Find the Nash equilibrium outcome for both treatments of the multi-stage bargaining game. In the first treatment, the pie shrinks from $5 to $4 and in the second treatment, the pie shrinks from $5 to $2. In both treatments, only integer dollar amounts are allowable.

For various values of X(for player1 and player 2), find all Nash equilibria of the following game with von Neumann-Morgenstern preferences:

Consider the following situation: five individuals are participating in an auction for an old bicycle used by a famous cyclist. The table below provides the bidders' valuations of the cycle. The auctioneer starts the bid at an offer price far above the bidders' values and lowers the price in increments until one of the bidders accepts the offer.   Bidder Value ($) Roberto 750 Claudia 700 Mario 650 Bradley 600 Michelle 550   What is the optimal strategy of each player in this case? Who will win the auction if each bidder places his or her optimal bid? If Claudia wins the auction, how much surplus will she earn?

We can see from the payoff matrix that there are no pure strategy Nash equilibrium in this game because at least one firm would always have an incentive to change its behavior. ​ From​ Nash's​ theorem, we know there must be at least one Nash equilibrium so there must be a mixed strategy Nash equilibrium for this game. Find the mixed strategy Nash equilibrium by first deleting all dominated strategies in the game What's the expected payoff to Firm 2 in the equilibrium?