3. Consider the following two-player game:HLDT2,3 0,24,0 1,1(a) What are (pure- and mixed-strategy) Nash equilibria of this game?(b) Suppose the game is repeated twice, and each player's payoff is the sum of thepayoffs they obtain in the two periods. What are the subgame perfect equilibriaof the game?(c) Suppose the game is repeated indefinitely, and each player discounts his/her payoffwith a discount factor 8 € (0, 1). Find a subgame perfect equilibrium in which(H, T) is played in every period on the equilibrium path. Compute the discountfactor & needed for this equilibrium.(d) Suppose the game is repeated indefinitely, and each player discounts his/her payoffwith a discount factor & € (0, 1). Find a subgame perfect equilibrium in which(H,T) and (L,T) are played alternately on the equilibrium path. Compute thediscount factor & needed for this equilibrium.(e) Suppose the game is repeated indefinitely. Player 1 (the row player) discountsher payoff with a discount factor 8₁ € (0,1). Player 2 discounts his payoff witha discount factor d₂ = 0. That is, in any given period, player 2 only cares abouthis payoff in that period. Can you find a subgame perfect equilibrium in which(H,T) is played in every period on the equilibrium path. If no, explain. If yes,compute the discount factor 8₁ needed for this equilibrium.(f) Suppose the game is repeated indefinitely. Player 1 (the row player) discountsher payoff with a discount factor 8₁ € (0,1). Player 2 discounts his payoff witha discount factor d2 0. Can you find a subgame perfect equilibrium in which(H,T) and (L,T) are played alternately on the equilibrium path? If no, explain.If yes, compute the discount factor 81 needed for this equilibrium.(g) Suppose the game is repeated indefinitely. Player 1 (the row player) discountsher payoff with a discount factor d₁ € (0,1). Player 2 discounts his payoff witha discount factor 82 = 0. Can you find a subgame perfect equilibrium in which(H,T) and (L, D) are played alternately on the equilibrium path? If no, explain.If yes, compute the discount factor 8₁ needed for this equilibrium.2(h) Bonus problem: Suppose the game is repeated indefinitely. Player 1 (the rowplayer) discounts her payoff with a discount factor d₁ € (0, 1). Player 2 discountshis payoff with a discount factor d₂ = 0. In addition, player 2 is forgetful: in anygiven period, he can only remember player 1's action in the previous period (heforgets everything else, including his own actions in the past). Player 2's forget-fulness is commonly known. Player 1 never forgets. Can you find an equilibriumin which (L, D) is not played every period on the equilibrium path? Explain.

Given pay-off Player 2 T D Player 1 H 2,3 0,2 L 4,0 1,1

- Consider the following two-player game: H L T D 2,3 0,2 4,0 1,1 (a) What are (pure- and mixed-strategy) Nash equilibria of this game? (b) Suppose the game is repeated twice, and each player's payoff is the sum of the payoffs they obtain in the two periods. What are the subgame perfect equilibria of the game?

- Consider the following two-player game: H L T D 2,3 0,2 4,0 1,1 (a) What are (pure- and mixed-strategy) Nash equilibria of this game? (b) Suppose the game is repeated twice, and each player's payoff is the sum of the payoffs they obtain in the two periods. What are the subgame perfect equilibria of the game?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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