Question: A customer comes to a restaurant. There are two types of customer, sophisticated and opportunistic. Both types are equally probable. The restaurant offers a fancy


A customer comes to a restaurant. There are two types of customer, sophisticated and opportunistic. Both types are equally probable. The restaurant offers a fancy dish with no discount and a plain dish with a discount. A sophisticated customer gets utility equivalent to $1 from the fancy dish and utility equivalent to $0 from the plain dish with a discount. She values good service by a waiter at $3 and bad service at $0. Ifservice is good she gives the waiter a tip of $2 which is deducted from her utility and added to the waiter's utility. An opportunistic customer gets utility equivalent to $2 from the fancy dish and utility equivalent to $3 from the plain dish with a discount. He values good service by a waiter at $1 more than bad service. He never gives tips. Assume that the waiter observes what the customer orders but does not observe the customer's type. The waiter decides whether to give good or bad service. Good service requires extra effort from the waiter giving disutility equivalent to $1. Draw the extensive form of the game and find all the pure strategy weak sequential equilibria
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