Information, rational beliefs and equilibrium refinements

Given an extensive game G, three subsets of the normal-form equivalence class of G are defined: the subset of simultaneous games [denoted by Sim(G)] the subset of subgame-proserving quasi-simultaneous games [denoted by SubSim(G)] and, finally, the subset consisting of the game G itself. We show that by applying the notion of rational profile of beliefs (which is formulated independently of the notion of strategy and therefore of Nash equilibrium) to the games in Sim(G) one obtains exactly the Nash equilibria of G, by applying it to the games in SubSim(G) one obtains exactly the subgame-perfect equilibria of G and, finally, by applying it to G itself one obtains a (strict) refinement of subgame-perfect equilibrium.