Market clearing sealed-bid auctions for non-identical objects with single-unit demands

We consider a version of the cooperative buyer-seller market game of Shapley and Shubik (1972). For this market we propose a c1ass of sealed- bid auctions where objects are sold simultaneously at a market c1earing price rule. We ana1yze the strategic games induced by these mechanisms under the complete information approach. We show that these noncooperative games can be regarded as a competitive process for achieving a cooperative outcome: every Nash equilibrium payoff is a core outcome of the cooperative market game. Precise answers can be given to the strategic questions raised.

Auctions of identical objects with single-unit demands : a survey

The theory of auctions of a single object generalizes to a situation where identical objects are sold either sequentially or simultaneously but individuais can only buy one object. In this context, I will present a survey of the main results regarding the ranking of auctions based on revenue, bidding behaviour, effects of entry fees and reserve prices, and other strategic issues.

Optimal auctions with multidimensional types and the desirability of exclusion

Within the context of a single-unit, independent private values auction model, we show that if bidder types are multidimensional, then under the optimal auction exclusion of some bidder types will occur. A second contribution of the paper is methodological in nature. In particular, we identify conditions under which an auction model with multidimensional types can be reduced to a model with one dimensional types without loss of generality. Reduction results of this type have achieved the status of folklore in the mechanism design literature. Here, we provide a proof of the reduction result for auctions.

Synergies and price trends in sequential auctions

In this paper we consider sequential auctions where an individual’s value for a bundle of objects is either greater than the sum of the values for the objects separately (positive synergy) or less than the sum (negative synergy). We show that the existence of positive synergies implies declining expected prices. When synergies are negative, expected prices are increasing. There are several corollaries. First, the seller is indi¤erent between selling the objects simultaneously as a bundle or sequentially when synergies are positive. Second, when synergies are negative, the expected revenue generated by the simultaneous auction can be larger or smaller than the expected revenue generated by the sequential auction. In addition, in the presence of positive synergies, an option to buy the additional object at the price of the …rst object is never exercised in the symmetric equilibrium and the seller’s revenue is unchanged. Under negative synergies, in contrast, if there is an equilibrium where the option is never exercised, then equilibrium prices may either increase or decrease and, therefore, the net e¤ect on the seller’s revenue of the introduction of an option is ambiguous. Finally, we examine two special cases with asymmetric players. In the …rst case, players have distinct synergies. In this example, even if one player has positive synergies and the other has negative synergies, it is still possible for expected prices to decline. In the second case, one player wants two objects and the remaining players want one object each. For this example, we show that expected prices may not necessarily decrease as predicted by Branco (1997). The reason is that players with singleunit demand will generally bid less than their true valuations in the …rst period. Therefore, there are two opposing forces; the reduction in the bid of the player with multiple-demand in the last auction and less aggressive bidding in the …rst auction by the players with single-unit demand.