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48
Beyond equilibria: Mechanisms for repeated combinatorial auctions
, 2009
"... We study the design of mechanisms in combinatorial auction domains. We focus on settings where the auction is repeated, motivated by auctions for licenses or advertising space. We consider models of agent behaviour in which they either apply common learning techniques to minimize the regret of thei ..."
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Cited by 8 (5 self)
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We study the design of mechanisms in combinatorial auction domains. We focus on settings where the auction is repeated, motivated by auctions for licenses or advertising space. We consider models of agent behaviour in which they either apply common learning techniques to minimize the regret of their bidding strategies, or apply shortsighted bestresponse strategies. We ask: when can a blackbox approximation algorithm for the base auction problem be converted into a mechanism that approximately preserves the original algorithm’s approximation factor on average over many iterations? We present a general reduction for a broad class of algorithms when agents minimize external regret. We also present a mechanism for the combinatorial auction problem that attains an O (√m) approximation on average when agents apply bestresponse dynamics.
Simplicityexpressiveness tradeoffs in mechanism design
 In Proc. of 12th EC
, 2011
"... ABSTRACT A fundamental result in mechanism design theory, the socalled revelation principle, asserts that for many questions concerning the existence of mechanisms with a given outcome one can restrict attention to truthful directrevelation mechanisms. In practice, however, many mechanisms use a r ..."
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Cited by 7 (3 self)
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ABSTRACT A fundamental result in mechanism design theory, the socalled revelation principle, asserts that for many questions concerning the existence of mechanisms with a given outcome one can restrict attention to truthful directrevelation mechanisms. In practice, however, many mechanisms use a restricted message space. This motivates the study of the tradeoffs involved in choosing simplified mechanisms, which can sometimes bring benefits in precluding bad or promoting good equilibria, and other times impose costs on welfare and revenue. We study the simplicityexpressiveness tradeoff in two representative settings, sponsored search auctions and combinatorial auctions, each being a canonical example for complete information and incomplete information analysis, respectively. We observe that the amount of information available to the agents plays an important role for the tradeoff between simplicity and expressiveness.
Risk Sensitivity of Price of Anarchy under Uncertainty
, 2013
"... In algorithmic game theory, the price of anarchy framework studies efficiency loss in decentralized environments. In optimization and decision theory, the price of robustness framework explores the tradeoffs between optimality and robustness in the case of single agent decision making under uncertai ..."
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Cited by 6 (1 self)
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In algorithmic game theory, the price of anarchy framework studies efficiency loss in decentralized environments. In optimization and decision theory, the price of robustness framework explores the tradeoffs between optimality and robustness in the case of single agent decision making under uncertainty. We establish a connection between the two that provides a novel analytic framework for proving tight performance guarantees for distributed systems in uncertain environments. We present applications of this framework to novel variants of atomic congestion games with uncertain costs, for which we provide tight performance bounds under a wide range of risk attitudes. Our results establish that the individual’s attitude towards uncertainty has a critical effect on system performance and should therefore be a subject of close and systematic investigation.
Valuation compressions in vcgbased combinatorial auctions
 In WINE
, 2013
"... Abstract The focus of classic mechanism design has been on truthful directrevelation mechanisms. In the context of combinatorial auctions the truthful directrevelation mechanism that maximizes social welfare is the VCG mechanism. For many valuation spaces computing the allocation and payments of ..."
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Abstract The focus of classic mechanism design has been on truthful directrevelation mechanisms. In the context of combinatorial auctions the truthful directrevelation mechanism that maximizes social welfare is the VCG mechanism. For many valuation spaces computing the allocation and payments of the VCG mechanism, however, is a computationally hard problem. We thus study the performance of the VCG mechanism when bidders are forced to choose bids from a subspace of the valuation space for which the VCG outcome can be computed efficiently. We prove improved upper bounds on the welfare loss for restrictions to additive bids and upper and lower bounds for restrictions to nonadditive bids. These bounds show that the welfare loss increases in expressiveness. All our bounds apply to equilibrium concepts that can be computed in polynomial time as well as to learning outcomes.
Bayesian sequential auctions
 in Proceedings of the ACM Conference on Electronic Commerce
"... In many natural settings agents participate in multiple different auctions that are not simultaneous. In such auctions, future opportunities affect strategic considerations of the players. The goal of this paper is to develop a quantitative understanding of outcomes of such sequential auctions. In e ..."
