3. Consider a race between 2 candidates. Whoever spends the most money in their campaign wins the election and gets a utility v3. 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 vci, and otherwise, it is simply 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, find one mixed strategy equilibrium where each player randomizes among {0,1,2}. (Try to write down the normal form game.) 3. Consider a race between 2 candidates. Whoever spends the most money in their campaign wins the election and gets a utility v3. 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 vci, and otherwise, it is simply 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, find one mixed strategy equilibrium where each player randomizes among {0,1,2}. (Try to write down the normal form game.)