Local Smoothness and the Price of Anarchy in Atomic Splittable Congestion Games

Roughgarden, Tim; Schoppmann, Florian

doi:10.1137/1.9781611973082.22

Cited by 38 publications

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“…A celebrated result of Roughgarden [25], and Roughgarden and Tardos [30] gives tight bounds on the PoA for nonatomic routing games for the social welfare objective. Recently, similar results were obtained for the PoA in atomic splittable routing games [13,29].…”

Section: Related Worksupporting

confidence: 76%

Achieving target equilibria in network routing games without knowing the latency functions

Bhaskar

Ligett

Schulman

et al. 2019

Games and Economic Behavior

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The analysis of network routing games typically assumes, right at the onset, precise and detailed information about the latency functions. Such information may, however, be unavailable or difficult to obtain. Moreover, one is often primarily interested in enforcing a desired target flow as the equilibrium by suitably influencing player behavior in the routing game. We ask whether one can achieve target flows as equilibria without knowing the underlying latency functions.Our main result gives a crisp positive answer to this question. We show that, under fairly general settings, one can efficiently compute edge tolls that induce a given target multicommodity flow in a nonatomic routing game using a polynomial number of queries to an oracle that takes candidate tolls as input and returns the resulting equilibrium flow. This result is obtained via a novel application of the ellipsoid method. Our algorithm extends easily to many other settings, such as (i) when certain edges cannot be tolled or there is an upper bound on the total toll paid by a user, and (ii) general nonatomic congestion games. We obtain tighter bounds on the query complexity for series-parallel networks, and single-commodity routing games with linear latency functions, and complement these with a query-complexity lower bound. We also obtain strong positive results for Stackelberg routing to achieve target equilibria in series-parallel graphs.Our results build upon various new techniques that we develop pertaining to the computation of, and connections between, different notions of approximate equilibrium; properties of multicommodity flows and tolls in series-parallel graphs; and sensitivity of equilibrium flow with respect to tolls. Our results demonstrate that one can indeed circumvent the potentially-onerous task of modeling latency functions, and yet obtain meaningful results for the underlying routing game. *

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Section: Related Worksupporting

confidence: 76%

Achieving target equilibria in network routing games without knowing the latency functions

Bhaskar

Ligett

Schulman

et al. 2019

Games and Economic Behavior

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“…In particular in light of several known hardness results for finding Nash equilibria, this assumption is very suspect for computationally bounded players. In response, recent work has begun analyzing the outcomes of natural response dynamics [Blum et al 2006[Blum et al , 2008Roughgarden 2009], as well as other permissive solution concepts such as correlated or coarse correlated equilibria [Aumann 1974;Hannan 1957;Roughgarden and Schoppmann 2011]. This general direction of inquiry has become known as "robust price of anarchy.…”

Section: Introductionmentioning

confidence: 99%

Altruism and Its Impact on the Price of Anarchy

Chen

Keijzer

Kempe

et al. 2014

ACM Trans. Econ. Comput.

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We study the inefficiency of equilibria for congestion games when players are (partially) altruistic. We model altruistic behavior by assuming that player i's perceived cost is a convex combination of 1 − α i times his direct cost and α i times the social cost. Tuning the parameters α i allows smooth interpolation between purely selfish and purely altruistic behavior. Within this framework, we study primarily altruistic extensions of (atomic and nonatomic) congestion games, but also obtain some results on fair cost-sharing games and valid utility games.We derive (tight) bounds on the price of anarchy of these games for several solution concepts. Thereto, we suitably adapt the smoothness notion introduced by Roughgarden and show that it captures the essential properties to determine the robust price of anarchy of these games. Our bounds show that for atomic congestion games and cost-sharing games, the robust price of anarchy gets worse with increasing altruism, while for valid utility games, it remains constant and is not affected by altruism.However, the increase in the price of anarchy is not a universal phenomenon: For general nonatomic congestion games with uniform altruism, the price of anarchy improves with increasing altruism. For atomic and nonatomic symmetric singleton congestion games, we derive bounds on the pure price of anarchy that improve as the average level of altruism increases. (For atomic games, we only derive such bounds when cost functions are linear.) Since the bounds are also strictly lower than the robust price of anarchy, these games exhibit natural examples in which pure Nash equilibria are more efficient than more permissive notions of equilibrium.

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“…This bound is tight, as shown in Roughgarden and Schoppmann (2011). An important difference between our model and that of Hayrapetyan et al (2006) and Cominetti et al (2009) is that our model involves elastic demands that are varied by players.…”

Section: Related Workmentioning

confidence: 73%

The Worst-Case Efficiency of Cost Sharing Methods in Resource Allocation Games

Harks

Miller

2011

Operations Research

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Resource allocation problems play a key role in many applications, including traffic networks, telecommunication networks, and economics. In most applications, the allocation of resources is determined by a finite number of independent players, each optimizing an individual objective function. An important question in all these applications is the degree of suboptimality caused by selfish resource allocation. We consider the worst-case efficiency of cost sharing methods in resource allocation games in terms of the ratio of the minimum guaranteed surplus of a Nash equilibrium and the maximal surplus. Our main technical result is an upper bound on the efficiency loss that depends on the class of allowable cost functions and the class of allowable cost sharing methods. We demonstrate the power of this bound by evaluating the worst-case efficiency loss for three well-known cost sharing methods: incremental cost sharing, marginal cost pricing, and average cost sharing.

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Local Smoothness and the Price of Anarchy in Atomic Splittable Congestion Games

Cited by 38 publications

References 0 publications

Achieving target equilibria in network routing games without knowing the latency functions

Achieving target equilibria in network routing games without knowing the latency functions

Altruism and Its Impact on the Price of Anarchy

The Worst-Case Efficiency of Cost Sharing Methods in Resource Allocation Games

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