Values for Interior Operator Games

The aim of this paper is to study a new class of cooperative games called interior operator games. These games are additive games restricted by antimatroids. We consider several types of cooperative games as peer group games, big boss games, clan games and information market games and show that all of them are interior operator games. Next, we analyze the properties of these games and compute the Shapley, Banzhaf and Tijs values.

[1]  R. P. Dilworth Lattices with Unique Irreducible Decompositions , 1940 .

[2]  G. Owen Values of graph-restricted games , 1986 .

[3]  Peter Borm,et al.  On the Position Value for Communication Situations , 1992, SIAM J. Discret. Math..

[4]  Paul H. Edelman Meet-distributive lattices and the anti-exchange closure , 1980 .

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

[6]  Pradeep Dubey,et al.  Mathematical Properties of the Banzhaf Power Index , 1979, Math. Oper. Res..

[7]  Vito Fragnelli,et al.  Tree-connected peer group situations and peer group games , 2002, Math. Methods Oper. Res..

[8]  László Lovász,et al.  Examples and algorithmic properties of Greedoids , 1989 .

[9]  J. Nash,et al.  NON-COOPERATIVE GAMES , 1951, Classics in Game Theory.

[10]  Roger B. Myerson,et al.  Graphs and Cooperation in Games , 1977, Math. Oper. Res..

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

[12]  John C. Harsanyi,et al.  Общая теория выбора равновесия в играх / A General Theory of Equilibrium Selection in Games , 1989 .

[13]  Nimrod Megiddo,et al.  Computational Complexity of the Game Theory Approach to Cost Allocation for a Tree , 1978, Math. Oper. Res..

[14]  R. Brink An axiomatization of the disjunctive permission value for games with a permission structure , 1997 .

[15]  Paul H. Edelman,et al.  The theory of convex geometries , 1985 .

[16]  M. V. Semyonova,et al.  Lattices with unique irreducible decompositions , 2000 .

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

[18]  Shigeo Muto,et al.  On Big Boss Games , 1988 .

[19]  U. Faigle,et al.  The Shapley value for cooperative games under precedence constraints , 1992 .

[20]  李幼升,et al.  Ph , 1989 .

[21]  Shigeo Muto,et al.  Information market games , 1989 .

[22]  Jesús Mario Bilbao,et al.  Cooperative games on antimatroids , 2004, Discret. Math..