GraduateGameTheoryHomework2-Answers - Homework Assignment#2 Graduate Game Theory 1 Sequential Strategic Voting Suppose three legislators are voting on

GraduateGameTheoryHomework2-Answers - Homework Assignment#2...

This preview shows page 1 - 2 out of 4 pages.

Homework Assignment #2 Graduate Game Theory 1. Sequential Strategic Voting. Suppose three legislators are voting on whether to give them- selves a pay raise. In order for the raise to take effect, at least 2 of the 3 legislators must vote in favor of it. Each legislator’s payoff is a function of his or her vote choice and the outcome of the vote. Specifically, a legislator incurs a cost of c > 0 if he or she votes in favor of the pay raise and receives a benefit of b > c if the pay raise is enacted. (a) Assuming that the legislators vote sequentially and publicly ( i.e. , legislators observe any votes cast prior to making their decision), draw the extensive form game. 1 2 3 n n n n n n n y y y y y y y 0 0 0 0 0 -c 0 -c 0 -c 0 0 b b-c b-c b-c b b-c b-c b-c b b-c b-c b-c (b) Find a Nash equilibrium of this game by backward induction. Which (if any) legislator is advantaged in this equilibrium, the one to vote first, second, or third? Answer. The equilibrium is displayed graphically below. Notice that the first legis- lator to vote gets the pay raise at no cost to himself or herself. 1 2 3 n n n n n n n y y y y y y y 0 0 0 0 0 -c 0 -c 0 -c 0 0 b b-c b-c b-c b b-c b-c b-c b b-c b-c b-c (c) Show that there is a Nash equilibrium in which the third legislator votes “no,” re- gardless of how the other legislators vote. Why can’t this equilibrium be found by backward induction?
Image of page 1
Image of page 2

You've reached the end of your free preview.

Want to read all 4 pages?

  • Spring '11
  • JohnPaddy
  • Game Theory, Nash, b-c b-c b-c

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture