100%(1)1 out of 1 people found this document helpful
This preview shows page 1 - 2 out of 4 pages.
Homework Assignment #2Graduate Game Theory1.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 mustvote in favor of it. Each legislator’s payoff is a function of his or her vote choice and theoutcome of the vote. Specifically, a legislator incurs a cost ofc >0 if he or she votes infavor of the pay raise and receives a benefit ofb > cif the pay raise is enacted.(a) Assuming that the legislators vote sequentially and publicly (i.e., legislators observeany votes cast prior to making their decision), draw the extensive form game.123nnnnnnnyyyyyyy00000-c0-c0-c00bb-cb-cb-cbb-cb-cb-cbb-cb-cb-c(b) Find a Nash equilibrium of this game by backward induction. Which (if any) legislatoris 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.123nnnnnnnyyyyyyy00000-c0-c0-c00bb-cb-cb-cbb-cb-cb-cbb-cb-cb-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 bybackward induction?