Abby and Brooke are back on the campaign trail once more. Each political candidate is strategizing their campaign's advertising budget. The amount of money that each invests in advertising directly influences their chances of winning the election. We'll assume that both candidates have extremely deep pockets so that they can each allocate any positive amount of money towards their advertising campaign. Let x denote Abby's advertising expenditure, let y denote Brooke's, and assume that both candidates must select their levels simultaneously. Given that Abby spends x and Brooke spends y, the probability of Abby winning the election is x x+y and the probability of Brooke winning is y x+y . The winning candidate gains value v > 0 and the losing candidate gains nothing. Each candidate must pay for their advertising, whether or not they win the election. Write out the expected payoff functions A and B for the two players as a function of advertising budget levels x and y. (b) (2 marks) By fixing one variable and differentiating with respect to the other, try to optimize each player's payoff by looking for a best response function. What do you notice that is different from other examples we've seen in the course? (c) (2 marks) Find the Nash equilibrium spending levels for Abby and Brooke's advertising campaigns. What are each candidate's expected payoffs at this equilibrium