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.
Query complexity and communication complexity of equilibria have been actively studied in the past decade. Recent progress in these fields of informational complexity has led to a quite good understanding of equilibria. This survey summarizes the established results for the three most common solution concepts: Nash equilibria, correlated equilibria, and coarse correlated equilibria. The survey provides a high-level idea of the techniques that are utilized to deduce recently developed lower bounds on Nash equilibria.
Already in 1981 Myerson gave a characterization of the optimal mechanism for a single parameter Bayesian mechanism design. However, till today we have no idea for how such a characterization for the multi-dimensional setting could even look like. Moreover, it wasn't until no that long time ago that we could not develop mechanisms for such setting with any reasonable and provable performance guarantees. The seminal work of [Chawla et al. 2009] on sequential posted pricing mechanisms gave us an approach for approximately solving the Bayesian multi-parameter unit-demand mechanism design problem (BMUMD). The paper left open the question on how to obtain a constant approximation for the matroid setting. Two mathematically beautiful results from combinatorial optimization under uncertainty where devised in order to answer this question. First, Kleinberg and Weinberg in 2011 extended the classical Prophet Inequality result into the matroid setting to give a 2-approximation for BMUMD for a single matroid setting. Second, Feldman, Svensson and Zenklusen in 2016 adapted the Contention Resolution Scheme framework for online settings. We add to this line of work by considering the Contention Resolution Scheme framework in the random order setting. The most impressive implication of this research are the new algorithms for BMUMD which improve the previous results in the multimatroid setting. Although the range of implications of the CR Scheme framework in the random order is reasonably wide, we shall focus in this letter on presenting only the single matroid setting and how it is connected to BMUMD.
Consider a fundamental problem in microeconomics: selling a single item to a number of potential buyers, who independently draw their values from regular and publicly known distributions. There are four mechanisms widely studied in the literature and widely used in practice: Myerson Auction (OPT), Sequential Posted Pricing (SPM), Second-Price Auction with Anonymous Reserve (AR) , and Anonymous Pricing (AP). OPT is revenue-optimal but complicated, which also experiences several practical issues such as fairness. AP is the simplest mechanism, but also generates the lowest revenue among these four mechanisms. SPM and AR are of intermediate complexity and revenue. A quantitative approach to comparing the relative power of these mechanisms is to study their revenue gaps, each of which is defined as the largest ratio between the revenues from a pair of mechanisms. This letter surveys some recent developments on establishing tight revenue gaps, and highlights some open questions.
It is standard in computational social choice to analyse welfare considerations under the assumptions of normalized utilities. In this note, we summarize some common reasons for this approach. We then mention another justification which is ignored but has solid normative appeal. The central concept used in the `new' justification can also be used more widely as a social objective.
This is the fourth annual collection of profiles of the junior faculty job market candidates of the SIGecom community. The twenty five candidates for 2019 are listed alphabetically and indexed by research areas that define the interests of the community. The candidates can be contacted individually or via the moderated mailing list ecom-candidates2019@acm.org.
We introduce a combinatorial variant of the cost sharing problem: several services can be provided to each player and each player values every combination of services differently. A publicly known cost function specifies the cost of providing every possible combination of services. A combinatorial cost sharing mechanism is a protocol that decides which services each player gets and at what price. We look for dominant strategy mechanisms that are (economically) efficient and cover the cost, ideally without overcharging (i.e., budget balanced). Note that unlike the standard cost sharing setting, combinatorial cost sharing is a multi-parameter domain. This makes designing dominant strategy mechanisms with good guarantees a challenging task. We present the Potential Mechanism -- a combination of the VCG mechanism and a well-known tool from the theory of cooperative games: Hart and Mas-Colell's potential function. The potential mechanism is a dominant strategy mechanism that always covers the incurred cost. When the cost function is subadditive the same mechanism is also approximately efficient. Our main technical contribution shows that when the cost function is submodular the potential mechanism is approximately budget balanced in three settings: supermodular valuations, symmetric cost function and general symmetric valuations, and two players with general valuations.
This article gives a (very) brief exposition of what market design is, along with four examples of market design in action. Loosely themed after Robert Frost's poem "Mending Wall," the examples demonstrate ways in which market design can break barriers---physical, political, and/or metaphorical. Each example also illustrates one of four broader classes of ways that market design can create positive change: marketplace mechanism (re-)design, information provision, (re-)shaping the extensive margin, and market(place) creation.
Learning dynamics have traditionally taken a secondary role to Nash equilibria in game theory. We propose a new approach that places the understanding of game dynamics over mixed strategy profiles as the central object of inquiry. We focus on the stable recurrent points of the dynamics, i.e. states which are likely to be revisited infinitely often; obviously, pure Nash equilibria are a special case of such behavior. We propose a new solution concept, the Markov-Conley Chain (MCC), which has several favorable properties: It is a simple randomized generalization of the pure Nash equilibrium, just like the mixed Nash equilibrium; every game has at least one MCC; an MCC is invariant under additive constants and positive multipliers of the players' utilities; there is a polynomial number of MCCs in any game, and they can be all computed in polynomial time; the MCCs can be shown to be, in a well defined sense, surrogates or traces of an important but elusive topological object called the sink chain component of the dynamics; finally, it can be shown that a natural game dynamics surely ends up at one of the MCCs of the game.
