Question

1. Suppose two small-town video stores, store A and store B, compete. The two stores collude and agree to share the market equally. If neither store cheats on the agreement, each store will make $2,500 a day in economic profits. If only one store cheats, the cheater will increase its economic profits to $4,000 and the store that abides by the agreement will incur an economic loss of $1,000. If both firms cheat, they both will earn zero economic profits. Neither store has any way of policing the actions of the other. (a) What is the payoff matrix if the game is played just once? (b) What is the equilibrium if the game is played only once? Explain. (c) What do you think will happen if the game is played many times? Why? (d) What do you think will happen if a third firm comes into the market? Will it be harder or easier to achieve cooperation among the three firms? Why?

Answer 1

                                                                                    B

                                                           Collude                                       Cheat

Collude     A    Cheat	2500,2500	-1000,4000
4000,-1000	0,0

B) Given firm B move collude , firm A best move us cheat.

Given firm B move cheat , firm A best move is cheat.

So firm A has dominant strategy of cheat.

And by same reasoning , firm B also have dominant strategy of cheat.

So in equilibrium both firm will choose dominant straight.

And nash equilibrium payoff:(0,0)

C) When game played many times so most likely equilibrium will be when both choose to collude.

If someone cheat in first period and then it have to earn zero profit in rest of the period so it wont cheat

So both firms choose collude.

D) It will be easier to achieve cooperation.

If one firm cheat then rest two firm will react and lower prices which result in lost for cheating firm , knowing this no firm would cheat.