Given the stage game above/below. Suppose that the players play (C,C) in period t = 1; 3; 5; ::: and plays (D,D) in period t = 2; 4; 6; ::. Compute the discounted payoff of each player. Repeated GameConsider the game below, which is infinitely repeated at t = 1, 2, .... Both players discountthe future at rate d E (0, 1). The stage game isCDC 5,5 | 0,6D 6,0 1,1

Given, Two Players : Player1 and Player2 Player 1 has two options : Cooperate and Defect and Player 2 has two options : Cooperate and Defect Discount rate is given as : rate δ ∈ (0,1)The Pay-off Matrix is given as : Player 2 Cooperate Defect Player 1 Cooperate 5,5 0,6 Defect 6,0 1,1 Now, For Player 1 : When Player2 plays cooperate, Player1 plays Defect When Player2 plays Defect, Plater1 plays Defect For Player 2 : When Player 1 plays Cooperate, Player2 plays Defect When Player1 plays Defect, Player2 plays Defect Therefore, Nash Equilibrium is obtained at (Defect, Defect) i.e. (1,1) This can be shown in the following matrix :Now, But we have another available outcome which will make both these players better off by providing higher payoff than that of Nash equilibrium. This pareto optimal outcome is (Cooperate, Cooperate) =(5,5) Therefore in a grim-trigger strategy game both players can mutually agree to choose a strategy "Cooperate" in current period and if the co-operation is obeyed then continue with this strategy else play dominant strategy eternally. Having this condition set forth we can find the discount rate "d" such that cooperation is honoured Economic Value(EV) of obeying co-operation >Economic Value of defecting co-operation Economic Value(EV) for player 1 of obeying co-operation is obtained by discounting future payoff from the co-operation= 5+5d+5d^2+... We have d<1, therefore using geometric sum formula EV for Player 1 from co-operation = 5/(1-d) Defecting by Player 1 will result in an outcome equals to (Defect, Cooperate) =(6,0) Similarly when Player 1 defect he gets the highest possible payoff equals to 6 but after that both players will choose a Nash equilibrium and earn payoff of 1 EV for Player 1 from defect = 6+d+d^2+... = 5+1+d+d^2 =5+1/(1-d) Now as we discussed earlier Economic Value(EV) of obeying co-operation for Player 1>= Economic Value(EV) of defecting co-operation for Player 1 5/(1-d)>=5+1/(1-d) 4/(1-d)>=5 0.8>=1-d d>=0.2 ( for player 1)..If d is greater than 0.2 then Player 1 will always honour the cooperation else defect.For Player 2, Economic Value(EV) of obeying co-operation for Player 2>= Economic Value(EV) of defecting co-operation for Player 2 5/(1-d)>=5+1/(1-d) 4/(1-d)>=5 0.8>=1-d d>=0.2 ( for player 2)..If d is greater than 0.2 then Player 2 will always honour the cooperation else defect.

Answered: Given the stage game above/below.…

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Given the stage game above/below. Suppose that the players play (C,C) in period t = 1; 3; 5; ::: and plays (D,D) in period t = 2; 4; 6; ::. Compute the discounted payoff of each playe

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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