Rationalizability
The set of strategies surviving iterated elimination of strategies that are never a best response.
Definition
A strategy is rationalizable if it survives iterated deletion of never-best-responses, i.e., it is a best response to some belief over the surviving opponent strategies.
Formally the largest fixed point of the best-response operator.
Intuition
A strategy is rationalizable if you can construct a chain of consistent beliefs that makes it optimal.
Weaker than Nash equilibrium — imposes common knowledge of rationality but not of beliefs.
Worked example
In a game with a strictly dominated action, only the dominant strategy is rationalizable.
In zero-sum games, rationalizable strategies coincide with minimax strategies.
The math
Bernheim and Pearce (1984): rationalizability is the common-knowledge-of-rationality solution concept.
In two-player games, rationalizability equals iterated strict dominance.
Where it is used
Useful for analyzing games where beliefs about equilibrium play are hard to justify.
Foundation of epistemic game theory.
More in Game theory
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