{"title":"Greedy Algorithms Make Efficient Mechanisms","authors":"Brendan Lucier, Vasilis Syrgkanis","doi":"10.1145/2764468.2764506","DOIUrl":"https://doi.org/10.1145/2764468.2764506","url":null,"abstract":"We study mechanisms that use greedy allocation rules and pay-your-bid pricing to allocate resources subject to a matroid constraint. We show that all such mechanisms obtain a constant fraction of the optimal welfare at any equilibrium of bidder behavior, via a smoothness argument. This unifies numerous recent results on the price of anarchy of simple auctions. Our results extend to polymatroid and matching constraints, and we discuss extensions to more general matroid intersections.","PeriodicalId":376992,"journal":{"name":"Proceedings of the Sixteenth ACM Conference on Economics and Computation","volume":"90 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116648598","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Sound Auction Specification and Implementation","authors":"M. Caminati, Manfred Kerber, C. Lange, C. Rowat","doi":"10.1145/2764468.2764511","DOIUrl":"https://doi.org/10.1145/2764468.2764511","url":null,"abstract":"We introduce `formal methods' of mechanized reasoning from computer science to address two problems in auction design and practice: is a given auction design soundly specified, possessing its intended properties; and, is the design faithfully implemented when actually run? Failure on either front can be hugely costly in large auctions. In the familiar setting of the combinatorial Vickrey auction, we use a mechanized reasoner, Isabelle, to first ensure that the auction has a set of desired properties (e.g. allocating all items at non-negative prices), and to then generate verified executable code directly from the specified design. Having established the expected results in a known context, we intend next to use formal methods to verify new auction designs.","PeriodicalId":376992,"journal":{"name":"Proceedings of the Sixteenth ACM Conference on Economics and Computation","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127710131","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Coalition Games on Interaction Graphs: A Horticultural Perspective","authors":"N. Bousquet, Zhentao Li, A. Vetta","doi":"10.1145/2764468.2764477","DOIUrl":"https://doi.org/10.1145/2764468.2764477","url":null,"abstract":"We examine cooperative games where the viability of a coalition is determined by whether or not its members have the ability to communicate amongst themselves independently of non-members. This necessary condition for viability was proposed by Myerson [1977] and is modeled via an interaction graph G=(V,E); a coalition S ⊆ V is then viable if and only if the induced graph G[S] is connected. The non-emptiness of the core of a coalition game can be tested by a well-known covering LP. Moreover, the integrality gap of its dual packing LP defines exactly the multiplicative least-core and the relative cost of stability of the coalition game. This gap is upper bounded by the packing-covering ratio which, for graphical coalition games, is known to be at most the treewidth of the interaction graph plus one [Meir et al. 2013]. We examine the packing-covering ratio and integrality gaps of graphical coalition games in more detail. We introduce the thicket parameter of a graph, and prove it precisely measures the packing-covering ratio. It also approximately measures the primal and dual integrality gaps. The thicket number provides an upper bound of both integrality gaps. Moreover we show that for any interaction graph, the primal integrality gap is, in the worst case, linear in terms of the thicket number while the dual integrality gap is polynomial in terms of it. At the heart of our results, is a graph theoretic minmax theorem showing the thicket number is equal to the minimum width of a vine decomposition of the coalition graph (a vine decomposition is a generalization of a tree decomposition). We also explain how the thicket number relates to the VC-dimension of the set system produced by the game.","PeriodicalId":376992,"journal":{"name":"Proceedings of the Sixteenth ACM Conference on Economics and Computation","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125744147","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ryan M. Rogers, Aaron Roth, Jonathan Ullman, Zhiwei Steven Wu
{"title":"Inducing Approximately Optimal Flow Using Truthful Mediators","authors":"Ryan M. Rogers, Aaron Roth, Jonathan Ullman, Zhiwei Steven Wu","doi":"10.1145/2764468.2764509","DOIUrl":"https://doi.org/10.1145/2764468.2764509","url":null,"abstract":"We revisit a classic coordination problem from the perspective of mechanism design: how can we coordinate a social welfare maximizing flow in a network congestion game with selfish players? The classical approach, which computes tolls as a function of known demands, fails when the demands are unknown to the mechanism designer, and naively eliciting them does not necessarily yield a truthful mechanism. Instead, we introduce a weak mediator that can provide suggested routes to players and set tolls as a function of reported demands. However, players can choose to ignore or misreport their type to this mediator. Using techniques from differential privacy, we show how to design a weak mediator such that it is an asymptotic ex-post Nash equilibrium for all players to truthfully report their types to the mediator and faithfully follow its suggestion, and that when they do, they end up playing a nearly optimal flow. Notably, our solution works in settings of incomplete information even in the absence of a prior distribution on player types. Along the way, we develop new techniques for privately solving convex programs which may be of independent interest.","PeriodicalId":376992,"journal":{"name":"Proceedings of the Sixteenth ACM Conference on Economics and Computation","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130766308","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Y. Mansour, Aleksandrs Slivkins, Vasilis Syrgkanis
