Using the same prices and payoff matrix as in #3, now suppose the duopolists play the game repeatedly, forever (even though forever is weird). Each period they play the same game, setting prices 2 simultaneously at the beginning of the period, and then getting payoffs that period according to the matrix. They know they are playing this infinitely repeated game. State strategies that, for a condition you will present, imply that in Nash equilibrium they will sustain the higher price each period. What is the condition for this on the discount rate (use r to denote it)? In this outcome an equilibrium because the duopolists care about one another's profits? Explain your answer to the latter briefly.

Duopolist 2: 500 550 200,000 180,000 500 200,000 220,000 Duopolist 1: 220,000 210,000 550 180,000 210,000