To Vote or Not to Vote: Two candidates, D and R, are running for mayor in a town with n residents. A total of 0 < d < n residents support candidate D, while the remainder, r = n − d, support candidate R. The value for each resident for having his candidate win is 4, for having him tie is 2, and for having him lose is 0. Going to vote costs each resident 1.
a. Let n = 2 and d = 1. Write down this game as a matrix and solve for the Nash equilibrium.
b. Let n > 2 be an even number and let d = r = n/2. Find all the Nash equilibrium.
c. Assume now that the cost of voting is equal to 3. How does your answer to (a) and (b) change?