## (Solved) (Question 6, chapter 11) The owner of a new restaurant is planning to advertise to attract customers. In the Bayesian game, Nature determines the...

1. (Question 6, chapter 11) The owner of a new restaurant is planning to advertise to attract customers. In the Bayesian game, Nature determines the restaurantâ€™s quality, which is either high or low. Assume that each quality occurs with equal probability. After the owner learns about quality, he decides how much to advertise. Let A denote the amount of advertising expenditure. Assume there is a single consumer. The consumer observes how much advertising is conducted, updates her beliefs about the quality of the restaurant and then decides whether or not to go to the restaurant. Assume that the price of a meal is fixed at \$50. The value of a high quality meal to a consumer is \$85 and of a low quality meal is \$30. A consumer who goes to the restaurant and finds out that the food is of low quality ends up with a payoff of -20. If the food is of high quality, then the consumer receives a value of 35. Upon learning of the high quality, a consumer anticipates going to the restaurant a second time. Thus, the payoff to a consumer from visiting a high-quality restaurant is actually 70 (2 x 35). For the restaurant owner, assume the cost of providing a meal is 35 whether it is of low or high quality. If the restaurant is of high quality, the consumer goes to the restaurant, and the restaurant spends A in advertising, then its profit is 2 x (50 â€“ 35) â€“ A = 30 â€“ A. If the restaurant is of low quality and the consumer goes, the restaurant spends A, then its profit is (50 â€“ 30) â€“ A = 15 â€“ A. These payoffs are summarized below. If the consumer does not go to the restaurant, her payoff is zero and the ownerâ€™s payoff is â€“A. Find a separating perfect Bayes-Nash equilibrium.

2. Define (in your own words) a separating equilibrium and a pooling equilibrium.Â

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