Question

2. Three city politicians vote on whether to allow themselves a salary increase of $2,500 per year; if at least two of the politicians vote in favour of the increase, then it is implemented. A politician who votes for a salary increase would face public scorn from citizens. Assume that public scorn costs a politician $1,000 per year. Suppose that the politicians vote at the same time, and cannot observe each others’ voting (that is, this is a simultaneous game). What is this game’s Nash equilibrium? Is there more than one? (15%)

Answer 1

As all players want the outcome ,where other two chose to vote in favour and he not to choose.so its payoff will be 2500.

But while taking decision every player thing rationally ,there can be three situations for him.

First when both others choose to vote then his best move is not to choose. Payoff will 2500

Second when both choose not to vote then his best move is not to choose and payoff will 0

Third when among others two one choose to vote and other not to vote ,then his best move will be choose to vote and payoff will 1500.

So not to vote is most prefer move for each player ,so

As all three choose not to vote,and outcome would be all three would get nothing and payoff would be 0.

,There is an other nash equilibrium other than this one.

,when two players choose to vote and one choose not to vote and payoff would be ,for the player not choose it would be 2500 and for other two 1500. And no players want to change its move given other players move .