B is offering to buy an object from S. S values the good at $4 (type...

 

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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 to all three possibilities, a fact known commonly to both players. B values the good at $5. B makes a take-it-or-leave-it offer to S. (a) Analyze the perfect Bayesian equilibrium of this game. (b) What if S's valuation is distributed uniformly over [2, 4]? Repeat the same exercise as in (a). 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 to all three possibilities, a fact known commonly to both players. B values the good at $5. B makes a take-it-or-leave-it offer to S. (a) Analyze the perfect Bayesian equilibrium of this game. (b) What if S's valuation is distributed uniformly over [2, 4]? Repeat the same exercise as in (a).