Question

TI (5,5) | (3,10) (0,4) M (10,3) (4,4)2,2) B (4,0) (2,-2) (-10,-10) Let G(8) denote the game in which the game G is played by the same players at times 0, 1,2,3,... and payoff streams are evaluated using the common discount factor a. For which values of is it possible to sustain the vector (5, 5) as a subgame per- fect equilibrium payoff, by using Nash reversion (playing Nash eq. strategy infinitely upon a deviation) as the punishment strategy.

Answer 1

NE of stage Game = < M, C > Now let using G-T rightarrow Grim Trigger strategy, where 2 players cooperate in playing < T, L > as long as other player also cooperates, It any one deviates to play M (by P1) & C(by P2), then Move to NE of stage Game < M, C > forever as a punishment then present value of cooperation payoff = 5 + 5 delta + 5 delta^2 + V^c = 5/1 - delta Now P. V. of deviation payoff = 10 + 4 delta + 4 delta^2 + V^D = 10 + 4 delta/(1 - delta) Now cooperate if V^C greaterthanorequalto V^D 5/1 - delta greaterthanorequalto 10 + 4 delta/(1 - delta) implies 5 greaterthanorequalto 10 - 10 delta + 4 delta implies 6 delta greaterthanorequalto 5, delta greaterthanorequalto 5/6 Thus delta elementof [5/6, 1] Ans