A town council consists of three members who vote every year on their own salary increases. Two Yes votes are needed to pass the increase. Each mem ber would like a higher salary but would like to vote against it herself because that looks good to the voters. Specifically, the payoffs of each are as follows:
Raise passes, own vote is No: Raise fails, own vote is No: Raise passes, own vote is Yes: Raise fails, own vote is Yes:
Voting is simultaneous. Write down the (three-dimensional) payoff table, and show that in the Nash equilibrium the raise fails unanimously. Examine how a repeated relationship among the members can secure them salary in creases every year if (1) every member serves a 3-year term, and every year in rotation one of them is up for reelection, and (2) the townspeople have short memories, remembering only the votes on the salary-increase motion of the current year and not those of past years.