Slightly Altruistic Equilibria in Normal Form Games

We introduce a refinement concept for Nash equilibria (slightly altruistic equilibrium) defined by a limit process and which captures the idea of reciprocal altruism as presented in Binmore (2003). Existence is guaranteed for every finite game and for a large class of games with a continuum of strategies. Results and examples emphasize the (lack of) connections with classical refinement concepts. Finally, it is shown that under a pseudo-monotonicity assumption on a particular operator associated to the game it is possible, by selecting slightly altruistic equilibria, to eliminate those equilibria in which a player can switch to a strategy that is better for the others without leaving the set of equilibria.

[1]  E. Fehr.  A Theory of Fairness, Competition and Cooperation , 1998 .

[2]  Martin Dufwenberg,et al.  A theory of sequential reciprocity , 2004, Games Econ. Behav..

[3]  Armin Falk,et al.  A Theory of Reciprocity , 2001, Games Econ. Behav..

[4]  E. Damme.  Refinements of the Nash Equilibrium Concept , 1983 .

[5]  Eric van Damme,et al.  Chapter 41 Strategic equilibrium , 2002 .

[6]  D. Levine.  Modeling Altruism and Spitefulness in Experiments , 1998 .

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

[8]  Jacqueline Morgan,et al.  Generalized Variational Inequalities with Pseudomonotone Operators Under Perturbations , 1999 .

[9]  Akira Okada,et al.  On stability of perfect equilibrium points , 1981 .

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

[11]  O. Mangasarian.  PSEUDO-CONVEX FUNCTIONS , 1965 .

[12]  R. Aumann.  Rationality and Bounded Rationality , 1997 .

[13]  J. Nash.  Equilibrium Points in N-Person Games. , 1950, Proceedings of the National Academy of Sciences of the United States of America.

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

[15]  Rajiv Sethi,et al.  Preference Evolution and Reciprocity , 2001, J. Econ. Theory.

[16]  E. Damme.  Stability and perfection of Nash equilibria , 1987 .

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

[18]  Giuseppe De Marco,et al.  Friendliness and Reciprocity in Equilibrium Selection , 2008, IGTR.

[19]  Dries Vermeulen,et al.  On the Relation Among Some Definitions of Strategic Stability , 2001, Math. Oper. Res..

[20]  J. Harsanyi.  Oddness of the number of equilibrium points: A new proof , 1973 .

[21]  Agnieszka Rusinowska.  Refinements of Nash Equilibria in View of Jealous or Friendly Behavior of Players , 2002, IGTR.

[22]  Klaus Ritzberger,et al.  The theory of normal form games from the differentiable viewpoint , 1994 .

[23]  J. Mertens,et al.  ON THE STRATEGIC STABILITY OF EQUILIBRIA , 1986 .

[24]  R. Selten.  Reexamination of the perfectness concept for equilibrium points in extensive games , 1975, Classics in Game Theory.

[25]  G. Stampacchia,et al.  A remark on Ky fan's minimax principle , 2008 .

[26]  Maxwell B. Stinchcombe,et al.  Equilibrium Refinement for Infinite Normal-Form Games , 1995 .

[27]  J. Goodman.  Note on Existence and Uniqueness of Equilibrium Points for Concave N-Person Games , 1965 .