A town council consists of three members who vote every year on their own salary increases. Two

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Question:

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 their 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 of the current year and not those of past years.