17. We are asked to find the smallest value for X in the game to the left for which Firm 1 Low Firm 2 High is a Nash equilibrium. So, X must be large enough to lead Firm 2 to choose High if Firm 1 chooses Low. Since the value of X is a payoff to Firm 2 all we need to find is the smallest number among the choices greater than 6.

   Firm 2 will switch to Low if the payoff to playing High is less that 6, the payoff it earns for playing Low when Firm 1 plays Low. Thus we can rule out answers a, b, and c, (3, 4, and 5) respectively since all these values are below 6. However if X = 7 Firm 2 will stay with High and we have a Nash equilibrium.

Copyright © 1995-2004 OnLineTexts.com, Inc. - All Rights Reserved