Section 2.B illustrates how to graph best-response curves for the tennis-point game. Section 4.B notes that when there are multiple equilibria, they can be identified from multiple intersections of the best-response curves. For the battle-of-the-sexes game in from Chapter 4, graph the best responses of Harry and Sally on a p-q coordinate plane. Label all of the Nash equilibria.
S8. Consider the following game:
(a) For what values of x does this game have a unique Nash equilibrium? What is that equilibrium?
(b) For what values of x does this game have a mixed-strategy Nash equilibrium? With what probability, expressed in terms of x, does each player play Yes in this mixed-strategy equilibrium?
(c) For the values of x found in part (b), is the game an example of an assurance game, a game of chicken, or a game similar to tennis? Explain.
(d) Let x 5 3. Graph the best-response curves of Rowena and Colin on a p-q coordinate plane. Label all the Nash equilibria in pure and mixed strategies.
(e) Let x 5 1. Graph the best-response curves of Rowena and Colin on a p-q coordinate plane. Label all the Nash equilibria in pure and mixed strategies.