lecture3to5_bidding_behavior

lecture3to5_bidding_behavior - Bidding Behavior We assume...

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Bidding Behavior We assume people attempt to maximize their payoff from participating in an auction. Hence, we are in a sense trying to determine their optimal bids. However, an auction is a game in which the payoff an individual earns from any given bid depends on the bids placed by others. Hence, the notion of an optimal or “best” bid cannot usually be defined in isolation. We need some conjecture about how others will bid. Rod Garratt ECON 177: Auction Theory With Experiments
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Bayes Nash Equilibrium Our prediction for bidding behavior is based on the idea that people bid optimally based on their predictions about how others will bid and that these predictions are correct. How everyone bids depends, of course, on their values. It is assumed that each bidder knows her own value, but only knows the probability distribution function that determines other bidders’ values. Hence, bidders must best respond to their beliefs regarding the bid functions used by other bidders and the likelihood of the values that will enter into these bid functions. In other words, our predictions for bidding behavior are the Bayes Nash equilibrium bid functions. Rod Garratt ECON 177: Auction Theory With Experiments
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Definition A Bayes Nash equilibrium for an auction is a bid-function profile b = ( b 1 ( · ) ,..., b n ( · )) such that for each bidder i and each possible value v i for bidder i, the bid b i ( v i ) maximizes bidder i’s expected payoff given the vector b - i = ( b 1 ( · ) b i - 1 ( · ) , b i +1 ( · ) b n ( · )) of bid functions for the other n - 1 bidders. This definition is not quite operational yet, since we do not explain how to compute the expected payoff to a bid. We will do this explicitly in the following sections, using the particulars of the different auction formats. Rod Garratt ECON 177: Auction Theory With Experiments
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Second-Price Auctions In the second-price auction the bidder who places the highest bid wins and she pays the amount of the second-highest bid. In these auctions, your bid determines whether or not you are the auction winner, but it does not determine how much you pay. You might think that this suggests you should bid very high to ensure that you win the auction. - happens in laboratory experiments Faulty logic! Rod Garratt ECON 177: Auction Theory With Experiments
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Hypothetical scenario I Suppose your value is $52, you bid $90, and the only other player bids $70. In this case, because you have the highest bid you win the auction. However, your earnings from the auction would be $52 - $70 = $-18. That is, you lose $18. In fact, whenever you bid above your value you run the risk of losing money in this way. Moreover, it is important to understand that you cannot improve your payoff by bidding more than your value! If you need to bid more than your value to win the auction, it means the price you will have to pay is more than your value, in which case you will lose money by winning the auction. If the second-highest bid is below your value, then a bid equal to your value will win the auction anyway and earn the same payoff as a higher bid.
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This note was uploaded on 12/26/2011 for the course ECON 177 taught by Professor Garratt during the Fall '09 term at UCSB.

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lecture3to5_bidding_behavior - Bidding Behavior We assume...

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