In each of the three games shown below, let p be the probability that player 1 plays coop… Show more Problem 1 In each of the three games shown below, let p be the probability that player 1 plays cooperates (and 1- p the probability that player 1 defects), and let q be the probability that Player 2 plays cooperates (and 1- q the probability that player 2 defects). Prisonerâ€™s Dilemma Player 2 Player 2 Player 2 Player 1 cooperate defect Player 1 cooperate 70,70 10,80 Player 1 defect 80,10 40,40 Stag Hunt Player 2 Player 2 Player 2 Player 1 cooperate defect Player 1 cooperate 70,70 5,40 Player 1 defect 40,5 40,40 Chicken Player 2 Player 2 Player 2 Player 1 cooperate defect Player 1 cooperate 70,70 50,80 Player 1 defect 80,50 40,40 1. For each game, draw a graph with player 1â€™s best response function (choice of p as a function of q), and player 2â€™s best response function (choice of q as a function of p), with p on the horizontal axis and q on the vertical axis. 2. Using this graphs, find all the Nash equilibriums for the game, both pure and mixed strategy Nash equilibriums (if any). Label these equilibriums on the corresponding graph. 3. In those games that have multiple pure strategy Nash equilibriums, how do the expected payoffs from playing the mixed strategy Nash equilibrium compare with the payoffs from playing the pure strategy Nash equilibriums? Which type of strategy (mixed or pure) would players prefer to play in these games? Problem 2 Two people are involved in a dispute. Player 1 does not know whether player 2 is strong or weak; she assigns probability Î± to player 2 being strong. Player 2 is fully informed. Each player can either fight or yield. Each player obtains a payoff of 0 is she yields (regardless of the other personâ€™s action) and a payoff of 1 if she fights and her opponent yields. If both players fight, then their payoffs are (-1; 1) if player 2 is strong and (1;-1) if player 2 is weak. The Bayesian game is the following, depending on the type of player 2: Y F Y F F Y 0, 0 0, 1 Y 0, 0 0, 1 0, 1 F 1, 0 -1, 1 F 1, 0 1, -1 1, -1 Player 2 is strong (Î±) Player 2 is strong (Î±) Player 2 is strong (Î±) Player 2 is weak (1-Î±) Player 2 is weak (1-Î±) Player 2 is weak (1-Î±) Player 2 is strong (Î±) After writing all the strategies and payoffs in the same matrix, find the Bayesian Nash equilibriums, depending on the value of Î± (Î± â‰¤ 1/2 or Î± â‰¥1/2). • Show less