Two firms A and B are engaged in an advertising contest. Each firm can choose its advertising spending a 0 and b 0. Given their ad spendings a, b, Firm A's profit equals

and Firm B's profit equals

a = 9a a2 ab b = 12bb2 ab

(a) (3pts) Find firm A's best response function, namely find A's optimal strategy a as a function of B's strategy b.

(b) (3pts) Find firm B's best response function.

(c) (3pts) Use the two best response functions to find the Nash equilibrium.

5. (6pts; for students in 505 only) Each of three players simultaneously announces an integer between 1 and 10 (including 1 and 10). Let a be the average of the three integers announced. A person whose integer is the closest to the number ta, where 0 ? t ? 1, is a winner. All winners evenly split 1$; other players receive nothing.

For what values of t will both (1, 1, 1) and (3, 3, 3) be Nash equilibria? Try to provide as answer as possible.