Question

All of the action is on Advertising budgets. Specifically, total value s (in dollars) get splits between two competitors according to their advertising shares. If a_1 is firm ones advertising investment (in dollars close parentheses, then its profit is given by:

[(a_1)/(a_1 + a_2)] * S - a_1

(the same applies for firm 2) Both a_1 and a_2 must be non negative. If both firms invest zero in advertising, then they split the market.

a.) Determine the synthetic Nash Equilibrium of the game whereby firms choose a_i independently and simultaneously.

b.) Determine the jointly optimal level of advertising that is the level a* that maximizes joint profits.

c.) Given firm 2 sets a_2 to a*, determine firms 1's optimal advertising level.

d.) Suppose that firms compete indefinitely in each period t= 1,2..., and that the discount factor is given by \delta \in [0,1]. Determine the lowest value of \delta such that, by playing grim strategies, firms can sustain an agreement to set a* in each period.

Answer 1