Slightly altruistic equilibria

We introduce a refinement concept for Nash equilibria (slightly altruistic equilibrium) defined by a limit process and which captures the idea of reciprocal altruism. 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 pseudomonotonicity 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.