Divisible Good Auctions Research Articles

Competition and Cooperation in Divisible Good Auctions: An Experimental Examination

An experimental approach is used to examine the performance of three different multi-unit auction designs: discriminatory, uniform-price with fixed supply, and uniform-price with endogenous supply. We find that the strategies of the individual bidders and the aggregate demand curves are inconsistent with theoretically identified equilibrium strategies. The discriminatory auction is found to be more susceptible to collusion than are the uniform-price auctions, and so contrary to theoretical predictions and previous experimental results, the discriminatory auction provides the lowest average revenue. Consistent with theoretical predictions, bidder demands are more elastic with reducible supply or discriminatory pricing than in the uniform-price auction with fixed supply. Despite a lack of a priori differences across bidders, the discriminatory auction results in significantly more symmetric allocations.

Do Uniform Price Auctions Trade‐off Higher Risk for Higher Return?*

AbstractResults of the recent US Treasury experiment comparing uniform and discriminatory price auctions suggest that uniform price auctions achieve lower award concentration and higher average revenues but experience higher variance of revenues from auction to auction relative to discriminatory price auctions. In other words, uniform pricing offers higher risk for higher return. This apparent trade‐off may deter some sellers considering the switch from discriminatory to uniform pricing; thus, it is important to investigate whether these results can be generalized. The Treasury's results are driven by the tendency for bidders in the uniform auctions to submit multiple bids at a wide range of prices, essentially steep bid curves, instead of the flat bids submitted in the discriminatory auctions. However, theory and data from discriminatory auctions in Sweden and Portugal suggest that bidders in discriminatory auctions will submit steeper bids when there is more potential for winner's curse. It is possible that bidders in the US auctions, which are preceded by a when‐issued market, are relatively unconcerned with the winner's curse. We examine the auction formats in an environment much more likely to generate the winner's curse: the initial public offering market. We compare discriminatory price auctions in Japan and uniform price auctions in Israel on the basis of revenue and slope of the demand curves and test a number of divisible good auction theory implications. In contrast with the Treasury's results, we find that revenues are likely to be insignificantly different in the discriminatory and uniform price auctions and that bid curves may be equally steep under both formats in markets with information asymmetry. The winner's curse increases underpricing and steepens demand curves in Japan's discriminatory price auctions but not in Israel's uniform price auctions.

Auctioning divisible goods

We derive equilibrium bidding strategies in divisible good auctions for asymmetrically informed risk neutral and risk averse bidders when there is random noncompetitive demand. The equilibrium bid schedules contain both strategic considerations and explicit allowances for the winner's curse. When the bidders' information is symmetric, the strategic aspects of bidding imply that there always exist equilibria of a uniform-price auction with lower expected revenue than provided by a discriminatory auction. When bidders are risk averse, there may exist equilibria of the uniform-price auction that provide higher expected revenue than a discriminatory auction.

Auctions of Divisible Goods: On the Rationale for the Treasury Experiment

We compare a sealed-bid uniform-price auction (the Treasury's experimentalformat) with a sealedbid discriminatory auction (tbe Treasury'sformat beretofore), assuming the good is perfectly divisible. We show that the auction theory thatprompted the experiment, which assumes single-unit demands, does not adequately describe the bidding game for Treasury securities. Collusive strategies are self-enforcing in uniform-price divisible-good auctions. In these equilibria, the sellers expected revenue is lower than in equilibria of discriminatory auctions.