Two firms are playing a pricing game of the following form

Firm 2

low price high price

Firm 1 low price 3,3 8,-2

high price -2,8 4,4

1/Find all Nash equilibria if the game is played only once.

2/ Suppose the firms play the game 10 times. What is the subgame perfect Nash equilibrium in this 10-5imes repeated game? What is the average payoff per round in the Nash equilibrium?

3/Now assume that the game is repeated infinitely and taht future payoffs(profits) are discounted using the interest rate r.

i. Does this infinitely-repeated game have a Nash equilibrium in which both firms set low prices in every round? Explain your answer.

ii. If r =0.5, does this infinitely-repeated game have a Nash equilibrium in which bothe forms set a high price in every round?

iii. If r=0.2, does this infinitely-repeated game have a Nash equilibrium in which both forms set a high price in every round?