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In many natural settings agents participate in multiple different auctions that are not simultaneous. In such auctions, future opportunities affect strategic considerations of the players. The goal of this paper is to develop a quantitative understanding of outcomes of such sequential auctions. In earlier work (Paes Leme et al. 2012) we initiated the study of the price of anarchy in sequential auctions. We considered sequential first price auctions in the full information model, where players are aware of all future opportunities, as well as the valuation of all players. In this paper, we study efficiency in sequential auctions in the Bayesian environment, relaxing the informational assumption on the players. We focus on two environments, both studied in the full information model in Paes Leme et al. 2012, matching markets and matroid auctions. In the full information environment, a sequential first price cut auction for matroid settings is efficient. In Bayesian environments this is no longer the case, as we show using a simple example with three players. Our main result is a bound of 3 on the price of anarchy in both matroid auctions and matching markets. To bound the price of anarchy we need to consider possible deviations at an equilibrium. In a sequential Bayesian environment the effect of deviations is more complex than in oneshot games; early bids allow others to infer information about the player’s value. We create effective deviations despite the presence of this difficulty by introducing a bluffing technique of independent interest.
Uniform Price Auctions: Equilibria and Efficiency
 SAGT 2012. LNCS
, 2012
"... We present our results on Uniform Price Auctions, one of the standard sealedbid multiunit auction formats, for selling multiple identical units of a single good to multidemand bidders. Contrary to the truthful and economically efficient multiunit Vickrey auction, the Uniform Price Auction enc ..."
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We present our results on Uniform Price Auctions, one of the standard sealedbid multiunit auction formats, for selling multiple identical units of a single good to multidemand bidders. Contrary to the truthful and economically efficient multiunit Vickrey auction, the Uniform Price Auction encourages strategic bidding and is socially inefficient in general, partly due to a ”Demand Reduction ” effect; bidders tend to bid for fewer (identical) units, so as to receive them at a lower uniform price. Despite its inefficiency, the uniform pricing rule is widely popular by its appeal to the natural anticipation, that identical items should be identically priced. Application domains of its variants include sales of U.S. Treasury bonds to investors, trade exchanges over the internet facilitated by popular online brokers, allocation of radio spectrum licenses etc. In this work we study equilibria of the Uniform Price Auction in undominated strategies. We characterize a class of undominated pure Nash equilibria and quantify the social inefficiency of pure and (mixed) BayesNash equilibria by means of bounds on the Price of Anarchy.
Do Externalities Degrade GSP’s Efficiency?
, 2012
"... We consider variants of the cascade model of externalities in sponsored search auctions introduced independently by Aggrawal et al. and Kempe and Mahdian in 2008, where the clickthrough rate of a slot depends also on the ads assigned to earlier slots. Aggrawal et al. and Kempe and Mahdian give a dy ..."
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Cited by 3 (0 self)
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We consider variants of the cascade model of externalities in sponsored search auctions introduced independently by Aggrawal et al. and Kempe and Mahdian in 2008, where the clickthrough rate of a slot depends also on the ads assigned to earlier slots. Aggrawal et al. and Kempe and Mahdian give a dynamic programming algorithm for finding the efficient allocation in this model. We give worstcase efficiency bounds for a variant of the classical Generalized Second Price (GSP) auction in this model. Our technical approach is to first consider an idealized version of the model where an unlimited number of ads can be displayed on the same page; here, Aggrawal et al. and Kempe and Mahdian show that a greedy algorithm finds the optimal allocation. The game theoretic analog of this greedy algorithm can be thought of as a variant of the classical GSP auction. We give the first nontrivial worstcase efficiency bounds for GSP in this model. In the more general model with limited slots, greedy algorithms like GSP can compute extremely bad allocations. Nonetheless, we show that an appropriate extension of the greedy algorithm is approximately optimal, and that the worstcase equilibrium inefficiency in the corresponding analog of GSP also remains bounded. In the context of these models, the GSP mechanisms suffer from two forms of suboptimality: that from using a simple allocation rule (the greedy algorithm) rather than an optimal one (based on dynamic programming), and that from the strategic behavior of the bidders (caused by using the GSP’s critical bid pricing rule rather than one leading to a dominantstrategy implementation). Our results show that for this class of problems, the two causes of efficiency loss can be analyzed separately.
On the Limitations of Greedy Mechanism Design for Truthful Combinatorial Auctions
"... Abstract. We study the combinatorial auction (CA) problem, in which m objects are sold to rational agents and the goal is to maximize social welfare. Of particular interest is the special case in which agents are interested in sets of size at most s (sCAs), where a simple greedy algorithm obtains a ..."
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Abstract. We study the combinatorial auction (CA) problem, in which m objects are sold to rational agents and the goal is to maximize social welfare. Of particular interest is the special case in which agents are interested in sets of size at most s (sCAs), where a simple greedy algorithm obtains an s+1 approximation but no truthful algorithm is known to perform better than O(m / √ log m). As partial work towards resolving this gap, we ask: what is the power of truthful greedy algorithms for CA problems? The notion of greediness is associated with a broad class of algorithms, known as priority algorithms, which encapsulates many natural auction methods. We show that no truthful greedy priority algorithm can obtain an approximation to the CA problem that is sublinear in m, even for sCAs with s ≥ 2. 1