There are 6 voters. Voters 1, 2, 3 and 4 prefer candidate A and voters 5 and 6 prefer candidate B. Each voter cared about the number of votes cast for their preferred candidate - the more votes their preferred candidate got the better of the voter was.

In this problem we assume that voters care only about whether their preferred candidate wins the election (the best outcome), ties (the next best outcome), or loses (the worst outcome).

(a) Construct payoff functions for a representative voter who prefers can- didate A and for a representative voter who prefers candidate B. Un- derline the best responses. (b) Do voters have a dominant strategy in this game? (c) Use the best response functions to determine whether each of the fol- lowing is or is not a Nash equilibrium strategy combination: (A,A,A,A,B,B), (B,B,B,B,B,B), (A,A,A,A,B,A), (A,A,A,B,B,B), (A,B,B,B,B,B), (B,B,B,B,B,A,A). Then indicate for each equilibrium strategy combination, whether it is strict or not. (d) Find all the Nash equilibria of the game.