Using lotteries in auctions when buyers collude

Abstract : This paper studies the optimal auction for a seller who is bound to sell a single item to one of two potential buyers organized in a "well-coordinated" cartel. After discussing the way the cartel reacts to any auction mechanism, we show that if the seller has no way to deter collusion, he can still accomodate it optimally with a very simple mechanism, either having the cartel pay to get an efficient allocation or randomly allocating the item. We then discuss the way to implement this mechanism, so that it enables a fair amount of competition if the seller made a mistake and the buyers don't collude. We find that a simple implementation using reserve prices and lotteries may yield expected revenues close to the optimum if buyers compete, while highly increasing expected revenues if they collude. Finally, we discuss the extension to the n-buyers case.
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Rapport
2005
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https://hal-enac.archives-ouvertes.fr/hal-01021534
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Nicolas Gruyer. Using lotteries in auctions when buyers collude. 2005. 〈hal-01021534〉

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