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Rationalizability

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Rationalizable strategies are those that survive iterated removal of never-best-responses. (A best-response is a strategy that gives the maximum utility given what other players are doing.)

Rationalizable strategies can be mixed and are not necessarily unique. Also, every player always has at least one rationalizable strategy. This equilibrium concept is less restrictive than that of Nash equilibrium, implying that not all rationalizable strategies are part of a NE.

Consider the game below.

Left Right
Up 3,0 0,1
Mid 1,1 2,0
Down 0,0 1,2

What strategies are rationalizable for Player 1 (the row player) and Player 2?

A

All strategies are rationalizable for both players.

B

Player 1 has two rationalizable strategies: Up and Mid. Both of Player 2's options are rationalizable.

C

Player 1 has no rationalizable strategies. Both of Player 2's options are rationalizable.

D

Player 1 has two rationalizable strategies: Up and Mid. Player 2 has no rationalizable strategies