{"title":"Bayesian Incentive-Compatible Bandit Exploration","authors":"Y. Mansour, Aleksandrs Slivkins, Vasilis Syrgkanis","doi":"10.1145/2764468.2764508","DOIUrl":"https://doi.org/10.1145/2764468.2764508","url":null,"abstract":"Individual decision-makers consume information revealed by the previous decision makers, and produce information that may help in future decision makers. This phenomenon is common in a wide range of scenarios in the Internet economy, as well as elsewhere, such as medical decisions. Each decision maker when required to select an action, would individually prefer to exploit, select the highest expected reward action conditional on her information. At the same time, each decision maker would prefer previous decision makers to explore, producing information about the rewards of various actions. A social planner, by means of carefully designed information disclosure, can incentivize the agents to balance the exploration and exploitation, and maximize social welfare. We formulate this problem as a multi-arm bandit problem (and various generalizations thereof) under incentive-compatibility constraints induced by agents' Bayesian priors. We design an incentive-compatible bandit algorithm for the social planner with asymptotically optimal regret. Further, we provide a black-box reduction from an arbitrary multi-arm bandit algorithm to an incentive-compatible one, with only a constant multiplicative increase in regret. This reduction works for very general bandit settings, even ones that incorporate contexts and arbitrary partial feedback.","PeriodicalId":376992,"journal":{"name":"Proceedings of the Sixteenth ACM Conference on Economics and Computation","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124308748","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Simple Mechanisms for a Subadditive Buyer and Applications to Revenue Monotonicity","authors":"A. Rubinstein, S. Weinberg","doi":"10.1145/2764468.2764510","DOIUrl":"https://doi.org/10.1145/2764468.2764510","url":null,"abstract":"We study the revenue maximization problem of a seller with n heterogeneous items for sale to a single buyer whose valuation function for sets of items is unknown and drawn from some distribution D. We show that if D is 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 are k-demand, additive up to a matroid constraint, or additive up to constraints of any downwards-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 [Li and Yao 2013; Babaioff et al.2014]. In the second part of the paper, 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 strictly increasing buyers' values for every set can strictly decrease the revenue of the optimal mechanism [Hart and Reny 2012]. Using our main result, we derive a bound on how bad this degradation can be (and dub such a bound a proof of approximate revenue monotonicity); we further show that better bounds on approximate monotonicity imply a better analysis of our simple mechanisms.","PeriodicalId":376992,"journal":{"name":"Proceedings of the Sixteenth ACM Conference on Economics and Computation","volume":"127 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128153626","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Price Competition, Fluctuations and Welfare Guarantees","authors":"Moshe Babaioff, R. Leme, Balasubramanian Sivan","doi":"10.1145/2764468.2764493","DOIUrl":"https://doi.org/10.1145/2764468.2764493","url":null,"abstract":"In various markets where sellers compete in price, price oscillations are observed rather than convergence to equilibrium. Such fluctuations have been empirically observed in the retail market for gasoline, in airline pricing and in the online sale of consumer goods. Motivated by this, we study a model of price competition in which equilibria rarely exist. We seek to analyze the welfare, despite the nonexistence of equilibria, and present welfare guarantees as a function of the market power of the sellers. We first study best response dynamics in markets with sellers that provide a homogeneous good, and show that except for a modest number of initial rounds, the welfare is guaranteed to be high. We consider two variations: in the first the sellers have full information about the buyer's valuation. Here we show that if there are n items available across all sellers and nmax is the maximum number of items controlled by any given seller, then the ratio of the optimal welfare to the achieved welfare will be at most log n/(n-nmax + 1))+1. As the market power of the largest seller diminishes, the welfare becomes closer to optimal. In the second variation we consider an extended model in which sellers have uncertainty about the buyer's valuation. Here we similarly show that the welfare improves as the market power of the larger seller decreases, yet with a worse ratio of n/(n-nmax + 1). Our welfare bounds in both cases are essentially tight. The exponential gap in welfare between the two variations quantifies the value of accurately learning the buyer's valuation in such settings. Finally, we show that extending our results to heterogeneous goods in general is not possible. Even for the simple class of k-additive valuations, there exists a setting where the welfare approximates the optimal welfare within any non-zero factor only for O(1/s) fraction of the time, where s is the number of sellers.","PeriodicalId":376992,"journal":{"name":"Proceedings of the Sixteenth ACM Conference on Economics and Computation","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116968035","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Competitive