Optimization) , 1989 .

[11]  Debraj Ray,et al.  A Concept of Egalitarianism under Participation Constraints , 1989 .

[12]  D. Ray.  Credible Coalitions and the Core , 1989 .

[13]  Stef Tijs,et al.  Link formation in cooperative situations , 1998, Int. J. Game Theory.

[14]  Eyal Winter,et al.  Consistent Demands for Coalition Formation , 1994, Essays in Game Theory.

[15]  R. J. Aumann,et al.  Cooperative games with coalition structures , 1974 .

[16]  P. Reny,et al.  An extension of the KKMS theorem , 1998 .

[17]  Alexander Schrijver,et al.  Theory of linear and integer programming , 1986, Wiley-Interscience series in discrete mathematics and optimization.

[18]  H. Scarf.  The Core of an N Person Game , 1967 .

[19]  Lloyd S. Shapley,et al.  On balanced sets and cores , 1967 .

[20]  M. Maschler,et al.  The Structure of the Kernel of a Cooperative Game , 1967 .

[21]  Anne van den Nouweland,et al.  Strongly Stable Networks , 2002, Games Econ. Behav..

[22]  M. Maschler,et al.  A characterization, existence proof and dimension bounds for the kernel of a game. , 1966 .

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

[24]  Mamoru Kaneko,et al.  Cores of partitioning games , 1982, Math. Soc. Sci..

[25]  Debraj Ray,et al.  A CONCEPT OF EGALITARIANISM UNDER PARTICIPATION , 1989 .

[26]  D. Pallaschke,et al.  Game Theory and Related Topics , 1980 .

[27]  Oskar Morgenstern.  The Theory of Games , 1960 .

[28]  Shlomo Weber,et al.  Strongly balanced cooperative games , 1992 .

[29]  Yakar Kannai,et al.  A Further Extension of the KKMS Theorem , 2000, Math. Oper. Res..

[30]  The partnered core of an economy and the partnered competitive equilibrium , 1996 .