Suppose Grace and Lisa are to go to dinner. Lisa is visiting Grace from out of town, and they are to meet at a local restaurant. When Lisa lived in town, they had two favorite restaurants: Bel Loc Diner and the Corner Stable. Of course, Lisa’s information is out of date, but Grace knows which is better these days. Assume that the probability that the Bel Loc Diner is better is p > 1/2 and the probability that the Corner Stable is better is 1 - p. Nature determines which restaurant Grace thinks is better. Grace then sends a message to Lisa, either “Let’s go to the Bel Loc Diner,” “Let’s go to the Corner Stable,” or “I don’t know [which is better].” Lisa receives the message, and then Grace and Lisa simultaneously decide which restaurant to go to. Payoffs are such that Grace and Lisa want to go to the same restaurant, but they prefer it to be the one that Grace thinks is better. More specifically, if, in fact, the Bel Loc Diner is better, then the payoffs from their actions are as shown in the first as shown. If, instead, the Corner Stable is better, then the second as shown describes the payoffs. a. Find a perfect Bayes–Nash equilibrium in which Grace and Lisa always go to the better restaurant. b. Find a pooling perfect Bayes–Nash equilibrium.
Suppose Grace and Lisa are to go to dinner. Lisa is visiting Grace from out
of town, and they are to meet at a local restaurant. When Lisa lived in town,
they had two favorite restaurants: Bel Loc Diner and the Corner Stable. Of
course, Lisa’s information is out of date, but Grace knows which is better
these days. Assume that the probability that the Bel Loc Diner is better is
p > 1/2 and the probability that the Corner Stable is better is 1 - p. Nature
determines which restaurant Grace thinks is better. Grace then sends a
message to Lisa, either “Let’s go to the Bel Loc Diner,” “Let’s go to the
Corner Stable,” or “I don’t know [which is better].” Lisa receives the message, and then Grace and Lisa simultaneously decide which restaurant to go to. Payoffs are such that Grace and Lisa want to go to the same restaurant, but they prefer it to be the one that Grace thinks is better. More specifically, if, in fact, the Bel Loc Diner is better, then the payoffs from their
actions are as shown in the first as shown. If, instead, the Corner
Stable is better, then the second as shown describes the payoffs.
a. Find a perfect Bayes–Nash equilibrium in which Grace and Lisa always go to the better restaurant.
b. Find a pooling perfect Bayes–Nash equilibrium.
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