3. Consider the following two-player game:HLT D2,3 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 & € (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 8 € (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 d₁ € (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 d₁ € (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 d₂ = 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.

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 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? (c) Suppose the game is repeated indefinitely, and each player discounts his/her payoff with a discount factor 8 € (0, 1). Find a subgame perfect equilibrium in which (HT) is played in every period on the equilibrium nath Compute the discount.

Consider the following two-player game: H L T D 2,3 0,2 4,0 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? (c) Suppose the game is repeated indefinitely, and each player discounts his/her payoff with a discount factor 8 € (0, 1). Find a subgame perfect equilibrium in which (HT) is played in every period on the equilibrium nath Compute the discount.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.9P

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