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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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The game theory is always dominant when more than two players are involved in the game. In Nash Equilibrium, players use unique strategies to win the game. This is either dominant game or silent strategy.
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