This exercise asks you to combine the investment and hold-up issue from this chapter with the "demand" bargaining game explained in Exercise 4 of Chapter 19. Consider an investment and trade game whereby player 1 first must choose an investment level x ≥ 0 at a cost of x₂ . After player l's investment choice, which player 2 observes, the two players negotiate over how to divide the surplus x. Negotiation is modeled by a demand game, in which the players simultaneously and independently make demands m1 and m2. These numbers are required to be between 0 and x. If m₁ + m₂ ... x (compatible demands, given that the surplus to be divided equals x), then player 1 obtains the payoff m₁- x₂ and player 2 obtains m₂ . In contrast, if m₁ + m₂ ≤ x (incompatible demands), then player 1 gets -x² and player 2 gets 0. Note that player 1 must pay his investment cost even if the surplus is wasted owing to disagreement.

(a) Compute the efficient level of investment x*.

(b) Show that there is an equilibrium in which player 1 chooses the efficient level of investment. Completely describe the equilibrium strategies.

(c) Discuss the nature of the hold-up problem in this example. Offer an interpretation of the equilibrium of part (b) in terms of the parties' bargaining weights.