Question

The payoff matrix below shows how annual profits of two major computer sellers, Dell and Sony, will vary with and without advertising.

a. Are there dominant strategies for both firms? Explain.

b. What is the Nash equilibrium?

c. Is this game a prisoner’s deliema?

		Dell’s strategies
		Advertise	Don’t Advertise
Sony’s strategies	Advertise	Dell’s profit: 12 million Sony’s profit: 20 million	Dell’s profit: 6 million Sony’s profit: 28 million
	Don’t Advertise	Dell’s profit: 18 million Sony’s profit: 14 million	Dell’s profit: 8 million Sony’s profit: 36 million

Answer 1

(a)

A dominant strategy is the strategy chosen by one player, irrespective of strategy chosen by the other player.

Dell will choose Advertise whether Sony chooses Advertise or Don't Advertise, since payoff is higher in either case (12 > 6 and 18 > 8). So Dell's dominant strategy is to choose Advertise.

Sony will choose Advertise when Dell chooses Advertise since payoff is higher (20 > 14), but will choose Don't Advertise when Dell chooses Don't Advertise since payoff is higher (36 > 28). So Sony has no dominant strategy.

(b)

A Nash equilibrium will exist if each player chooses his strategy on basis of strategy chosen by the other player.

When Sony chooses Advertise, Dell's best strategy is Advertise since payoff is higher (12 > 6).

When Sony chooses Don't Advertise, Dell's best strategy is Advertise since payoff is higher (18 > 8).

When Dell chooses Advertise, Sony's best strategy is Advertise since payoff is higher (20 > 14).

When Dell chooses Don't Advertise, Sony's best strategy is Don't Advertise since payoff is higher (36 > 28).

Nash equilibrium is: (Advertise, Advertise). [See below].

(c)

If the players deviate from this equilibrium, in neither of the strategy profiles can both of them increase their individual payoff. Therefore this is not a Prisoners' Dilemma, since both firms will not have incentive to deviate at the same time.