Answer Happy

Problem #1: Separating Equilibria (10 pts) Consider the game of asymmetric information depicted in the game tree below: Cowboy is Coward (Prob. - p) Cowboy is Gunslinger (Prob. -1-p) Quiche Quiche Beer Fight Walk Fight Walk 0,1 5,0 -5,1 0,0 0,0 0,-1 1,0 In this game, the players are a Cowboy who wanders into a town in the Wild West, and an Outlaw who terrorizes the town. The Cowboy may be either a Coward or a Gunslinger; the probability of each state is 0.5 (i.e. p=0.5). The Cowboy knows which type they are but the Outlaw does not. The Cowboy's payoff is listed first and the Outlaw's second in each terminal node. The Cowboy wants breakfast, but the hotel serves only two things for breakfast: Quiche and Beer. The Outlaw enjoys picking on the weak, and would like to pick a fight with a Cowboy who is a Coward, but is not actually a good shot and would lose a fight to a Gunslinger. The Outlaw can observe what the Cowboy orders for breakfast before deciding whether to start a Fight or Walk away. Beer Fight Walk Fight Walk
b) Which of the Cowboy's strategies are signaling strategies? How does the Outlaw interpret what he observes under each of these strategies? c) For each of the signaling strategies from b), what is the Outlaw's best response? d) Based on your answers to c), for each of the signaling strategies from b), does the Cowboy have any incentive to "lie" by changing their strategy in either state of nature? e) The previous four parts have walked you through finding the separating equilibria of this game. What are they?