1. Two players will each be dealt one card from a shuffled deck containing one Ace, one King and one Queen. Each player only observes his/her own card. Model the situation by specifying a probability distribution on an appropriate set of type profiles and describe each player's beliefs for each possible realization of his/her type. Are the players' type independent?

2. Osborne 282.1 solve

EXERCISE 282.1 (Fighting an opponent of unknown strength) Two people are in- volved in a dispute. Person 1 does not know whether person 2 is strong or weak; she assigns probability a to person 2's being strong. Person 2 is fully informed. Each person can either fight or yield. Each person's preferences are represented by the expected value of a Bernoulli payoff function that assigns the payoff of 0 if she yields (regardless of the other person's action) and a payoff of 1 if she fights and her opponent yields; if both people fight, then their payoffs are (-1, 1) if person 2 is strong and (1, -1) if person 2 is weak. Formulate this situation as a Bayesian game and find its Nash equilibria if a