How a repeated relationship among members can secure them

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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 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.

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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.

Reference no: EM13873997

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