Microeconomic Theory Essay Example | Topics and Well Written Essays - 1250 words

Microeconomic Theory - Essay ExampleNow, if there is a PBNE where imposter one chooses both to play B or C, or randomizes between the two, his pass judgment payoff has to be greater than ? from such a move. Player 1s expected payoff on the other hand depends upon player 2s strategies and whether he randomizes and with what probabilities. Now, player 2s expected payoff from playing D is PB-(1- PB) and that from playing E is -PB+(1- PB). He will pick D iff PB-(1- PB) -PB+(1- PB)4PB2 PB1/2.He will be indifferent between playing D and E if PB=1/2 (and hence randomize between the two) and will pick E if PB1/2 is invalidated. Thus, we cannot have a PBNE with Player 1 choosing to play C and player 2 choosing D since this invalidates the required belief criterion. Similarly it can be shown that there cannot be a PBNE where 1 chooses B and 2 plays E that is concordant with the required beliefs for player 2. Finally, if player 2 randomizes, the maximal expected payoff for player 1 is 0 as well. Thus, in all PBNE, player 1 picks A. Since in the equilibrium path 2s turn never comes, he can pick either D or E or choose to randomize in this equilibrium. So we can have the following PBNE 1. (A, D) with PB1/2, 2.(A,E) with PB v2. This is true since by bidding b2= v2 he has already won the auctioneer and the final payment he has to make depends only on player 1s bid. On the other hand, bidding less than v2 doesnt tilt anything as long as the bid is greater than player 1s bid = player 1s valuation. However if b2