Consider two students looking for trouble on a Saturday night. After arguing about some silly topic, they are on the verge of a fight. Each individual only observes his own ability as fighter, which is summarized as the probability of winning the fight if both attack each other: either high, pH or low pL, where < pL < pH < 1. The probability that fighter is type pH is q. If a type K student chooses to attack and its rival does not, then he wins with probability pK, where K {H,L}. It must be noted that is such that pK < pK <1. If a type K student chooses not to attack but its rival does then the probability that the student (who did not attack) wins is pK where 0 < pK < pK. Finally if neither student attacks there is no fight. A student is then more likely to win the fight the higher is his type. A students payoff in case there is no fight is 0, the benefit of wining a fight is B > 0 and losing fight is L < 0. (a) Set up the Bayesian game. (b) A symmetric strategy is a strategy where both players use the same strategy. Under what conditions is there a symmetric Bayes Nash equilibrium where every student attacks regardless of his type. (c) Under what conditions is there symmetric Bayes Nash equilibrium in which every student attacks only if his type is high