A geometric approach to the price of anarchy in nonatomic congestion games

Correa, José R.; Schulz, Andreas S.; Stier-Moses, Nicolás E.

doi:10.1016/j.geb.2008.01.001

Cited by 100 publications

(98 citation statements)

References 27 publications

(35 reference statements)

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“…In fact, the proof is a minor variation of the standard smoothness argument, e.g. from [5,15]. A price of anarchy bound ofλ 1−μ follows as an immediate corollary.…”

Section: Smoothness For Biased Costsmentioning

confidence: 85%

Playing the Wrong Game

Meir

Parkes

2015

SIGMETRICS Perform. Eval. Rev.

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In many situations a player may act so as to maximize a perceived utility that is not exactly her utility function, but rather some other, biased, utility. Examples of such biased utility functions are common in behavioral economics, and include risk attitudes, altruism, present-bias and so on. When analyzing a game, one may ask how inefficiency, measured by the Price of Anarchy (PoA) is affected by the perceived utilities.The smoothness method [16,15] naturally extends to games with such perceived utilities or costs, regardless of the game or the behavioral bias. We show that such biased-smoothness is broadly applicable in the context of nonatomic congestion games. First, we show that on series-parallel networks we can use smoothness to yield PoA bounds even for diverse populations with different biases. Second, we identify various classes of cost functions and biases that are smooth, thereby substantially improving some recent results from the literature.

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“…In fact, the proof is a minor variation of the standard smoothness argument, e.g. from [5,15]. A price of anarchy bound ofλ 1−μ follows as an immediate corollary.…”

Section: Smoothness For Biased Costsmentioning

confidence: 85%

Playing the Wrong Game

Meir

Parkes

2015

SIGMETRICS Perform. Eval. Rev.

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“…However, using the latter term would be potentially confusing, since the literature on congestion games (e.g., Milchtaich, 2006a;Correa et al, 2008) already assigns it several meanings that are substantially different from the meaning of separability in this paper and others.…”

mentioning

confidence: 81%

Weighted congestion games with separable preferences

Milchtaich

2009

Games and Economic Behavior

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Players in a congestion game may differ from one another in their intrinsic preferences (e.g., the benefit they get from using a specific resource), their contribution to congestion, or both. In many cases of interest, intrinsic preferences and the negative effect of congestion are (additively or multiplicatively) separable. This paper considers the implications of separability for the existence of pure-strategy Nash equilibrium and the prospects of spontaneous convergence to equilibrium. It is shown that these properties may or may not be guaranteed, depending on the exact nature of player heterogeneity.

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“…Proof We use a similar approach as Correa et al [6]. Since x is a deviated Nash flow with respect to l + δ, the following variational inequality holds:…”

Section: Moreover This Bound Is Tight If L Contains All Constant Funmentioning

confidence: 99%

The Impact of Worst-Case Deviations in Non-Atomic Network Routing Games

Kleer¹,

Schäfer

2017

Theory Comput Syst

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We introduce a unifying model to study the impact of worst-case latency deviations in non-atomic selfish routing games. In our model, latencies are subject to (bounded) deviations which are taken into account by the players. The quality deterioration caused by such deviations is assessed by the Deviation Ratio, i.e., the worst case ratio of the cost of a Nash flow with respect to deviated latencies and the cost of a Nash flow with respect to the unaltered latencies. This notion is inspired by the Price of Risk Aversion recently studied by Nikolova and Stier-Moses (Nikolova and Stier-Moses 2015). Here we generalize their model and results. In particular, we derive tight bounds on the Deviation Ratio for multi-commodity instances with a common source and arbitrary non-negative and non-decreasing latency functions. These bounds exhibit a linear dependency on the size of the network (besides other parameters). In contrast, we show that for general multi-commodity networks an

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A geometric approach to the price of anarchy in nonatomic congestion games

Cited by 100 publications

References 27 publications

Playing the Wrong Game

Playing the Wrong Game

Weighted congestion games with separable preferences

The Impact of Worst-Case Deviations in Non-Atomic Network Routing Games

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