Consider an election contested by two parties, 1 and 2. Each is trying to win votes away from the other by advertising. Namely, if party 1 spends x 0 millions of dollars on advertising and party 2 spends y 0 millions, party 1 gets the share x/(x + y) of the votes and party 2 gets the share y/(x + y) of the votes. The parties' costs of advertising are proportional to x and y. Namely, if x + y > 0, then party 1's payoff is equal to its vote share minus its advertising costs, x/(x + y) - x, and party 2's payoff is equal to y/(x + y) - y. If x = y = 0, then each party gets 0. Parties move sequentially. First, party 1 selects x. Then, party 2 observes x and selects y.

(a) Find the best response function of party 2.

(b) Find the subgame-perfect Nash equilibrium (SPNE). Which party gets more votes in it?

(c) Is there a Nash equilibrium (not SPNE) in which party 2 gets more votes than party 1? If yes, then find any (just one) such an equilibrium. If not, then show that for any such a strategy profile some player has a profitable deviation.