(A fight with imperfect information about strengths) Two

(A fight with imperfect information about strengths) Two peopleare involved in a dispute. Person 1 does not know whether person 2 is strongor weak; she assigns probability a to person 2’s being strong. Person 2 is fullyinformed. Each person can either fight or yield. Each person’s preferences arerepresented by the expected value of a Bernoulli payoff function that assigns thepayoff of 0 if she yields (regardless of the other person’s action) and a payoff of1 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 isweak. Formulate this situationas a Bayesian game and find its Nash equilibria if a < 12and if a > 12.