Thanks for any help! Suppose the game is repeated forever and both firms always

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Thanks for any help!

Suppose the game is repeated forever and both firms always discount the next period's profit at a rate of delta = 0.5 relative to the current period's profit. Firm 1 announces and (somehow) commits to a strategy of producing at the Cartel output (or price) in the first round of the game, and continuing at this level as long as Firm 2 cooperates and produces at the Cartel output (or price); but, if Firm 2 ever fails to cooperate, Firm 2 will play its single-period game Nash Equilibrium strategy forever after. What is the payoff of the game for Firm 2 (its discounted flow of profits) if it cooperates forever? For the Cournot, Stackelberg, and Bertrand Models, what is the payoff in the first period for Firm 2 if. instead of cooperating, it maximizes its single period profits? Will Firm 2 choose to cooperate in the repeated Cournot game? Stackelberg? Bertrand? Explain.

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