Question

Consider the following one-shot simultaneous game:

		Firm 2
		Advertising campaign	Do nothing
Firm 1	Advertising campain	3, 8	20, 8
	Offer discounts	6, 8	9, 2
	Do nothing	7, 10	9, 12

a. State all the dominated strategies in the game, by which strategy they are dominated, and whether weakly or strictly.
b. What is the equilibrium outcome by dominance (by elimination of dominated strategies), if any?
c. What is (or are) the pure strategy Nash equilibria of this game?

Answer 1

a) Firm 2 : Advertising Campaign weakly dominate Do nothing.

Advertising Campaign is at least as good as Do nothing but sometimes better.

So Do nothing is a weakly dominated strategy for firm 2.

b) (Do Nothing, Advertising Campaign) That is (7,10) is the equilibrium outcome by dominance.

c) (Do Nothing, Advertising Campaign) That is (7,10) and (Advertising Campaign, Do nothing) That is (20,8)

are the Nash Equilibria but Firm 2 prefers (7,10) and force Firm 1 to play down and go ahead with this nash equilibrium.