Question

Question 2 8 pts (8 points) Use the payoff matrix to answer the following questions. Firm Strategy A X 8,8 18,-4 Firm Y -4, 18 10, 10 1. (2 points) Does Firm Jhave a dominant strategy? If so, what is it? 2. (2 points) Identify all of the Nash equilibrium positions. If there is no Nash equilibrium, indicate "None." 3. (2 points) Assume this is a one-shot, simultaneous game. Where will the game end? If the end game cannot be predicted indicate "No prediction possible." 4. (2 points) What is the maximum interest rate at which collusion could occur between these firms with a trigger strategy if the game is played an infinite number of times? You must show your calculation to receive credit.

Answer 1

Table

J/K	A	B
X	(8*,8•)	(18*,-4)
Y	(-4,18•)	(10,10)

A) both firm have dominant strategy

For J : dominant Strategy: X

For K, strategy which is Dominant : A

B) pure STRATEGY NE exists : (X,A)

c) yes, if game is static , played only for one period, then

it ends at NE : (X,A)

d) collusion will be sustained if both play (Y,B) every period, as each gets higher payoff as compared to NE payoff of 8 for both

We use grim trigger strategy to sustain Collusion every period,

if any player deviates then it gets 18 in that period and punishment start next period onwards and both play only Nash equilibrium of static game always, where it gets only 8.

so if d is the discount factor, then present discount value of payoff if sustains Collusion is

Vc = 10+ 10d + 10d² + 10d³ +...

= 10/(1-d)

PDV of cheating payoff

Vd = 18+8d + 8d² + 8d³ + ....

= 18+8/(1-d)

Sustain Collusion if

Vc > Vd

10/(1-d) > 18+8/(1-d)

10d>8

d >.8

as d = 1/(1+r), r : interest rate

1/(1+r) > .8

r < 1/4 = .25

Maximum Interest rate = 25%