AEM414 - notes2_Notes

# AEM414 - notes2_Notes - Auctions The Vickrey auction(also...

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Auctions The Vickrey auction (also called a second price sealed bid auction) is designed as follows: Each individual has some certain private value. None of the participants knows the value given to any of the other participants. However, we usually set this up so each knows the distribution of values from which each participant’s value is drawn. Each of the participants submits a sealed bid. The participant who submits the highest bid wins the auction but must pay the price submitted by the second highest bidder. The Vickrey auction is named for the British economist who first derived the Nash equilibrium for such an auction assuming participants are risk neutral. Let’s examine this Nash equilibrium as a baseline for comparison. Suppose each of n individuals’ private values are drawn from a uniform distribution on [ ] , x x . Then one individual’s payout function can be represented ( 29 1 if | 0 if n n n x x x x b x x x x - - = = < ± ± where x ± is this individual’s value, n x is the highest bid, 1 n x - is the next highest, and so on. For a first pass, suppose we bid our value, x ± . If we won, we would be assured that the next highest bid is lower than our value. Hence, we could only obtain non-negative profits. In this case, increasing our bid would have no effect on profits because we paid the second highest price which we have no control over. On the other hand suppose we did not win the auction but instead came in second. In this case we can only win by increasing our bid above our value. But remember that the price bid we lost to was already above our private value. Thus increasing our bid in this case to win the auction would cause us a loss instead of a profit. An argument similar to this shows us that the

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best we can do in a Vickrey auction is to bid our value. This would be the rational thing to do. Let’ s examine the behavioral motivations behind the behavior we observe. Without reasoning that everyone is rational, an individual first notices that they will not ever have to pay the price they have bid. For many, this frees them from the notion that they need to bid at or below their value. For this reason we expect that Vickrey bids will often be above the individual’ s true value. This, even though it is not in the individual’ s
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AEM414 - notes2_Notes - Auctions The Vickrey auction(also...

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