In two-sided multi-unit auctions having a variety of payment rules, including uniform-price and discriminatory auctions, a monotone pure-strategy equilibrium (MPSE) exists when bidders are risk neutral with independent multi-dimensional types and interdependent values. In fact, all mixed-strategy equilibria are ex post allocation and interim expected payment equivalent to MPSE. Thus, for standard expected surplus/revenue analysis, there is no loss restricting attention to monotone strategies. Copyright 2006, Wiley-Blackwell.

An isotone pure strategy equilibrium exists in any game of incomplete information in which (1) each player i's action set is a finite sublattice of multi-dimensional Euclidean space, (2) types are multidimensional and atomless, and each player's interim expected payoff function satisfies two "non-primitive conditions" whenever others adopt isotone pure strategies: (3) single-crossing in own action and type and (4) quasisupermodularity in own action.Similarly, given that ( 134) and (2') types are multi-dimensional (with atoms) an isotone mixed strategy equilibrium exists.Conditions (34) are satisfied in supermodular and log-supermodular games given affiliated types, and in games with independent types in which each player's ex post payoff satisfies (a) supermodularity in own action and (b) non-decreasing differences in own action and type.These results also extend to games with a continuum action space when each player's ex post payoff is also continuous in his and others' actions.

Abundant data has led to new opportunities for empirical auctions research in recent years, with much of the newest work on auctions of multiple objects, including: (1) auctions of ranked objects (such as sponsored search ads), (2) auctions of identical objects (such as Treasury bonds), and (3) auctions of dissimilar objects (such as FCC spectrum licenses). This paper surveys recent developments in the empirical analysis of such auctions. (JEL D44, H82)

We consider a seller who faces several buyers and lacks access to an institution to credibly close a sale. If buyers anticipate that the seller may negotiate further, they will prefer to wait before making their best and final offers. This in turn induces the seller to bargain at length with buyers, even if doing so is costly. When the seller's cost of soliciting another round of offers is either very large or very small, the seller credibly commits to an auction and experiences negligible bargaining costs. Otherwise, there may be several rounds of increasing offers and significant seller losses. In these situations, an intermediary with a sufficiently valuable reputation and/or weak marginal incentives regarding price can create value by credibly committing to help sell the object without delay. (JEL C78, D44)

We propose an estimation method to bound bidders’ marginal valuations in discriminatory auctions using individual bid-level data and apply the method to data from the Turkish Treasury auction market. Using estimated bounds on marginal values, we compute an upper bound on the inefficiency of realized allocations as well as bounds on how much additional revenue could have been realized in a counterfactual uniform price or Vickrey auction. We conclude that switching from a discriminatory auction to a uniform price or Vickrey auction would not significantly increase revenue. Moreover, such a switch would increase bidder expected surplus by at most 0.02 percent.

Bounding Revenue Comparisons across Multi-Unit Auction Formats under ε-Best Response by James T. E. Chapman, David McAdams and Harry J. Paarsch. Published in volume 97, issue 2, pages 455-458 of American Economic Review, May 2007