Cooperative games with nontransferable utility on antimatroids

ABSTRACT This paper introduces a new family of nontransferable utility (NTU) games with partial cooperation. Games with transferable utility (TU) restricted by antimatroids were studied since 2004. Antimatroids are known combinatorial structures which are interpreted in games as dependency situations among a group of agents, and they generalize several other hierarchical structures studied in the literature. Now we define projected NTU games over antimatroids following the same idea. We have needed to build a new theory about projections between two coalitions. In this case, an outcome is feasible for a coalition if and only if its projection is feasible in the NTU game. This paper studies several properties of the projected games and the relations between these games and the original game for some interesting cases: TU games, hyperplane games and bargaining problems.

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

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

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

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

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

[6]  R. Brink.  Games with a permission structure - A survey on generalizations and applications , 2017, TOP.

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

[8]  Sergiu Hart,et al.  A comparison of non-transferable utility values , 2004 .

[9]  Andrés Jiménez-Losada,et al.  Duality on combinatorial structures. An application to cooperative games , 2017, Int. J. Gen. Syst..

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

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

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

[13]  E. Rowland.  Theory of Games and Economic Behavior , 1946, Nature.

[14]  Andrés Jiménez-Losada,et al.  Fuzzy restrictions and an application to cooperative games with restricted cooperation , 2017, Int. J. Gen. Syst..

[15]  G. Owen,et al.  Games with permission structures: The conjunctive approach , 1992 .

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

[17]  Andrés Jiménez-Losada,et al.  Games with fuzzy authorization structure: A Shapley value , 2015, Fuzzy Sets Syst..

[18]  W. Thomson.  Chapter 35 Cooperative models of bargaining , 1994 .

[19]  T. Driessen.  Cooperative Games, Solutions and Applications , 1988 .

[20]  Andrés Jiménez-Losada,et al.  Soft cooperation systems and games , 2018, Int. J. Gen. Syst..

[21]  Richard P. McLean,et al.  Chapter 55 Values of non-transferable utility games , 2002 .

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

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

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

[25]  R. Aumann,et al.  VON NEUMANN-MORGENSTERN SOLUTIONS TO COOPERATIVE GAMES WITHOUT SIDE PAYMENTS , 1960, Classics in Game Theory.

[26]  Sergiu Hart,et al.  On Prize Games , 1994, Essays in Game Theory.