Our second definition is motivated by Pearce's original extensive-form rationalizability and is based on a reduction procedure. We show the equivalence of our two definitions of social rationalizability. Our main results are the following. The set of socially rationalizable outcomes is non-empty for the entire class of social environments. When we apply social rationalizability to the prisoner's dilemma, it follows that cooperation is sustained.
Social environments deal with coalitional moves.
It is therefore important that social rationalizability not only guarantees individual rationality, but also coalitional rationality. Among a set of Pareto ranked alternatives a coalition should be able to coordinate on the Pareto optimal one. Social rationalizability is shown to satisfy coalitional rationality.