Question

answer parts e f g pls

4. Consider the following game presented in the strategic form: A B C W X Y Z 8,9 14,9 5,0 1,4 8,0 19,13 7,18 9.16 9,80 33, 335, 130, 84 (a) What is the relationship between an equilibrium concept and predic- tions regarding the outcome of a game? (b) Find all the Nash equilibrium strategy combinations. For each equilib- rium, discuss whether it is or it is not strong dominant strategy equi- librium. (c) For each equilibrium from the previous part, find all the strategy com- binations that Pareto-dominate the Nash equilibrium strategy combi- nation. (d) Find all the Pareto-optimal strategy combinations. Now consider that two players with discount factor 0 < < 1 play the following stage game in each of an infinite number of periods. (e) Imagine that you have been asked for advice on how to play the game. What wold be the intended equilibrium path that you would try to attain? Why did you choose it? (f) What is your punishment threat? Why did you choose it? Is it credi- ble? Explain. (g) What are the no-defection conditions?

Answer 1

Answer:

Given that:

Now consider that two players with discount factor 0 < $\delta$ < 1 play the stage game in each of an infinate number of periods.

Payoff matrix

	W	X	Y	Z
A	8,9	14,9	5,0	1,4
B	8,0	19,13	7,18	9,16
C	9,80	33,33	5,13	0,84

NE : (B,Y)

e)

$\rightarrow$ The possible cooperative eqm should be (C,X)

$\rightarrow$ Where both get 33, Both are better off as compared to (B,Y)

f)

$\rightarrow$ punishment threat, NE : (B,Y) will be played each period .

$\rightarrow$ Both will be worse off, as compared to Cooperation payoff

since it's the NE, so it's credible

g)

$\rightarrow$ P1 will not deviate, bcoz he is getting Maximum payoff of 33

using Grim trigger strategy;

$\rightarrow$ p2 has incentive to deviate, so if P1 plays C , p2 has incentive to play Z , as it gets 84

$\rightarrow$ next period onwards, punishment starts,

so NE is played

so, if discount factor is d

$\rightarrow$ then present discount value PDV of Cooperation payoff

Vc = 33+33d + 33d2+33d3+ ...

= 33/(1-d)

Vd = 84+ 18d +18d2 + 18d3 +....

= 84 + 18d/(1-d)

Cooperate if, Vc > Vd

33/(1-d) > 84+ 18d/(1-d)

33 > 84-84d + 18d

66d > 51

d > 51/66 = .772

$\rightarrow$ So discount factor should be between .772 & 1, for no defection