1. [Normal Form Game] Consider the following game on advertising and price strategy between two local...

1. [Normal Form Game] Consider the following game on advertising and price strategy between two local businesses (P is price and A is advertising). Payoffs are representative of profits. Find the Nash equilibrium. If there was collusion between the two businesses, could they cooperate and improve their profits?

			Sarah’s Sandwiches
Bandit’s Bagels		Low P, Low A	Low P, High A	High P, Low A	High P, High A
	Low P, Low A	30, 20	20, 25	35, 15	30, 30
	Low P, High A	35, 15	40, 30	45, 8	40, 25
	High P, Low A	25, 25	25, 35	53, 47	25, 50
	High P, High A	30, 20	40, 30	55, 20	50, 45

Solutions

Expert Solution

When Sarah Sandwich chooses (Low P, Low A), Bandit Bagel chooses (Low P, High A) since payoff is maximum (35 > 30, 30 > 25).

When Sarah Sandwich chooses (Low P, High A), Bandit Bagel chooses either (Low P, High A) or (High P, High A) since payoff is maximum (40, 40 > 25 > 20).

When Sarah Sandwich chooses (High P, Low A), Bandit Bagel chooses (High P, High A) since payoff is maximum (55 > 53 > 45 > 35).

When Sarah Sandwich chooses (High P, High A), Bandit Bagel chooses (High P, High A) since payoff is maximum (50 > 40 > 30 > 25).

When Bandit Bagel chooses (Low P, Low A), Sarah Sandwich chooses (High P, High A) since payoff is maximum (30 > 25 > 20 > 15).

When Bandit Bagel chooses (Low P, High A), Sarah Sandwich chooses either (Low P, High A) since payoff is maximum (30 > 25 > 15 > 8).

When Bandit Bagel chooses (High P, Low A), Sarah Sandwich chooses (High P, High A) since payoff is maximum (50 > 47 > 35 > 25).

When Bandit Bagel chooses (High P, High A), Sarah Sandwich chooses (High P, High A) since payoff is maximum (45 > 30 > 20, 20).

Therefore, there are two Nash Equilibria:

(1) Sarah Sandwich chooses (Low P, High A) and Bandit Bagel chooses (Low P, High A), or

(2) Sarah Sandwich chooses (High P, High A) and Bandit Bagel chooses (High P, High A). [See below]

(b) If they could cooperate, they would choose to maximize joint profit and would both choose (High P, High A) since joint profit is maximized (= 50 + 45 = 95).

Rahul Sunny answered 1 year ago

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