Question

1. 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. However, a politician who votes for a salary increase faces 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? (Hint: there is more than one.) (60%)

Answer 1

SOLUTION:-

Nash Equilibrium is a stable state where no patricipant can gain by making a change in strategy if all others' strategies remains unchanged, with this in mind:

There are 4 Nash equilibrium in the game:

* 1 when none of the politicians vote for an increase in their salary, if any 1 politician changes his vote at a time, he would face a negative payoff of -1000$ due to public scorn, thus neither has any incentive to deviate from this.

* 3 each when 1 of the politicians doesn't vote towards getting an increase in their salary and the other 2 vote towards getting it, The politician who chooses not to vote towards it would have a payoff of 2500$(Through increase in salary) and the other 2 will have a payoff of 1500$ (2500 increase -1000 due to public scorn because of their vote). Again noone has a reason to deviate, if one of the politicians who voted would deviate, there would be only 1 politician voting for it who will have a payoff of -1000(Instead of 1500) and the other 2 with 0(Instead of 2500 and 1500 respectively)

* All 3 voting for the increase in salary will not be a Nash equilibrium as all 3 have an incentive to deviate and not vote so that they have a payoff of 2500(When other 2 vote for increase, and they don't get any public scorn) instead of the 1500 now.

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