Aya and I paired up together for this activity to construct a matrix based on game theory. We were inspired by the recent Year 12 assembly that took place on Monday about the recruitment process of school prefects. For our matrix, Aya and I decided that this matrix would work in such a way whereby there are two students running for prefect, which are represented by Aya and I. Both Aya and I have two choices: which is to vote (in which I vote for her, vice versa) or not to vote (in which I do not vote for her, vice versa). In order for it to be a win-win situation for the both of us, we have to each cast a vote to each other, in which I cast a vote for Aya and she reciprocates, therefore in order for both parties to be satisfied and for this to be impartial for the both of us, this has to be built on trust in which I trust Aya to vote for me as I shall do the same for her.
As illustrated in the image above, here are the possibilities of our matrix:
#1. 1-1 situation - If both Aya and I decided not to cast in any votes for each other, we would have 1 vote each which is the vote that we have as individuals. Which leaves both of us in the same position, neither one of us being better off than the other.
#2. 0-3 situation - If Aya kept to her word as we agreed on before the voting by casting a vote but little did she know that I would be double-crossing her by not casting a vote for her in order to be ahead of her in terms of votes as I decided to exploit her trust in me, that would leave her with 0 votes and me with 3 votes. In a situation like this whereby one party votes for the other whereas the other does not, the party who voted is left with 0 votes as he/she gave his/her vote away but does not receive anything in return and for the party who did not vote, it proves to be an advantage for him/her as by not giving his/her vote away, he/she receives an extra vote from the party who voted on top of the existing vote that he/she has with another vote kept for by himself/herself, which leaves him/her with 3 votes in total. (vice versa for subject, Grace)
#1. 1-1 situation - If both Aya and I decided not to cast in any votes for each other, we would have 1 vote each which is the vote that we have as individuals. Which leaves both of us in the same position, neither one of us being better off than the other.
#2. 0-3 situation - If Aya kept to her word as we agreed on before the voting by casting a vote but little did she know that I would be double-crossing her by not casting a vote for her in order to be ahead of her in terms of votes as I decided to exploit her trust in me, that would leave her with 0 votes and me with 3 votes. In a situation like this whereby one party votes for the other whereas the other does not, the party who voted is left with 0 votes as he/she gave his/her vote away but does not receive anything in return and for the party who did not vote, it proves to be an advantage for him/her as by not giving his/her vote away, he/she receives an extra vote from the party who voted on top of the existing vote that he/she has with another vote kept for by himself/herself, which leaves him/her with 3 votes in total. (vice versa for subject, Grace)
#3. 2-2 situation - If Aya and Grace went along with their agreement before the voting which is to both cast a vote for each other, they would have 2 votes each as on top of their existing vote that they individually started with, they would have an extra vote casted from each other.
Conclusion:
Nash Equilibrium - The Nash equilibrium for our matrix is when both parties do not cast a vote for each other, which is depicted and explained in the 1-1 situation. Both parties are in Nash equilibrium when each party goes with the decision that would place them in the best situation after evaluating the possible decisions that could be taken by the opposing party, vice versa. In this situation, both Aya and I are in Nash equilibrium when we go with the best decision for ourselves taking into consideration of the decision of the other. Therefore, the safest decision Aya could make is to not vote (in which she will either be left with 1 or 3) as she will have to consider the possibility of me deceiving her which will put her in a worse off position if she were to vote (in which she will be either be left with 0 or 2), vice versa. Therefore, both parties would go without voting for each other in order to be in the safest position which will leave them in the 1-1 situation.
Dominant strategy - The dominant strategy for Aya and myself would be to go without casting a vote for the other party as by choosing this strategy, if the opposing party were to decide to not vote, you will be left with 1 and if the opposing party were to decide to vote, you will be left with 3 which leaves you in a better position than if you were to vote which will leave you with either 0 or 2 which is a smaller payoff than going with the other strategy which is not to vote.
**Please note that Aya's blog commentary is interpreted differently from mine despite us devising our subject of our game theory and matrix together. Thank you. :D Bye now. :)