Question: Continuing with problem 2, assume that each firm can choose only two outputs-the ones from parts a and \(\mathrm{b}\) in question $2 .$ Denote these outputs \(q_{a}\) and \(q_{b}\).

1. Compute the payoff/profit matrix showing the four possible outcomes.
2. Show that this game has the same basic properties as the Advertising Game. In particular, each firm's optimal output is independent of what the other firm produces. Now consider firms playing an infinitely repeated version of this game and consider the following strategy for each firm: (i) produce \(q_{b}\) in period 1 , (ii) produce \(q_{b}\) in period \(t\) if both firms produced \(q_{b}\) in all preceding periods, and (iii) produce \(q_{a}\) in period \(t\) if one or more firms did not produce \(q_{b}\) in some past period. Assume each firm acts to maximize its sum of discounted profits where the discount rate is \(r\).
3. Find the values for \(r\) such that this strategy pair is a Nash equilibrium.

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