Grace and I applied the idea of game theory to the voting for prefects. We assumed that we both want to be selected as one of the members of prefects. The matrix is illustrated below. The points (0, 1, 2, 3) represent the possibility of being selected.
We have 2 choices between voting for each other ( trusting the partner or voting for other people (not trusting the partner). Assuming that both of us cannot vote for ourselves.
As you can see in the matrix, there are 3 possible situations;
3 points / 0 point - If one voted for the other and one did not, the one that obtained vote is more superior since she has one more vote than the one who voted for her. Thus she gets 3 points.
Whereas the one who voted for the partner gets 0 points because she has made her partner more superior, and also, she has also gave voted to someone else which means that she has made the someone to be more superior than her.
2 points - If they voted for each other, they get the same opportunity to be elected and both of them have 1 guaranteed vote. Thus, they are more superior than the other candidates.
1 point - If they voted other candidates doubting each other, neither of them get any votes. Yet, within the two the possibility of being elected is the same so none is superior.
DOMINANT STRATEGY
There is a dominant strategy here which is to "No Vote". If you choose to vote for the other, you will only get 2 or 0 points where as if you do not vote for the other, you will either get 3 or 1 points. Therefore, you will most likely to choose to vote for each other.
NASH EQUILIBRIUM
There is a Nash equilibrium here which is to "No Vote". If the opponent choose not to vote and do not have incentives to change her decision, It is better off for you not to vote because of the points gained.
As both Grace and I know the dominant strategy and the Nash equilibrium, we ended up choosing not to vote for each other. ;)
As you can see in the matrix, there are 3 possible situations;
3 points / 0 point - If one voted for the other and one did not, the one that obtained vote is more superior since she has one more vote than the one who voted for her. Thus she gets 3 points.
Whereas the one who voted for the partner gets 0 points because she has made her partner more superior, and also, she has also gave voted to someone else which means that she has made the someone to be more superior than her.
2 points - If they voted for each other, they get the same opportunity to be elected and both of them have 1 guaranteed vote. Thus, they are more superior than the other candidates.
1 point - If they voted other candidates doubting each other, neither of them get any votes. Yet, within the two the possibility of being elected is the same so none is superior.
DOMINANT STRATEGY
There is a dominant strategy here which is to "No Vote". If you choose to vote for the other, you will only get 2 or 0 points where as if you do not vote for the other, you will either get 3 or 1 points. Therefore, you will most likely to choose to vote for each other.
NASH EQUILIBRIUM
There is a Nash equilibrium here which is to "No Vote". If the opponent choose not to vote and do not have incentives to change her decision, It is better off for you not to vote because of the points gained.
As both Grace and I know the dominant strategy and the Nash equilibrium, we ended up choosing not to vote for each other. ;)