Efficiency in coalition games with externalities

A natural extension of superadditivity is not sufficient to imply that the grand coalition is efficient when externalities are present. We provide a condition, analogous to convexity, that is sufficient for the grand coalition to be efficient and show that this also implies that the (appropriately defined) core is nonempty. Moreover, we propose a mechanism which implements the most efficient partition for all coalition formation games and characterizes the resulting payoff division.

[1]  W. Lucas,et al.  N‐person games in partition function form , 1963 .

[2]  H. Norde,et al.  The Shapley Value for Partition Function Form Games , 2002, IGTR.

[3]  H. Moulin.  Axioms of Cooperative Decision Making , 1988 .

[4]  The hybrid solutions of an N-person game , 1992 .

[5]  L. Shapley.  Cores of convex games , 1971 .

[6]  Herbert E. Scarf,et al.  On the existence of a coopertive solution for a general class of N-person games☆ , 1971 .

[7]  E. M. Bolger.  A set of axioms for a value for partition function games , 1989 .

[8]  Francis Bloch.  Sequential Formation of Coalitions in Games with Externalities and Fixed Payoff Division , 1996 .

[9]  David Wettstein,et al.  Sharing the surplus: An extension of the Shapley value for environments with externalities , 2007, J. Econ. Theory.

[10]  R. Myerson.  Conference structures and fair allocation rules , 1978 .

[11]  Sergio Currarini,et al.  On the Stability of Hierarchies in Games with Externalities , 2003 .

[12]  T. Ichiishi.  A Social Coalitional Equilibrium Existence Lemma , 1981 .

[13]  Debraj Ray,et al.  A Theory of Endogenous Coalition Structures , 1998 .

[14]  Sang-Seung Yi.  Stable Coalition Structures with Externalities , 1997 .

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

[16]  R. Myerson.  Values of games in partition function form , 1977 .

[17]  Javier Arin,et al.  An Axiom System for a Value for Games in Partition Function Form , 2005, IGTR.

[18]  R. Serrano,et al.  Marginal Contributions and Externalities in the Value , 2005 .

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

[20]  Henk Norde,et al.  The Shapley Value for Partition Function Form Games , 2007, IGTR.

[21]  L. Shapley.  A Value for n-person Games , 1988 .