Suppose two players are bargaining with each other If a deal

Suppose two players are bargaining with each other. If a deal is reached, Player A\'s payoff is x_A - w, and Player B\'s payoff is x_B + w. If a deal is not reached, Player A will get a, and Player B will get b. The variable x can be one of three possible values: 5, 10, or 15. Total value (v) is x_A + x_B. Player A\'s bargaining power is h, and Player B\'s bargaining power is k, where h + k = 1. For each of the scenarios below, find the maximized joint value x, each players final payoffs (A and B), and the negotiated w. In your answer, show all your work and include a graph that displays the total value given x, the Best Alternative to a Negotiated Ageement (BATNA), and the final payoffs (A and B).

a) x_A = x_B = x, a = 0, b = 0, h = 1/2, k = 1/2

b) x_A = x_B = x, a = 2, b = 4, h = 1/2, k = 1/2

c) x_A = x_B = x, a = 2, b = 4, h = 1/4, k = 3/4

d) x_A = 20x, x_B = -(x²), a = 0, b = 0, h = 1/4, k = 3/4

Solution

b) x_A = x_B = x, a = 2, b = 4, h = 1/2, k = 1/2