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

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. Specifically, the payoffs of
each are as follows:

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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

(i) every member serves a 3-year term,

(ii) every year in rotation one of them is up for
reelection, and

(iii) 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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