Question

Problem : Signaling Games (12 pts) Consider the game of imperfect information depicted in the game tree below: BE Cowboy is coward Cowboy is Gunslinger Prob. - Quiche Quiche 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 p of each state is 0.5. The Cowboy knows which type they are but the Outlaw does not. 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. a) List all of the strategies belonging to each player. Note that each player has two information sets. Cowboy: PC (Continued on next page)

Answer 1

	Cowboy	outlaw
Fight	(0,1)	(-5,1)
Walk	(5,0)	(0,0)

This is the strategy table if the cowboy is coward.

Now here is the table if the cowboy is not a coward.

	Cowboy	outlaw
Fight	(-1,-1)	(0,-1)
Walk	(0,0)	(1,0)

These are the strategy table of the game.