rationalizability

Rationalizability is a solution concept in game theory that identifies the strategies players can choose rationally when they hold beliefs about others’ behavior and these beliefs are common knowledge of rationality. It was introduced independently by Bernheim and by Pearce in the 1980s.

A strategy is rationalizable if it can be a best response to some belief about the other players’ strategies, where the belief assigns positive probability only to strategies that are themselves rationalizable. This concept is applied through an iterative procedure: start with the full set of strategies for every player; delete any strategy that is never a best response to any belief about the opponents’ strategies, given the current set of surviving strategies. Replace the remaining sets with these reduced sets and repeat until no further deletions are possible. The strategies that remain constitute the rationalizable sets.

Epistemically, rationalizability corresponds to the idea that players are rational and that this rationality is common knowledge; there exists a self-consistent set of beliefs about others that supports each surviving strategy as a best response.

Relation to other concepts: rationalizability generalizes the idea behind iterated elimination of strictly dominated strategies but is typically stricter. Every strictly dominated strategy is not rationalizable, yet rationalizability can exclude strategies that are not strictly dominated. The concept can also be extended to extensive-form games as extensive-form rationalizability, which adapts the idea to dynamic settings and information sets.

In sum, rationalizability captures what players can justifiably do under mutual rationality and common knowledge, focusing on consistency between actions and beliefs about rational opponents.