Revenue Monotonicity Research Articles

Rank-preserving multidimensional mechanisms: An equivalence between identical-object and heterogeneous-object models

We show that the mechanism-design problem for a monopolist selling multiple, heterogeneous objects to a buyer with ex ante symmetric and additive values is equivalent to the mechanism-design problem for a monopolist selling identical objects to a buyer with decreasing marginal values. We derive three new results for the identical-objects model: (i) a new condition for revenue monotonicity of stochastic mechanisms, (ii) a sufficient condition on priors, such that prices in optimal deterministic mechanism are not increasing, and (iii) a simplification of incentive constraints for deterministic mechanisms. We use the equivalence to establish corresponding results in the heterogeneous-objects model.

Sample complexity of single-parameter revenue maximization

The sample complexity of learning Myerson's optimal auction from i.i.d. samples of bidders' values has received much attention since its introduction by Cole and Roughgarden (STOC 2014). This letter gives a brief introduction of a recent work that settles the sample complexity by showing matching upper and lower bounds, up to a poly-logarithmic factor, for all families of value distributions that have been considered in the literature. The upper bounds are unified under a novel framework, which builds on the strong revenue monotonicity by Devanur, Huang, and Psomas (STOC 2016), and an information theoretic argument. This is fundamentally different from the previous approaches that rely on either constructing an ∈-net of the mechanism space, either explicitly, or implicitly via statistical learning theory, or learning an approximately accurate version of the virtual values. To our knowledge, it is the first time information theoretical arguments are used to show sample complexity upper bounds, instead of lower bounds. The lower bounds are also unified under a meta construction of hard instances.

Simple Mechanisms for a Subadditive Buyer and Applications to Revenue Monotonicity

We study the revenue maximization problem of a seller withnheterogeneous items for sale to a single buyer whose valuation function for sets of items is unknown and drawn from some distributionD. We show that ifDis a distribution over subadditive valuations with independent items, then the better of pricing each item separately or pricing only the grand bundle achieves a constant-factor approximation to the revenue of the optimal mechanism. This includes buyers who arek-demand, additive up to a matroid constraint, or additive up to constraints of any downward-closed set system (and whose values for the individual items are sampled independently), as well as buyers who are fractionally subadditive with item multipliers drawn independently. Our proof makes use of the core-tail decomposition framework developed in prior work showing similar results for the significantly simpler class of additive buyers.In the second part of the article, we develop a connection between approximately optimal simple mechanisms and approximate revenue monotonicity with respect to buyers’ valuations. Revenue non-monotonicity is the phenomenon that sometimes strictlyincreasingbuyers’ values for every set can strictlydecreasethe revenue of the optimal mechanism. Using our main result, we derive a bound on how bad this degradation can be (and dub such a bound a proof ofapproximaterevenue monotonicity); we further show that better bounds on approximate monotonicity imply a better analysis of our simple mechanisms.

Characterizing Strategy-proof, Revenue Monotone Allocation Rules in Auction Mechanisms

This paper proposes a novel Peer-to-Peer Information Retrieval (P2PIR) method using user feedback and query-destination-learning. The method uses positive feedback information effectively for getting documents relevant to a query by giving higher score to them. The method also utilize negative feedback information actively so that other agents can filter it out with itself. Using query-destination-learning, the method can not only accumulate relevant information from all the member agents in a community, but also reduce communication loads by caching queries and their sender-responder agent addresses in the community. Experiments were carried out on multiple communities constructed with multi-agent framework Kodama. The experimental results illustrated that the proposed method effectively increased retrieval accuracy.

Revenue monotonicity in deterministic, dominant-strategy combinatorial auctions

In combinatorial auctions using VCG, a seller can sometimes increase revenue by dropping bidders. In this paper we investigate the extent to which this counterintuitive phenomenon can also occur under other deterministic, dominant-strategy combinatorial auction mechanisms. Our main result is that such failures of “revenue monotonicity” can occur under any such mechanism that is weakly maximal—meaning roughly that it chooses allocations that cannot be augmented to cause a losing bidder to win without hurting winning bidders—and that allows bidders to express arbitrary known single-minded preferences. We also give a set of other impossibility results as corollaries, concerning revenue when the set of goods changes, false-name-proofness, and the core. 1 1 We previously published a six-page preliminary version of our main result at a conference (Rastegari et al., 2007) [24]. Among other differences, this work considered a very limited version of our weak maximality condition that can be understood as requiring Pareto efficiency with respect to bidder valuations (i.e., ignoring payments).

Revenue monotonicity in combinatorial auctions

In recent work [Rastegari et al. 2007a; 2007b] we study revenue properties of combinatorial auctions. Consider a well-known drawback of the famous VCG mechanism: a seller’s revenue can go down when bidders are added to an auction, contrary to the intuition that having more bidders should increase competition. Following an example due to Ausubel and Milgrom [2006], consider an auction with three bidders and two goods for sale. Suppose that bidder 2 wants both goods for the price of $2 billion whereas bidder 1 and bidder 3 are willing to pay $2 billion for the first and the second good respectively (see Figure 1). The VCG mechanism awards the goods to bidders 1 and 3 for the price of zero, yielding the seller zero revenue. However, in the absence of either bidder 1 or bidder 3, the revenue of the auction would be $2 billion. We say that an auction mechanism is revenue monotonic if the seller’s revenue is …

On the Equivalence between Progressive Taxation and Inequality Reduction

We establish the precise connections between progressive taxation and inequality reduction, in a setting where the level of tax revenue to be raised is endogenously fixed and tax schemes are balanced. We show that, in contrast with the traditional literature on taxation, the equivalence between inequality reduction and the combination of progressivity and income order preservation does not always hold in this setting. However, we show that, among rules satisfying consistency and, either revenue continuity, or revenue monotonicity, the equivalence remains intact.