Introspection and equilibrium selection in 2 × 2 matrix games

Game theory lacks an explanation of how players' beliefs are formed and why they are in equilibrium. This is the reason why it has failed to make significant advances with the problem of equilibrium selection even for quite simple games, as 2 × 2 games with two strict Nash equilibria. Our paper models the introspection process by which the selected equilibrium is achieved in this class of games. Players begin their analysis with imprecise priors, obtained under weak restrictions formulated as Axioms. For a large class of reasoning dynamics we obtain as the solution the risk dominant Nash equilibrium.