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25
Intrinsic Robustness of the Price of Anarchy
 STOC'09
, 2009
"... The price of anarchy (POA) is a worstcase measure of the inefficiency of selfish behavior, defined as the ratio of the objective function value of a worst Nash equilibrium of a game and that of an optimal outcome. This measure implicitly assumes that players successfully reach some Nash equilibrium ..."
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The price of anarchy (POA) is a worstcase measure of the inefficiency of selfish behavior, defined as the ratio of the objective function value of a worst Nash equilibrium of a game and that of an optimal outcome. This measure implicitly assumes that players successfully reach some Nash equilibrium. This drawback motivates the search for inefficiency bounds that apply more generally to weaker notions of equilibria, such as mixed Nash and correlated equilibria; or to sequences of outcomes generated by natural experimentation strategies, such as successive best responses or simultaneous regretminimization. We prove a general and fundamental connection between the price of anarchy and its seemingly stronger relatives in classes of games with a sum objective. First, we identify a “canonical sufficient condition ” for an upper bound of the POA for pure Nash equilibria, which we call a smoothness argument. Second, we show that every bound derived via a smoothness argument extends automatically, with no quantitative degradation in the bound, to mixed Nash equilibria, correlated equilibria, and the average objective function value of regretminimizing players (or “price of total anarchy”). Smoothness arguments also have automatic implications for the inefficiency of approximate and BayesianNash equilibria and, under mild additional assumptions, for bicriteria bounds and for polynomiallength bestresponse sequences. We also identify classes of games — most notably, congestion games with cost functions restricted to an arbitrary fixed set — that are tight, in the sense that smoothness arguments are guaranteed to produce an optimal worstcase upper bound on the POA, even for the smallest set of interest (pure Nash equilibria). Byproducts of our proof of this result include the first tight bounds on the POA in congestion games with nonpolynomial cost functions, and the first
Simultaneous Auctions are (almost) Efficient
, 2012
"... Simultaneous item auctions are simple procedures for allocating items to bidders with potentially complex preferences over different item sets. In a simultaneous auction, every bidder submits bids on all items simultaneously. The allocation and prices are then resolved for each item separately, base ..."
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Cited by 21 (5 self)
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Simultaneous item auctions are simple procedures for allocating items to bidders with potentially complex preferences over different item sets. In a simultaneous auction, every bidder submits bids on all items simultaneously. The allocation and prices are then resolved for each item separately, based solely on the bids submitted on that item. Such procedures occur in practice (e.g. eBay) but are not truthful. We study the efficiency of Bayesian Nash equilibrium (BNE) outcomes of simultaneous first and secondprice auctions when bidders have complementfree (a.k.a. subadditive) valuations. We show that the expected social welfare of any BNE is at least 1 2 of the optimal social welfare in the case of firstprice auctions, and at least 1 4 in the case of secondprice auctions. These results improve upon the previouslyknown logarithmic bounds, which wereestablished by Hassidim et al. (2011) for firstpriceauctions and by Bhawalkar and Roughgarden (2011) for secondprice auctions. 1
Mechanism design in large games: Incentives and privacy. arXiv preprint arXiv:1207.4084,
, 2013
"... ABSTRACT We study the problem of implementing equilibria of complete information games in settings of incomplete information, and address this problem using "recommender mechanisms." A recommender mechanism is one that does not have the power to enforce outcomes or to force participation, ..."
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ABSTRACT We study the problem of implementing equilibria of complete information games in settings of incomplete information, and address this problem using "recommender mechanisms." A recommender mechanism is one that does not have the power to enforce outcomes or to force participation, rather it only has the power to suggestion outcomes on the basis of voluntary participation. We show that despite these restrictions, recommender mechanisms can implement equilibria of complete information games in settings of incomplete information under the condition that the game is largei.e. that there are a large number of players, and any player's action affects any other's payoff by at most a small amount. Our result follows from a novel application of differential privacy. We show that any algorithm that computes a correlated equilibrium of a complete information game while satisfying a variant of differential privacywhich we call joint differential privacycan be used as a recommender mechanism while satisfying our desired incentive properties. Our main technical result is an algorithm for computing a * We gratefully acknowledge the support of NSF Grant CCF1101389. We thank Nabil AlNajjar, Eduardo Azevdeo, Eric Budish, Tymofiy Mylovanov, Andy Postlewaite, Al Roth and Tim Roughgarden for helpful comments and discussions. correlated equilibrium of a large game while satisfying joint differential privacy. Although our recommender mechanisms are designed to satisfy gametheoretic properties, our solution ends up satisfying a strong privacy property as well. No group of players can learn "much" about the type of any player outside the group from the recommendations of the mechanism, even if these players collude in an arbitrary way. As such, our algorithm is able to implement equilibria of complete information games, without revealing information about the realized types.
