Pooling Equilibrium - Lecture notes First semester PDF

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Pooling Equilibrium...

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Pooling Equilibrium   

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Each type takes identical actions Uninformed player cannot update its belief about its opponent after observing an equilibrium moveTo see that the strategy combination is a Nash equilibrium, check that there are no incentives to deviate by both players A sequential equilibrium needs to be consistent in terms of the beliefs o If I believe that the player would act like this I will do exactly the equilibrium path  For every player How to find pooling equilibria? 1. Identify a set of poling strategies 2. Solve for the other players best response to those strategies 3. Check whether the first player can profitably deviate 4. Repeat step 1 until you have exhausted all sets

Step 2:

Probabilities are copied So what is the optimal strategy? (in a Sequential equilibrium strategies are sequentianally rational given the players beliefs (=consistent))

Step 3:

Player 1 is satisfied with his strategy So we have a pooling equilibrium:  Both types hide  Player 2 quits, when the strong type reveals, fights when the weak type reveals, and quits when she observes player 1 hide  After observing Player 1 hide, Player 2 believes he is strong with probability 0.6...