Efficiency Guarantees in Auctions with Budgets

In settings where players have a limited access to liquidity, represented in the form of budget constraints, efficiency maximization has proven to be a challenging goal. In particular, the social welfare cannot be approximated by a better factor then the number of players. Therefore, the literature has mainly resorted to Pareto-efficiency as a way to achieve efficiency in such settings. While successful in some important scenarios, in many settings it is known that either exactly one incentive-compatible auction that always outputs a Pareto-efficient solution, or that no truthful mechanism can always guarantee a Pareto-efficient outcome. Traditionally, impossibility results can be avoided by considering approximations. However, Pareto-efficiency is a binary property (is either satisfied or not), which does not allow for approximations. In this paper we propose a new notion of efficiency, called \emph{liquid welfare}. This is the maximum amount of revenue an omniscient seller would be able to extract from a certain instance. We explain the intuition behind this objective function and show that it can be 2-approximated by two different auctions. Moreover, we show that no truthful algorithm can guarantee an approximation factor better than 4/3 with respect to the liquid welfare, and provide a truthful auction that attains this bound in a special case. Importantly, the liquid welfare benchmark also overcomes impossibilities for some settings. While it is impossible to design Pareto-efficient auctions for multi-unit auctions where players have decreasing marginal values, we give a deterministic $O(\log n)$-approximation for the liquid welfare in this setting

Reduced Form Auctions Revisited

Asymmetric auction, Reduced form auction, Theorem of the alternative, D44,

Numerical Solutions of Asymmetric, First-Price, Independent Private Values Auctions

Auctions, Numerical solution, Asymmetric first price, Independent private values, Ex-ante heterogeneity, Expected revenues, Optimal reserve, Collusion,

Unconditional competitive auctions with copy and budget constraints

This paper investigates a new auction model in which bidders have both copy and budget constraints. The new model has extensive and interesting applications in auctions of online ad-words, software licenses, etc. We consider the following problem: Suppose all the participators are rational, how to allocate the objects at what price so as to guarantee auctioneer's high revenue, and how high it is. We introduce a new kind of mechanisms called win-win mechanisms and present the notion of unconditional competitive auctions. A notably interesting property of win-win mechanisms is that each bidder's self-interested strategy brings better utility not only to himself but also to the auctioneer. Then we present win-win mechanisms for multi-unit auctions with copy and budget constraints. We prove that these auctions are unconditional competitive under the situation of both limited and unlimited supply. © 2006 Springer-Verlag

Optimal sale across venues and auctions with a buy-now option

Optimal auction, eBay auctions, Temporary buy-now option, Permanent buy-now option, Heterogeneous sales venues, Posted price, Price discrimination, D44,

Monotonicity and its Cognates in the Theory of Choice

The standard requirement of monotonicity of a voting procedurestates that an improvement in the ranking of the winningalternative, ceteris paribus, should not make itnon-winning. A concept apparently closely linked tomonotonicity is known as the participation axiom whichrequires that it should never be advantageous for a voter toabstain rather than to vote according to his/her preferences.Situations in which a group of voters may end up with a betteroutcome by not voting at all than by voting according to theirpreferences are called instances of the no-show paradox. Astrong version of the paradox occurs when the abstainers endup with their most preferred outcome by abstaining. A thirdrelated concept is invulnerability to preference truncation.This is satisfied by such procedures that make itadvantageous for voters to always reveal their entirepreference rankings. The fourth concept, Maskin monotonicity,plays an important role in mechanism design literature. Wediscuss these requirements in the context of votingprocedures. Particular attention is paid to the plausibilityof conditions guaranteeing various forms of monotonicity. Copyright Kluwer Academic Publishers 2004