We present a report on the first Workshop on Mechanism Design for Social Good (MD4SG '17), which took place at the 18th ACM Conference on Economics and Computation (EC '17), and discuss unifying themes for research at this interface.
In this letter, we discuss the correlation-robust framework proposed by Carroll [Econometrica 2017] and our new development [SODA 2018]. Consider a monopolist seller that has n heterogeneous items to sell to a single buyer with the objective of maximizing the seller's revenue. In the correlation-robust framework, the seller only knows marginal distribution of each item but has no information about the correlation across different items in the joint distribution. Any mechanism is then evaluated according to its expected profit in the worst-case over all possible joint distributions with the given marginal distributions. Carroll's main result states that when the buyer's value for any set of her items is the sum of the values of individual items in the set, the optimal correlation-robust mechanism should sell items separately. We extend this result to the case where the buyer has a budget constraint on her total payment. Namely, we show that the optimal robust mechanism splits the total budget in a fixed way across different items independent of the bids, and then sells each item separately with a per item budget constraint. We highlight an alternative approach via a dual Linear Programming formulation for the optimal correlation-robust mechanism design problem. This LP can be used to compute optimal mechanisms in general (other than additive) settings. It also yields an alternative proof for the additive monopoly problem without constructing the worst-case distribution and allows us to extend the proof to the budget setting.
Dear colleagues: We are writing to share our vision about the recently formed Revenue Management and Market Analytics department in Management Science. We welcome papers from the SIGecom community!
This paper is part of an emerging line of work at the intersection of machine learning and mechanism design, which aims to avoid noise in training data by correctly aligning the incentives of data sources. Specifically, we focus on the ubiquitous problem of linear regression, where strategyproof mechanisms have previously been identified in two dimensions. In our setting, agents have single-peaked preferences and can manipulate only their response variables. Our main contribution is the discovery of a family of group strategyproof linear regression mechanisms in any number of dimensions, which we call generalized resistant hyperplane mechanisms. The game-theoretic properties of these mechanisms - and, in fact, their very existence - are established through a connection to a discrete version of the Ham Sandwich Theorem.
We explore the impact of private information in sealed-bid first-price auctions. For a given symmetric and arbitrarily correlated prior distribution over values, we characterize the impact that the structure of private information has on bidding behavior, and the sharing of surplus between the seller and the bidder. Our results provide lower bounds and upper bounds for bids and revenues across all information structures. Our work has implications for the identification of value distributions from data on winning bids and for the informationally robust comparison of alternative bidding mechanisms.
We highlight recent progress in worst-case analysis of welfare in first price auctions. It was shown in [Syrgkanis and Tardos 2013] that in any Bayes-Nash equilibrium of a first-price auction, the expected social welfare is at least a (1 - 1/e) ≈ .63-fraction of optimal. This result uses smoothness, the standard technique for worst-case welfare analysis of games, and is tight if bidders' value distributions are permitted to be correlated. With independent distributions, however, the worst-known example, due to [Hartline et al. 2014], exhibits welfare that is a ≈ .89-fraction of optimal. This gap has persisted in spite of the canonical nature of the first-price auction and the prevalence of the independence assumption. In [Hoy et al. 2018], we improve the worst-case lower bound on first-price auction welfare assuming independently distributed values from (1 - 1/e) to ≈ .743. Notably, the proof of this result eschews smoothness in favor of techniques which exploit independence. This note overviews the new approach, and discusses research directions opened up by the result.
In this letter, we report on our work providing a polynomial time reduction from Bayesian incentive compatible mechanism design to Bayesian algorithm design for welfare maximization problems. Unlike prior results, our reduction achieves exact incentive compatibility for problems with multidimensional and continuous type spaces.
This letter describes an exercise in market mechanism refinement that was recently undertaken on a major electronic trading venue: Thomson Reuters Matching. The exercise sought to address problems associated with continuous markets that have been described in recent literature. To this end, the design of the refinement is described, and its consequences are discussed.
We propose definitions for when signals are "substitutes" and "complements". These give a characterization of equilibria of prediction markets and are relevant to the complexity of information acquisition under constraints.
Over the past decade, an exciting connection has developed between the theory of posted-price mechanisms and the prophet inequality, a result from the theory of optimal stopping. This survey provides an overview of this literature, covering extensions and applications of the prophet inequality through the lens of an economic proof of this classic result. We focus on highlighting ways in which the economic perspective drives new advances in the theory of online stochastic optimization, and vice versa.
