Question

Synergy and Dynaco are the only two firms in a specific high-tech industry. They face the following payoff matrix as they decide upon the size of their research budget:

		Synergy’s Decision
		Large Budget	Small Budget
Dynaco’s Decision	Large Budget	$30 million, $20 billion	$70 million, $0
	Small Budget	$0, $30 million	$50 million, $40 million

1. If Synergy believes Dynaco will go with a large budget, it will choose a SMALL OR LARGE?? budget. If Synergy believes Dynaco will go with a small budget, it will choose a SMALL OR LARGE?? budget. Therefore, Synergy DOES OR DOES NOT?? have a dominant strategy.

2. If Dynaco believes Synergy will go with a large budget, it will choose a SMALL OR LARGE?? budget. If Dynaco believes Synergy will go with a small budget, it will choose a SMALL OR LARGE?? budget. Therefore, Dynaco DOES OR DOES NOT?? have a dominant strategy.

3. True or False: There is a Nash equilibrium for this scenario. (Hint: Look closely at the definition of Nash equilibrium.)

Answer 1

1.

If Synergy believes Dynaco will go with a large budget, it will choose a LARGE budget since payoff is higher ($20 million > 0).

If Synergy believes Dynaco will go with a small budget, it will choose a SMALL budget since payoff is higher ($30 million > $20 million).

Therefore, Synergy DOES NOT have a dominant strategy.

2.

If Dynaco believes Synergy will go with a large budget, it will choose a LARGE budget since payoff is higher ($30 million > 0).

If Dynaco believes Synergy will go with a small budget, it will choose a LARGE budget since payoff is higher ($70 million > $50 million).

Therefore, Dynaco DOES have a dominant strategy.

(3) TRUE

When Dynaco chooses Large budget, Synergy chooses Large budget since payoff is higher (20 million > 0).

When Dynaco chooses Small budget, Synergy chooses Small budget since payoff is higher (40 million > 30 million).

When Synergy chooses Large budget, Dynaco chooses Large budget since payoff is higher (30 million > 0).

When Synergy chooses Small budget, Dynaco chooses Large budget since payoff is higher (70 million > 50 million).

Therefore, Nash equilibrium is: (Large budget, Large budget) [See below]