In the following normal-form game, what strategies survive iterated elimination of strictly dominated strategies? What are the pure-strategy Nash equilibria? L R T 2,0 1,1 4,2 M 3,4 1,2 2,3 1,3 0,2 3,0
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- The mixed stratergy nash equalibrium consists of : the probability of firm A selecting October is 0.692 and probability of firm A selecting December is 0.309. The probability of firm B selecting October is 0.5 and probability of firm selecting December is 0.5. In the equilibrium you calculated above, what is the probability that both consoles are released in October? In December? What are the expected payoffs of firm A and of firm B in equilibrium?Explain all will rate what is always true for a pure nash equilibrium of a two-person non zero-sum game A.No player can improve his payoff with a unilateral change of strategy B. it is a Pareto maximum of the payoff matrix C. No player can worsen the payoff of his opponent with a unilateral change of strategy D. It gives worse payoffs to both players than any berge equilibriumSuppose t = 1 and c = 3/5, what is the payoff matrix for the game and state all Nash equilibria in pure strategies. Also find the unique Nash equilibirum in mixed strategies.
- Consider the two-player game illustrated here. a. For each player, derive those strategies which survive the iterativedeletion of strictly dominated strategies.b. Derive all strategy pairs that are Nash equilibria.if Y = 4 (a) If ⟨a,d⟩ is played in the first period and ⟨b,e⟩ is played in the second period, what is the resulting (repeated game) payoff for the row player? (b) What is the highest payoff any player can receive in any subgame perfect Nash equilibrium of the repeated game?Two players bargain over $20. Player 1 first proposes a split of(n, 20 - n), where n is an integer in {0, 1, ..., 20}. Player 2 can either accept or reject this proposal. If player accepts it, player 1 obtains $n and player 2 obtains $(20 - n). If player 2 rejects it, the money is taken away from them and both players will get $0. Question: Find two subgame perfect Nash equilibria of this game and state clearly each player's equilibrium strategies (recall that in a dynamic game, a player's strategy is a complete-contingent plan). Explain why the strategy profiles form a subgame perfect equilibrium.
- Find mixed-strategy Nash equilibria for the following two games.Is the set of SPE of any extensive form game with perfect information is identical to the set of Nash Equilibria of the induced normal form game? If yes, provide a proof. If no, provide an explanation by illustrating a game. [Maximum word limit for this question is 80 words.]if Y =4 (b) What is the highest payoff any player can receive in any subgame perfect Nash equilibrium of the repeated game?
- Firm A Firm B Low Price High Price Low Price (2, 2) (10, −8) High Price (−8, 10) (15, 15) Suppose the game is infinitely repeated, and the interest rate is 10 percent. The firms are allowed to collude and make joint decisions. Both firms agree to charge a high price, provided no player has charged a low price in the past. This collusive outcome will be implemented with a trigger strategy that states that if any firm cheats (by charging a low price), then the agreement is no longer valid and each firm may make their own independent decisions. Will the trigger strategy be effective in implementing the collusive agreement? Please explain and show all necessary calculations.Players 1, 2, and 3 are playing a game in which the strategy of player i isdenoted yi and can be any nonnegative real number. The payoff function for player 1 is V1(y1,y2,y3) = y1 + y1y2 - (y1)2,for player 2 is V2(y1,y2,y3) = y2 + y1y2 - (y2)2,and for player 3 is V3(y1,y2,y3) = (10 - y1 - y2 - y3)y3.These payoff functions are hill shaped. Find a Nash equilibrium. (Hint: Thepayoff functions are symmetric for players 1 and 2.)The Nash equilibrium of the accompanying game is Player 1 Multiple Choice O O O (Y. B). (X, B). X Y Z (Z. C). Player 2 A 9, 8 5, 6 10, 9 none of the provided answers because there is no Nash equilibrium in this game. B 10, 12 12, 20 13, 4 C 3, 15 4, 10 8, 12
