Almost Common Value Auctions and Discontinuous Equilibria

Abstract

In almost common value auctions, even a very small private payoff advantage is usually supposed to have an explosive effect on the outcomes in a second-price sealed-bid common value auction. According to Bikhchandani (1988) and Klemperer (1998) the large set of equilibria obtained for common value auction games drastically shrinks, so that the advantaged player always wins the auction, at a price that sharply decreases the seller’s payoff. Yet this result has not been observed experimentally. In this paper, we show that Bikhchandani’s equilibria are not the only equilibria of the game. By allowing bids to not continuously depend on private information, we establish a new family of perfect equilibria with nice properties: (i) the advantaged bidder does no longer win the auction regardless of her private information, (ii) she may pay a much higher price than in Bikhchandani’s equilibria, (iii) there is no ex-post regret for both the winner and the looser, and (iv) the equilibria give partial support to some naïve behaviour observed experimentally. Moreover the intersection between these equilibria, level-k reasoning and cursed equilibria is not empty.

Keywords: common value auctions, second-price sealed-bid auctions, nash equilibrium, perfect equilibrium, level-k reasoning

JEL Classification: C72, D44