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

Budget Constrained Auctions with Heterogeneous Items

In this paper, we present the first approximation algorithms for the problem of designing revenue optimal Bayesian incentive compatible auctions when there are multiple (heterogeneous) items and when bidders can have arbitrary demand and budget constraints. Our mechanisms are surprisingly simple: We show that a sequential all-pay mechanism is a 4 approximation to the revenue of the optimal ex-interim truthful mechanism with discrete correlated type space for each bidder. We also show that a sequential posted price mechanism is a O(1) approximation to the revenue of the optimal ex-post truthful mechanism when the type space of each bidder is a product distribution that satisfies the standard hazard rate condition. We further show a logarithmic approximation when the hazard rate condition is removed, and complete the picture by showing that achieving a sub-logarithmic approximation, even for regular distributions and one bidder, requires pricing bundles of items. Our results are based on formulating novel LP relaxations for these problems, and developing generic rounding schemes from first principles. We believe this approach will be useful in other Bayesian mechanism design contexts.Comment: Final version accepted to STOC '10. Incorporates significant reviewer comment

Do people always pay less than they say? Testbed laboratory experiments with IV and HG values

Hypothetical bias is a long-standing issue in stated preference and contingent valuation studies - people tend to overstate their preferences when they do not experience the real monetary consequences of their decision. This view, however, has been challenged by recent evidence based on the elicitation of induced values (IV) in the lab and homegrown (HG) demand function from different countries. This paper uses an experimental design to assess the extent and relevance of hypothetical bias in demand elicitation exercises for both IV and HG values. For testbed purpose, we use a classic second-price auction to elicit preferences. Comparing the demand curve we elicit in both, hypothetical bias unambiguously (i) vanishes in an induced-value, private good context, and (ii) persists in homegrown values elicitation context. This suggests hypothetical bias in preference elicitation appears to be driven by "preference formation" rather than "preference elicitation". In addition, companion treatments highlight two sources of the discrepancy observed in the HG setting: the hypothetical context leads bidders to underestimate the constraints imposed by their budget limitations, whereas the real context creates pressure leading them to bid "zero" to opt out from the elicitation mechanism. As a result, there is a need for a demand elicitation procedure that helps subjects take the valuation exercise sincerely, but without putting extra pressure on them.Auctions; Demand revelation; Experimental valuation; Hypothetical bias

Do people always pay less than they say? Testbed laboratory experiments with IV and HG values

Hypothetical bias is a long-standing issue in stated preference and contingent valuation studies – people generally overstate their preferences when they do not experience the real monetary consequences of their decision. This view, however, has been challenged by recent evidence based on the elicitation of induced values (IV) in the lab and homegrown (HG) demand function from different countries. This paper uses a two experiments design to assess the extent and relevance of hypothetical bias in demand elicitation exercises for both IV and HG values. For testbed purpose, we use a classic second-price auction to elicit preferences. Comparing the demand curve we elicit in both, hypothetical bias unambiguously (i) vanishes in an induced-value, private good context, and (ii) persists in homegrown values elicitation context. This suggests hypothetical bias in preference elicitation appears to be driven by “preference formation” rather than “preference elicitation”. In addition, companion treatments highlight two sources of the discrepancy observed in the HG setting: the hypothetical context leads bidders to underestimate the constraints imposed by their budget limitations, whereas the real context creates pressure leading them to bid “zero” to opt out from the elicitation mechanism. As a result, there is a need for a demand elicitation procedure that helps subjects take the valuation exercise sincerely, but without putting extra pressure on them.Auctions; Demand revelation; Experimental valuation; Hypothetical bias

Foundations of mechanism design: a tutorial Part 1- Key concepts and classical results

Mechanism design, an important tool in microeconomics, has found widespread applications in modelling and solving decentralized design problems in many branches of engineering, notably computer science, electronic commerce, and network economics. Mechanism design is concerned with settings where a social planner faces the problem of aggregating the announced preferences of multiple agents into a collective decision when the agents exhibit strategic behaviour. The objective of this paper is to provide a tutorial introduction to the foundations and key results in mechanism design theory. The paper is in two parts. Part 1 focuses on basic concepts and classical results which form the foundation of mechanism design theory. Part 2 presents key advanced concepts and deeper results in mechanism design

Preference Elicitation under Oath

Eliciting sincere preferences for non-market goods remains a challenge due to hypothetical bias - the so-called gap between hypothetical monetary values and real economic commitments. The gap arises because people either overstate hypothetical values or understate real commitments or a combination of both. Herein we examine whether the traditional real-world institution of the solenn oath can improve preference elicitation. Applying the social psychology theory on the oath as a truth-telling-commitment device, we ask our bidders to swear on their honour to give honest answers prior to participating in an incentive-compatible second-price auction. Results from our induced valuation testbed treatments suggest the oath-only auctions outperform all other auctions (real, hypothetical, and real-with-oath). In our homegrown valuation treatments eliciting preferences for dolphin protection, the oath-only design induced people to treat as binding both their budget constraint (i.e., lower values on the high end of the value distribution) and participation constraint (i.e., positive values rather than zero bids used to opt out of auction). Our oath-only results are robust to extra training on the auction and to consequential wording about the reason for the oath.Oath, commitment, Vickrey auction, hypothetical bias, induced values, homegrown values.