Question
Consider a first-price sealed-bid auction for a single indivisible good with two bidders, i=1,2. Bidders is valuation, v i , is given by v i
Consider a first-price sealed-bid auction for a single indivisible good with two bidders, i=1,2. Bidders is valuation, vi, is given by
vi=ti +0,5
where ti is a random variable drawn independently from a commonly known uniform distribution over [0,1]. The realization of ti is privately observed by bidder i.
the object is awarded to the highest bidder who pays her own bid (i.e. first price). The losing bidder pays nothing. In the case of equal bids, each bidder wins the object with equal probability and pays her own bid.
a. Derive the symmetric Bayesian Nash equilibrium of this game where each bidder uses a linear function of her private information, i.e of the form bi=sigmati+betta.
b. What is the conditional expected payoff of bidder i with type ti in this equilibrium?
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