Strongly rational sets for normal-form games

We introduce the concept of minimal strong curb sets which is a set-theoretic coarsening of the notion of strong Nash equilibrium. Strong curb sets are product sets of pure strategies such that each player’s set of recommended strategies contains all actions she may rationally select in every coalition she might belong to, for any belief each coalition member may have that is consistent with the recommendations to the other players. Minimal strong curb sets are shown to exist and are compared with other well-known solution concepts. We provide a dynamic learning process leading the players to play strategies from a minimal strong curb set only.