Ex post implementation in environments with private goods

We prove by construction that ex post incentive compatible mechanisms exist in a private goods setting with multi-dimensional signals and interdependent values. The mechanism shares features with the generalized Vickrey auction of one-dimensional signal models. The construction implies that for environments with private goods, informational externalities (i.e., interdependent values) are compatible with ex post equilibrium in the presence of multi-dimensional signals.Ex post incentive compatibility, multi-dimensional information, interdependent values

Transitive regret

Preferences may arise from regret, i.e., from comparisons with alternatives forgone by the decision maker. We ask whether regret-based behavior is consistent with non-expected utility theories of transitive choice and show that the answer is no. If choices are governed by ex ante regret and rejoicing then non-expected utility preferences must be intransitive.Regret, transitivity, non-expected utility

Herd Behavior in Financial Markets

This paper provides an overview of the recent theoretical and empirical research on herd behavior in financial markets. It looks at what precisely is meant by herding, the causes of herd behavior, the success of existing studies in identifying the phenomenon, and the effect that herding has on financial markets. Copyright 2001, International Monetary Fund

Sequential item pricing for unlimited supply

We investigate the extent to which price updates can increase the revenue of a seller with little prior information on demand. We study prior-free revenue maximization for a seller with unlimited supply of n item types facing m myopic buyers present for k < log n days. For the static (k = 1) case, Balcan et al. [2] show that one random item price (the same on each item) yields revenue within a \Theta(log m + log n) factor of optimum and this factor is tight. We define the hereditary maximizers property of buyer valuations (satisfied by any multi-unit or gross substitutes valuation) that is sufficient for a significant improvement of the approximation factor in the dynamic (k > 1) setting. Our main result is a non-increasing, randomized, schedule of k equal item prices with expected revenue within a O((log m + log n) / k) factor of optimum for private valuations with hereditary maximizers. This factor is almost tight: we show that any pricing scheme over k days has a revenue approximation factor of at least (log m + log n) / (3k). We obtain analogous matching lower and upper bounds of \Theta((log n) / k) if all valuations have the same maximum. We expect our upper bound technique to be of broader interest; for example, it can significantly improve the result of Akhlaghpour et al. [1]. We also initiate the study of revenue maximization given allocative externalities (i.e. influences) between buyers with combinatorial valuations. We provide a rather general model of positive influence of others' ownership of items on a buyer's valuation. For affine, submodular externalities and valuations with hereditary maximizers we present an influence-and-exploit (Hartline et al. [13]) marketing strategy based on our algorithm for private valuations. This strategy preserves our approximation factor, despite an affine increase (due to externalities) in the optimum revenue.Comment: 18 pages, 1 figur

Rank-Preserving Multidimensional Mechanisms

We show that the mechanism design problem for a monopolist selling multiple heterogeneous objects with ex ante symmetric values for the buyer is equivalent to the mechanism design problem for a monopolist selling identical objects with decreasing marginal values. We apply this equivalence result to (a) give new sufficient conditions under which an optimal mechanism is revenue monotone in both the models; (b) derive new results on optimal deterministic mechanisms in the heterogeneous objects model; and (c) show that a uniform price mechanism is robustly optimal in the identical objects model when the monopolist knows the average of the marginal distributions of the units

Auctions with Heterogeneous Items and Budget Limits

We study individual rational, Pareto optimal, and incentive compatible mechanisms for auctions with heterogeneous items and budget limits. For multi-dimensional valuations we show that there can be no deterministic mechanism with these properties for divisible items. We use this to show that there can also be no randomized mechanism that achieves this for either divisible or indivisible items. For single-dimensional valuations we show that there can be no deterministic mechanism with these properties for indivisible items, but that there is a randomized mechanism that achieves this for either divisible or indivisible items. The impossibility results hold for public budgets, while the mechanism allows private budgets, which is in both cases the harder variant to show. While all positive results are polynomial-time algorithms, all negative results hold independent of complexity considerations

On the lowest-winning-bid and the highest-losing-bid auctions

Theoretical models of multi-unit, uniform-price auctions assume that the price is given by the highest losing bid. In practice, however, the price is usually given by the lowest winning bid. We derive the equilibrium bidding function of the lowest-winning-bid auction when there are k objects for sale and n bidders with unit demand, and prove that it converges to the bidding function of the highest-losing-bid auction if and only if the number of losers n - k gets large. When the number of losers grows large, the bidding functions converge at a linear rate and the prices in the two auctions converge in probability to the expected value of an object to the marginal winner