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.
On the efficiency of the Walrasian mechanism
 In Proceedings of the 15th ACM Conference on Economics and Computation
, 2014
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Restoring Pure Equilibria to Weighted Congestion Games
"... Congestion games model several interesting applications, including routing and network formation games, and also possess attractive theoretical properties, including the existence of and convergence of natural dynamics to a pure Nash equilibrium. Weighted variants of congestion games that rely on s ..."
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Congestion games model several interesting applications, including routing and network formation games, and also possess attractive theoretical properties, including the existence of and convergence of natural dynamics to a pure Nash equilibrium. Weighted variants of congestion games that rely on sharing costs proportional to players’ weights do not generally have purestrategy Nash equilibria. We propose a new way of assigning costs to players with weights in congestion games that recovers the important properties of the unweighted model. This method is derived from the Shapley value, and it always induces a game with a (weighted) potential function. For the special cases of weighted network costsharing and atomic selfish routing games (with Shapley valuebased cost shares), we prove tight bounds on the price of stability and price of anarchy, respectively.
Tight bounds for the price of anarchy of simultaneous first price auctions. arXiv:1312.2371
, 2013
"... We study the Price of Anarchy of simultaneous FirstPrice auctions for buyers with submodular and subadditive valuations. The current best upper bounds for the Bayesian Price of Anarchy of these auctions are e/(e − 1) [34] and 2 [16], respectively. We provide matching lower bounds for both cases ev ..."
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We study the Price of Anarchy of simultaneous FirstPrice auctions for buyers with submodular and subadditive valuations. The current best upper bounds for the Bayesian Price of Anarchy of these auctions are e/(e − 1) [34] and 2 [16], respectively. We provide matching lower bounds for both cases even for the case of the full information and for mixed Nash equilibria. An immediate consequence of our results, is that for both cases, the Price of Anarchy of these auctions stays the same, for mixed, correlated, coarsecorrelated, and Bayesian Nash equilibria. We bring some novel ideas to the theoretical discussion of upper bounding the Price of Anarchy in Bayesian Auctions settings. We suggest an alternative way to bid against price distributions. Using our approach we were able to reprovide the upper bounds of e/(e − 1) [34] for XOS bidders. An advantage of our approach, is that it reveals a worstcase price distribution, that is used as a building block for the matching lower bound construction. Finally, we apply our techniques on Discriminatory Price multiunit auctions. We complement the results of [13] for the case of subadditive valuations, by providing a matching lower bound of 2. For the case of submodular valuations, we provide a lower bound of 1.109. For the same class of valuations, we were able to reproduce the upper bound of e/(e − 1) using our nonsmooth approach. 1
Inefficiency of Games with Social Context
 In Proc. 6th International Symposium on Algorithmic Game Theory
, 2013
"... Abstract. The study of otherregarding player behavior such as altruism and spite in games has recently received quite some attention in the algorithmic game theory literature. Already for very simple models, it has been shown that altruistic behavior can actually be harmful for society in the sens ..."
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Abstract. The study of otherregarding player behavior such as altruism and spite in games has recently received quite some attention in the algorithmic game theory literature. Already for very simple models, it has been shown that altruistic behavior can actually be harmful for society in the sense that the price of anarchy may increase as the players become more altruistic. In this paper, we study the severity of this phenomenon for more realistic settings in which there is a complex underlying social structure, causing the players to direct their altruistic and spiteful behavior in a refined playerspecific sense (depending, for example, on friendships that exist among the players). Our findings show that the increase in the price of anarchy is modest for congestion games and minsum scheduling games, whereas it is drastic for generalized second price auctions. 1