Question

1. Suppose you and your partner typically vote oppositely in elections so that their your votes “cancel each other out.” Each one of you gains 2 units of happiness from a vote for your positions (and lose two units of happiness from a vote against their positions). However, the cost of voting for each one of you is 1 unit of happiness. Using a diagram (2X2 table) to represent a game in which you two choose whether to vote or not to vote.

2. You and your partner agreed not to vote in the coming presidential elections. Would such an agreement improve happiness? Explain your answer using the diagram from question 1. Would such an agreement be an equilibrium (Nash Equilibrium)? Explain your answer.

Answer 1

Part 1)

Let us construct a Payoff matrix for this case:

*	*	Your	Partner
*	Payoffs	Vote	Not Vote
You	Vote	(-1,-1)	(1,-2)
	Not Vote	(-2,1)	(0,0)

Part 2)

Now let us analyse the payoff matrix. At the position of (Vote,Vote); we can see that if You decide to change your strategy to Not Vote, keeping Your Partner's strategy the same, you will get lesser happiness(payoff). Hence there is no benefit for you to unilaterally change your strategy. We can say the same for Your Partner, there is no benefit for them to unilaterally change their strategy. Hence the strategy profile (Vote,Vote) is a Nash equilibrium where both of you get a payoff of -1.

Now, if You and Your Partner agree to not vote, both have happiness levels of 0, which are better than -1. Hence it is a better situation as compared to when both of you vote. Hence this agreement increases overall as well as individual happiness.

However, if one of you decides to unilaterally change your strategy from (Not Vote,Not Vote); then you will earn a better payoff of 1 as compared to 0. Hence this is NOT a Nash equilibrium.