Question

Anne and Bill are two travellers returning home from a tropical island where they both purchased an identical antique. At their arrival, they discover that the airline has smashed the antiques. The airline manager asks each traveler to write down the compensation desired, any whole number between $2 and $10 (the maximum the manager is allowed to give each traveler). Let n_i = {2, 3, . . . , 10} be the number written down by i = A, B. Assume that Anne and Bill each write the desired compensation in a sealed envelope that is given directly to the manager. If both write the same number, they each receive that amount. But if, say, n_A > n_B, then the manager gives each the smaller of the two (i.e., n_B) with an adjustment: believing that Anne is lying and Bill is being truthful, the manager punishes Anne by giving n_B − 2 compensation, while rewarding Bill for his supposed honesty by paying him n_B + 2.

(a) Represent this situation as a matrix game; i.e., write down the matrix representation of this game.

(b) What is Anne’s best response when Bill writes n_B = 7 as his desired compensation?

(c) What is Bill’s best response when Anne writes n_A = 5 as her desired compensation?

(d) Find all the pure strategy NE of the game.

Answer 1