Rationalizability

Rationalizability

Infobox equilibrium
name=Rationalizability
supersetof=Nash equilibrium
discoverer=D. Bernheim and D. Pearce
example=Matching pennies

In game theory, rationalizability or rationalizable equilibria is a solution concept which generalizes Nash equilibrium. The general idea is to provide the weakest constraints on players while still requiring rational players. It was first discovered independently by Bernheim (1984) and Pearce (1984).

Constraints on beliefs

As an example, consider the game matching pennies pictured to the right. In this game the only Nash equilibrium is row playing "h" and "t" with equal probability and column playing "H" and "T" with equal probability. However, all the pure strategies in this game are rationalizable.

Consider the following reasoning: row can play "h" if it is reasonable for her to believe that column will play "H". Column can play "H" if its reasonable for him to believe that row will play "t". Row can play "t" if its reasonable for her to believe that column will play "T". Column can play "T" if it reasonable for him to believe that row will play "h" (beginning the cycle again). This provides an infinite set of consistent beliefs that results in row playing "h". A similar argument can be given for row playing "t", and for column playing either "H" or "T".

References

*Bernheim, D. (1984) Rationalizable Strategic Behavior. "Econometrica" 52: 1007-1028.
*Fudenberg, Drew and Jean Tirole (1993) "Game Theory." Cambridge: MIT Press.
*Pearce, D. (1984) Rationalizable Strategic Behavior and the Problem of Perfection. "Econometrica" 52: 1029-1050.
*Ratcliff, J. (1992–1997) lecture notes on game theory, §2.2: [http://www.virtualperfection.com/gametheory/Section2.2.html "Iterated Dominance and Rationalizability"]


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