Composable and Efficient Mechanisms

We initiate the study of efficient mechanism design with guaranteed good properties even when players participate in multiple different mechanisms simultaneously or sequentially. We define the class of smooth mechanisms, related to smooth games defined by Roughgarden, that can be thought of as mechanisms that generate approximately market clearing prices. We show that smooth mechanisms result in high quality outcome in equilibrium both in the full information setting and in the Bayesian setting with uncertainty about participants, as well as in learning outcomes. Our main result is to show that such mechanisms compose well: smoothness locally at each mechanism implies efficiency globally. For mechanisms where good performance requires that bidders do not bid above their value, we identify the notion of a weakly smooth mechanism. Weakly smooth mechanisms, such as the Vickrey auction, are approximately efficient under the no-overbidding assumption. Similar to smooth mechanisms, weakly smooth mechanisms behave well in composition, and have high quality outcome in equilibrium (assuming no overbidding) both in the full information setting and in the Bayesian setting, as well as in learning outcomes. In most of the paper we assume participants have quasi-linear valuations. We also extend some of our results to settings where participants have budget constraints

FlexAuc: Serving Dynamic Demands in a Spectrum Trading Market with Flexible Auction

In secondary spectrum trading markets, auctions are widely used by spectrum holders (SHs) to redistribute their unused channels to secondary wireless service providers (WSPs). As sellers, the SHs design proper auction schemes to stimulate more participants and maximize the revenue from the auction. As buyers, the WSPs determine the bidding strategies in the auction to better serve their end users. In this paper, we consider a three-layered spectrum trading market consisting of the SH, the WSPs and the end users. We jointly study the strategies of the three parties. The SH determines the auction scheme and spectrum supplies to optimize its revenue. The WSPs have flexible bidding strategies in terms of both demands and valuations considering the strategies of the end users. We design FlexAuc, a novel auction mechanism for this market to enable dynamic supplies and demands in the auction. We prove theoretically that FlexAuc not only maximizes the social welfare but also preserves other nice properties such as truthfulness and computational tractability.Comment: 11 pages, 7 figures, Preliminary version accepted in INFOCOM 201

Matrix bids in combinatorial auctions: expressiveness and micro-economic properties

A combinatorial auction is an auction where multiple items are for sale simultaneously to a set of buyers. Furthermore, buyers are allowed to place bids on subsets of the available items. This paper focuses on a combinatorial auction where a bidder can express his preferences by means of a so-called ordered matrix bid. Ordered matrix bids are a bidding language that allows a compact representation of a bidder''s preferences, and was developed by Day (2004). We give an overview of how a combinatorial auction with matrix bids works. We elaborate on the relevance of the matrix bid auction and we develop methods to verify whether a given matrix bid satisfies properties related to micro-economic theory as free disposal, subadditivity, submodularity and the gross substitutes property. Finally, we investigate how a collection of arbitrary bids can be represented as a matrix bid.microeconomics ;

On the Equivalence of Bayesian and Dominant Strategy Implementation

We consider a standard social choice environment with linear utilities and independent, one-dimensional, private types. We prove that for any Bayesian incentive compatible mechanism there exists an equivalent dominant strategy incentive compatible mechanism that delivers the same interim expected utilities for all agents and the same ex ante expected social surplus. The short proof is based on an extension of an elegant result due to Gutmann et al. (Annals of Probability, 1991). We also show that the equivalence between Bayesian and dominant strategy implementation generally breaks down when the main assumptions underlying the social choice model are relaxed, or when the equivalence concept is strengthened to apply to interim expected allocations.Bayesian Implementation, Dominant Strategy Implementation, Equivalence