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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 member would like a higher salary, but would like to vote against it herself because that looks good to the voters (because the member is afraid that he/she is not re - elected as a town council next time). Specifically, the payoff s are as follows:
Raise passes, own vote is No: 10 points
Raise fails, own vote is No: 5 points
Raise passes, own vote is Yes: 4 points
Raise fails, own vote is Yes: 0 points
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 increases every year if a) every member serves a 3 - year term; b) every year in rotation one of them is up for reelection; and c) the townspeople have short memories, remembering only the votes on the salary-increase motion of the current year and not those of past years.
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