Analysis via Benchmark Decomposition","authors":"Ning Chen, N. Gravin, P. Lu","doi":"10.1145/2764468.2764491","DOIUrl":"https://doi.org/10.1145/2764468.2764491","url":null,"abstract":"We propose a uniform approach for the design and analysis of prior-free competitive auctions and online auctions. Our philosophy is to view the benchmark function as a variable parameter of the model and study a broad class of functions instead of a individual target benchmark. We consider a multitude of well-studied auction settings, and improve upon a few previous results. Multi-unit auctions. Given a β-competitive unlimited supply auction, the best previously known multi-unit auction is 2β-competitive. We design a (1+β)-competitive auction reducing the ratio from 4.84 to 3.24. These results carry over to matroid and position auctions. General downward-closed environments. We design a 6.5-competitive auction improving upon the ratio of 7.5. Our auction is noticeably simpler than the previous best one. Unlimited supply online auctions. Our analysis yields an auction with a competitive ratio of 4.12, which significantly narrows the margin of [4, 4.84] previously known for this problem. A particularly important tool in our analysis is a simple decomposition lemma, which allows us to bound the competitive ratio against a sum of benchmark functions. We use this lemma in a \"divide and conquer\" fashion by dividing the target benchmark into the sum of simpler functions.","PeriodicalId":376992,"journal":{"name":"Proceedings of the Sixteenth ACM Conference on Economics and Computation","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130327343","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Burden of Risk Aversion in Mean-Risk Selfish Routing","authors":"E. Nikolova, N. Stier-Moses","doi":"10.1145/2764468.2764485","DOIUrl":"https://doi.org/10.1145/2764468.2764485","url":null,"abstract":"Considering congestion games with uncertain delays, we compute the inefficiency introduced in network routing by risk-averse agents. At equilibrium, agents may select paths that do not minimize the expected latency so as to obtain lower variability. A social planner, who is likely to be more risk neutral than agents because it operates at a longer time-scale, quantifies social cost with the total expected delay along routes. From that perspective, agents may make suboptimal decisions that degrade long-term quality. We define the price of risk aversion (PRA) as the worst-case ratio of the social cost at a risk-averse Wardrop equilibrium to that where agents are risk-neutral. For networks with general delay functions and a single source-sink pair, we show that the PRA depends linearly on the agents' risk tolerance and on the degree of variability present in the network. In contrast to the price of anarchy, in general the PRA increases when the network gets larger but it does not depend on the shape of the delay functions. To get this result we rely on a combinatorial proof that employs alternating paths that are reminiscent of those used in max-flow algorithms. For series-parallel (SP) graphs, the PRA becomes independent of the network topology and its size. As a result of independent interest, we prove that for SP networks with deterministic delays, Wardrop equilibria maximize the shortest-path objective among all feasible flows.","PeriodicalId":376992,"journal":{"name":"Proceedings of the Sixteenth ACM Conference on Economics and Computation","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132582454","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Near-Optimum Online Ad Allocation for Targeted Advertising","authors":"J. Naor, David Wajc","doi":"10.1145/2764468.2764482","DOIUrl":"https://doi.org/10.1145/2764468.2764482","url":null,"abstract":"Motivated by Internet targeted advertising, we address several ad allocation problems. Prior work has established these problems admit no randomized online algorithm better than (1-1/e)-competitive ([Karp et al. 1990; Mehta et al. 2007]), yet simple heuristics have been observed to perform much better in practice. We explain this phenomenon by studying a generalization of the bounded-degree inputs considered by [Buchbinder et al. 2007), graphs which we call (k,d)-bounded. In such graphs the maximal degree on the online side is at most d and the minimal degree on the offline side is at least k. We prove that for such graphs, these problems' natural greedy algorithms attain competitive ratio 1-(d-1)/(k+d-1), tending to one as d/k tends to zero. We prove this bound is tight for these algorithms. Next, we develop deterministic primal-dual algorithms for the above problems achieving competitive ratio 1-(1-1/d)k>1-1/ek/d, or exponentially better loss as a function of k/d, and strictly better than 1-1/e whenever k ≥ d. We complement our lower bounds with matching upper bounds for the vertex-weighted problem. Finally, we use our deterministic algorithms to prove by dual-fitting that simple randomized algorithms achieve the same bounds in expectation. Our algorithms and analysis differ from previous ad allocation algorithms, which largely scale bids based on the spent fraction of their bidder's budget, whereas we scale bids according to the number of times the bidder could have spent as much as her current bid. Our algorithms differ from previous online primal-dual algorithms, as they do not maintain dual feasibility, but only primal-to-dual ratio, and only attain dual feasibility upon termination. We believe our techniques could find applications to other well-behaved online packing problems.","PeriodicalId":376992,"journal":{"name":"Proceedings of the Sixteenth ACM Conference on Economics and Computation","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132600617","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}