Assume you are one of the two bidders in a second-price sealed bid auction for a preserved grilled cheese sandwich which purportedly bore the portrait of the Virgin Mary: • This sandwich is worth $8000 to you. • You know that your rival bidder’s valuation is uniformly distributed between $0 and $12,000. a) What is the probability that your bid exceeds your rival’s bid given that you know your rival’s valuation is uniformly distributed between $0 and $12,000? (In other words, what is the probability that your rival’s bid is lower than your valuation?) Remember the equilibrium bidding strategies for a SPA in weakly dominant strategies ! b) What is your rival’s average bid, if you win the auction (considering that he must have bid below your bid)? c) What is your expected payoff from this auction, if you win the bidding ? (Hint: Combine b) and c), i.e. compute the payoff from winning giving the probability of winning)
Assume you are one of the two bidders in a second-price sealed bid auction for a preserved grilled cheese sandwich which purportedly bore the portrait of the Virgin Mary:
• This sandwich is worth $8000 to you.
• You know that your rival bidder’s valuation is uniformly distributed between $0 and $12,000.
a) What is the probability that your bid exceeds your rival’s bid given that you know your rival’s valuation is uniformly distributed between $0 and $12,000? (In other words, what is the probability that your rival’s bid is lower than your valuation?) Remember the equilibrium bidding strategies for a SPA in weakly dominant strategies !
b) What is your rival’s average bid, if you win the auction (considering that he must have bid below your bid)?
c) What is your expected payoff from this auction, if you win the bidding ? (Hint: Combine b) and c), i.e. compute the payoff from winning giving the probability of winning)
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