Wednesday, January 5, 2011

An analysis of the oldest auction in history

Homo economicus is not a recent phenomenon. Not only that, he design market mechanisms early in history that appear to be very subtle. The oldest known auction was designed by Illyria in Babylonic times. This is a marriage markets in its true sense, as it is about auctioning off potential brides. All eligible girls are assembled, and an auctioneer offers them to the highest bidders, starting with the one expected to fetch the highest price. Proceeds are used to sell the least attractive brides to the poorest men assembled.

Michael Baye, Dan Kovenock and Casper de Vries analysis this auction in a two-player environment and claim that there is something paradoxical. Assume complete information, which means the auctioneer will always earn zero profit. Then is appears players can earn a much larger surplus by playing a mixed strategy than with a pure strategy. And there a continuum of these mixed strategies, and the expected payoff for both players is arbitrarily high, but finite. The problem is the solution procedure used to solve for symmetric mixed strategies breaks down here, because it selects strategies that are not part of Nash equilibria. We should learn from that to be very careful when applying standard theorems. A similar reasoning applies to incomplete information where the bidders do not know how much the other player values the potential brides.

There is no recent literature on this auction. However, it was mentioned on the back cover of the August 2006 issue of the Journal of Political Economy. I suspect this is what inspired the authors to work on this. They could have mentioned this and acknowledged the submitter, Costas Meghir.

No comments: