Results 1  10
of
21
The Price of Anarchy in Games of Incomplete Information
 EC'12
, 2012
"... We define smooth games of incomplete information. We prove an “extension theorem” for such games: price of anarchy bounds for pure Nash equilibria for all induced fullinformation games extend automatically, without quantitative degradation, to all mixedstrategy BayesNash equilibria with respect t ..."
Abstract

Cited by 25 (2 self)
 Add to MetaCart
(Show Context)
We define smooth games of incomplete information. We prove an “extension theorem” for such games: price of anarchy bounds for pure Nash equilibria for all induced fullinformation games extend automatically, without quantitative degradation, to all mixedstrategy BayesNash equilibria with respect to a product prior distribution over players’ preferences. We also note that, for BayesNash equilibria in games with correlated player preferences, there is no general extension theorem for smooth games. We give several applications of our definition and extension theorem. First, we show that many games of incomplete information for which the price of anarchy has been studied are smooth in our sense. Thus our extension theorem unifies much of the known work on the price of anarchy in games of incomplete information. Second, we use our extension theorem to prove new bounds on the price of anarchy of BayesNash equilibria in congestion games with incomplete information.
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 ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
(Show Context)
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.
Barriers to nearoptimal equilibria
 IN PROCEEDINGS OF THE 55TH ANNUAL IEEE SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE (FOCS
"... This paper explains when and how communication and computational lower bounds for algorithms for an optimization problem translate to lower bounds on the worstcase quality of equilibria in games derived from the problem. We give three families of lower bounds on the quality of equilibria, each moti ..."
Abstract

Cited by 3 (3 self)
 Add to MetaCart
(Show Context)
This paper explains when and how communication and computational lower bounds for algorithms for an optimization problem translate to lower bounds on the worstcase quality of equilibria in games derived from the problem. We give three families of lower bounds on the quality of equilibria, each motivated by a different set of problems: congestion, scheduling, and distributed welfare games; welfaremaximization in combinatorial auctions with “blackbox” bidder valuations; and welfaremaximization in combinatorial auctions with succinctly described valuations. The most straightforward use of our lower bound framework is to harness an existing computational or communication lower bound to derive a lower bound on the worstcase price of anarchy (POA) in a class of games. This is a new approach to POA lower bounds, which relies on reductions in lieu of explicit constructions. More generally, the POA lower bounds implied by our framework apply to all classes of games that share the same underlying optimization problem, independent of the details of players’ utility functions. For this reason, our lower bounds are particularly significant for problems of game design — ranging from the design of simple combinatorial auctions to the existence of effective tolls for routing networks — where the goal is to design a game that has only nearoptimal equilibria. For example, our results imply that the simultaneous firstprice auction format is optimal among all “simple combinatorial auctions” in several settings.
On the efficiency of the Walrasian mechanism
 In Proceedings of the 15th ACM Conference on Economics and Computation
, 2014
"... ar ..."
(Show Context)
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 ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
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
Combinatorial Auctions via Posted Prices
 In Proceedings of the 26th Annual ACMSIAM Symposium on Discrete Algorithms
, 2015
"... ar ..."
Simultaneous Bayesian Auctions and Computational Complexity
"... as an alternative to the wellknown complexity issues plaguing combinatorial auctions with incomplete information, and some strong positive results have been shown about their performance. We point out some very serious complexity obstacles to this approach: Computing a Bayesian equilibrium in such ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
as an alternative to the wellknown complexity issues plaguing combinatorial auctions with incomplete information, and some strong positive results have been shown about their performance. We point out some very serious complexity obstacles to this approach: Computing a Bayesian equilibrium in such auctions is hard for PP — a complexity class between the polynomial hierarchy and PSPACE — and even finding an approximate such equilibrium is as hard as NP, for some small approximation ratio (additive or multiplicative); therefore, the assumption that such equilibria will be arrived at by rational agents is quite problematic. In fact, even recognizing a Bayesian Nash equilibrium is intractable. Furthermore, these results hold even if bidder valuations are quite benign: Only one bidder valuation in our construction is unit demand or monotone submodular, while all others are additive. We also explore the possibility of favorable price of anarchy results for noregret dynamics of the Bayesian simultaneous auctions game, and identify complexity obstacles there as well. 1.