Consider two firms: Apple and Banana.Each of them is considering whether to expand its capacity. The decision depends on the payoffs, which depend on what the other player does. Assume, for sake of simplicity, that each faces three possibilities: Do Nothing (DN), a Small expansion, or a Large expansion. The payoff matrix (giving net present values of profits) is given by (Apple's Payoff, Banana's Payoff):

Banana

AppleDN Small Large

DN$38m, $38m $30m, $40m $18m, $36m

Small $40m, $30m $32m, $32m $16m, $24m

Large $36m, $18m $24m, $16m $4m, $4m

(a)Suppose the game is played only once. What is the Nash Equilibrium?

(b)Assume now that this game is played repeatedly: the firms decide whether to expand capacity every 5 years, with the net present values of payoffs during those five years given by the payoffs shown there.For what values of the interest rate r [where this interest rate is the rate for a 5-year period - so $1 earned in 5 years is worth 1/(1+r) today] can both firms choosing to "do nothing" be sustained as an equilibrium if the firms play Nash reversion strategies?