Q. Consider a race between 2 candidates. Whoever spends the most money in their campaign wins the election and gets a utility v >= 3 (v more than equal to 3). They also value campaign funding in terms of dollars spent. Therefore, after spending ci on a campaign, if candidate i is elected, her utility is v-ci, and otherwise, it is simply be -ci. Ties are broken by a supreme court that is unpredictable and selects either candidate with probability 1/2. Both candidates are rich and have budgets B > v, and spend in whole dollars so that ci (0,1,....,v). The candidates simultaneously select ci.
a. Are there any pure-strategy Nash equilibria? If so, list them. If not, explain why not.
b. Suppose that v = 3, and one mixed strategy equilibrium where each player randomizes among (0,1,2).