Consider the ultimatum-offer bargaining game described in this chapter and recall the cutoff-rule strategy for player 2.

(a) Suppose that player 1 selects the strategy p = 50 and player 2 selects the cutoff-rule strategy with p - = 50. Verify that these strategies form a Nash equilibrium of the game. Do this by describing the payoffs players would get from deviating.

(b) Show that for any p ∈ [0, 100], there is a Nash equilibrium of the game in which an agreement is reached at this price.

Describe the equilibrium strategy profile and explain.