Snipers, Shills, and Sharks: eBay and Human Behavior
Ken Steiglitz, Princeton University Press, 2007

Theory Notes

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June 10, 2007:       Winner pays average losing bid

Here's an auction in Riley and Samuelson's class of symmetric, independent-private-value auctions, all revenue equivalent: The highest bidder wins the object and pays the average of all the losing bids. I leave it to you as an exercise to find the equilibrium for general value distributions F. Check this: when values are uniformly distributed, the equilibrium bid is exactly twice the equilibrium bid in the first-price auction. John Morgan points out the interesting asymptotic property that in the limit of many bidders with uniformly distributed values, your equilibrium bid in the uniform case approaches double your value.

What's the intuition for all this high bidding?

Eric Rasmusen lists a similar but different auction in his blog. He mentions the auction where the winner pays the average of all bids. I think the equilibrium bid in this variant is harder to find, and I haven't worked it out. Please let me know if you do.