B is offering to buy an object from S. S values the good at $4 ( type H), or $3 (type M), or $2 (type L). But S's exact valuation is unknown to B, who simply attaches equal probabilities, a fact commonly known to both players. B values the good at $5. B makes an ultimatum offer to S.
a) Analyze the perfect Bayesian equilibrium of this game.
b) What if S's valuation is distributed uniformly over [2,4]. What is the perfect Bayesian equilibrium?