Equivalence of strong and coalition-proof Nash equilibria in games without spillovers

SummaryThis paper examines the conditions which guarantee that the set of coalition-proof Nash equilibria coincides with the set of strong Nash equilibria in the normal form games withoutspillovers. We find thatpopulation monotonicity properties of the payoff functions, when the payoff of a player changes monotonically when the size of the group of players choosing the same strategy increases, are crucial to obtain the equivalence of these two solution concepts. We identify the classes of games, satisfying population monotonicity properties, which yield the equivalence of the set of coalition-proof Nash equilibria and the set of strong Nash equilibria. We also provide sufficient conditions for the equivalence result even when the population monotonicity assumptions are relaxed.

[1]  Shlomo Weber,et al.  Strong tiebout equilibrium under restricted preferences domain , 1986 .

[2]  B. Peleg.  Game Theoretic Analysis of Voting in Committees , 1984 .

[3]  Tatsuro Ichiishi,et al.  The cooperative nature of the firm , 1994 .

[4]  G. Demange.  Intermediate Preferences and Stable Coalition Structures , 1994 .

[5]  Joseph Greenberg,et al.  Deriving strong and coalition-proof nash equilibria from an abstract system , 1989 .

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

[7]  M. Whinston,et al.  Coalition-Proof Nash Equilibria I. Concepts , 1987 .

[8]  Robert J. Aumann,et al.  16. Acceptable Points in General Cooperative n-Person Games , 1959 .

[9]  Shlomo Weber,et al.  Stable Coalition Structures with a Unidimensional Set of Alternatives , 1993 .

[10]  Ehud Kalai,et al.  A group incentive compatible mechanism yielding core allocations , 1979 .

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

[12]  Shlomo Weber,et al.  Multiparty Equilibria under Proportional Representation , 1985, American Political Science Review.

[13]  Dilip Mookherjee,et al.  The good, the bad, and the ugly: Coalition proof equilibrium in infinite games☆ , 1992 .

[14]  Stef Tijs,et al.  Strategic claim games corresponding to an NTU-game , 1992 .

[15]  Roger Guesnerie,et al.  Second best taxation as a game , 1981 .

[16]  D. Henriet,et al.  Note, comment, and letter to the editorSustainable oligopolies , 1991 .

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

[18]  Shlomo Weber,et al.  Pure Strategy Nash Equilibrium in a Group Formation Game with Positive Externalities , 1997 .