3. (20 points) Suppose there is an upcoming presidential election between Cersei Lannister and Daenerys Targaryen. Cersei and Daenerys will choose how to position themselves on the political spectrum in order to win the election. Consider a population of 210 million voters, each of whom has a preferred position on a five-point political spectrum: Far Left (FL), Left (L), Center (C), Right (R), and Far Right (FR). We suppose that these voters are spread symmetrically around the center of the political spectrum. The discrete distribution of their locations is shown by a histogram, or bar chart, in the following figure.

The height of each bar indicates the number of voters located at that position. In this example, of the 210 million voters, 40 million are Far Left, 70 million are Left, 10 million are Center, 60 million are Right and 30 million is Far Right. Here are how the votes are allocated: When both candidates choose the same, each candidate gets exactly one-half of the votes. When the two candidates choose different positions, the more-left candidate gets all the votes at or to the left of her position while the more-right candidate gets all the votes at or to the right of her position. In addition, each candidate gets the votes in central positions closer to her than to her rival, and the two of them split the votes from any voters in a central position equidistant between them.

1. Fill the following game table for the optimal political position game by calculating the payoffs according to the information provided. Payoffs should reflect the number of voters each candidate will get when they position themselves in corresponding locations on the political spectrum. Briefly explain your answer

		Daenerys
		FL	L	C	R	FR
Cersei	FL
	L
	C
	R
	FR

2. What is the Nash Equilibrium of this game? That is, where should Cersei and Daenerys position themselves on the political spectrum at equilibrium? Explain your answer and interpret the result. Is the outcome consistent with what you have learned in the class?

70 65 60 55 50 45 40 35 L.L. 30 25 20 15 10 5 0 FL FR 70 65 60 55 50 45 40 35 L.L. 30 25 20 15 10 5 0 FL FR