I would like to find the set of rationalizable strategies for this 4x4 game:

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The first thing I did was try and find all PSNE. I found two, the ones I bolded.

Thus, my answer to this question is that the set of rationalizable strategies for Player 1 is {T, Y} and the set of rationalizable strategies for Player 2 is {B, C}.

Is this answer correct?


The set of rationalizable strategies is the set of strategies that survive the iterated elimination of strictly dominated strategies, i.e., strategies that are never a best response. It is a weaker concept than Nash equilibrium.

For player 1, you can eliminate strategy M, which is strictly dominated by T. You cannot eliminate any strategy for player 2 as there is only a weak dominance.

In a second step, you can eliminate A which is dominated by C.

As far as I can see, you cannot eliminate any other strategy in the next step and, hence, all remaining strategies are rationalizable.


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