Holdup: Consider an ultimatum game (T = 1 bargaining game) in which before player 1 makes his offer to player 2, player 2 can invest in the size of the pie. If player 2 chooses a low level of investment (L) then the size of the pie is small, equal to vL, while if player 2 chooses a high level of investment (H) then the size of the pie is large, equal to vH. The cost to player 2 of choosingLis cL, while the cost of choosing H is cH. Assume that vH > vL > 0, cH> cL > 0, and vH - cH > vL - cL.
a. What is the unique subgame-perfect equilibrium of this game? Is it Pareto optimal?
b. Can you find a Nash equilibrium of the game that results in an outcome that is better for both players as compared to the unique subgame perfect equilibrium?