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: 4points

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 of the current year and not those of past years.