3.Suppose that two clothing manufacturers, Lands' End and L.L. Bean, are deciding what price to charge for very similar field coats. The cost of producing these coats is $100. The coats are very close substitutes, so customers flock to the seller that offers the lowest price. If both firms offer identical prices, each receives half the customers. For simplicity, assume that the two firms have the choice of pricing at prices of $103, $102, or $101. The profit each firm would earn at various prices (Lands' Ends Profit, LL Bean's Profit) is shown in the payoff matrix below.

	LL Bean
Lands' End		$103	$102	$101
$103	($150, $150)	($0, $200)	($0, $120)
$102	($200, $0)	($100, $100)	($0, $120)
$101	($120, $0)	($120, $0)	($50, $50)

a. What is the Nash equilibrium and expected profits to LL Bean and Lands' End of this game?

b. Suppose this is a mixed strategy game in which LL Bean has a 25% percent chance of choosing a price of $101, a 25% chance of choosing price of $102, and a 50% chance of choosing $103, while Lands End has a 1/3 chance of choosing each strategy. What's the expected payoff to LL Bean? What's the expected payoff to Lands End?

c.Suppose that in hopes of raising prices, L.L. Bean announces a price of $103 for its coat before Lands' End announces their prices. Do you think this strategic move will be successful for LL Bean? Explain why or why not.