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Persons 1 and 2 are forming a firm. The value of their relationship depends on the effort that they each expend. Suppose that person i's utility from the relationship is is person i's effort and xj is the effort of the other person (i = 1, 2).
(a) Compute the partners' best-response functions and find the Nash equilibrium of this game. Is the Nash equilibrium efficient?
(b) Now suppose that the partners interact over time, which we model with the infinitely repeated version of the game. Let d denote the discount factor of the players. Under what conditions can the partners sustain some positive effort level x = x1 = x2 over time? (Postulate strategies and then derive a condition under which the strategies form an equilibrium in the repeated game.)
(c) Comment on how the maximum sustainable effort depends on the partners' patience.
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