Oregon EC 427 - Two people are involved in a dispute

Two people are involved in a dispute. Person 1 does not know whether person 2 is strong or weak; she assigns probability 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 ? < 1/2 and ? > 1/2.