Question

3. Consider the game illustrated by the payoff matrix below: Jeffrey B1 B2 -4,- 4 1 ,-6 Curtis A2 -6,1 0,0 b. Suppose that the game is repeated 10 times and assume a discount factor 8 (where 0< 8 < 1). i. [2] What does each player choose to do in the 10th round of play? ii. [2] Can Curtis and Jeffrey credibly commit to playing (A2, B2) in any of the rounds that they play? c. Suppose now that the game is repeated an infinite number of times. Consider the following strategies: Curtis and Jeffrey will play (A2, B2) every round, but if one of them deviates at any point, they will play (A1, B1) for every following period. i. [2] is the above a plausible Nash Equilibrium? ii. [8] Test your above response by calculating the values of d required to sustain cooperation.

Answer 1

Table

	B1	B2
A1	(-4*,-4•)	(1*,-6)
A2	(-6,1•)	(0,0)

NE of stage game : (A1,B1)

B) if game is repeated for a limited time period, such that the end period of game is known,

Then in every period, only NE of stage game is played, if the game has only one NE

Bcoz both players know, that in end period, 10th Period, only Credible NE is played : (A1,B1)

So in penultimate period, 9th Period, nobody will Cooperate, since in 10th Period, only NE is played

Similarly if we move backwards , in every period, only NE could be played only

ii) in neither of the rouds, that players can credibly commit to play (A1,B1)

c) yes, (A2,B2) could be sustained as SPNE in every period

ii) let discount factor : d

For P1, Cooperation payoff

I Present value of Cooperation payoff- UC=of odtodze - If any player defects, then it gets 1 & Next pd onwards, both get 4 so vd = 1 +48) + (-482) + (-483)+. = 1-48 Date I Page No. (15) 80 Cooperate of vicz vid 487 18 - 5821 18² 15 Ming needed= 15= 2. Ang