Question1 (a.b.c)

1. (14 pts) Consider the following game. Susan selects a pencil or a nickel and places the selected item in either her left or right hand. Placing a pencil in her left hand may be represented by (PL), placing a nickel in her right hand by (Np), etc. If Susan selects a pencil John can observe which hand holds it. If she selects a nickel he cannot. John then tries to guess which hand holds the item. He can guess either left (L) or right (R). If John guesses correctly he wins the item. If he guesses incorrectly Susan wins the item. The loser receives a payoff of 0. Winning the pencil results in a payoff of 10. Winning the nickel results a payoff of 5. a. Represent this game in the extensive form. That is graph the game tree. (Use the letters given in parenthesis to describe the pure strategies. If necessary attach primes (',", etc.) to distinguish them.) b. How many information sets are there for Susan? For John? c. Describe one specific strategy profile for this game. (Use the letters given in parenthesis to describe the pure strategies. If necessary (matching what you did in part (a)) attach primes (', ", etc.) to distinguish them.)