Weighted Congestion Games: Price of Anarchy, Universal Worst-Case Examples, and Tightness

Bhawalkar, Kshipra; Gairing, Martin; Roughgarden, Tim

doi:10.1007/978-3-642-15781-3_2

Cited by 52 publications

(71 citation statements)

References 21 publications

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“…On the other hand, our work reveals that for most classes of cost functions pure Nash equilibria as the stronger solution concept may fail to exist in weighted congestion games. Thus, our work provides additional justification to study the worst-case efficiency loss for different solution concepts, such as sink equilibria (Goemans et al [19]), correlated and coarse correlated equilibria (Bhawalkar et al [9], Roughgarden [34]). …”

Section: 2mentioning

confidence: 94%

On the Existence of Pure Nash Equilibria in Weighted Congestion Games

Harks

Klimm

2010

Automata, Languages and Programming

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We study the existence of pure Nash equilibria in weighted congestion games. Let denote a set of cost functions. We say that is consistent if every weighted congestion game with cost functions in possesses a pure Nash equilibrium. Our main contribution is a complete characterization of consistency of continuous cost functions. We prove that a set of continuous functions is consistent for two-player games if and only if contains only monotonic functions and for all nonconstant functions c 1 c 2 ∈ , there are constants a b ∈ such that c 1 x = a c 2 x + b for all x ∈ ≥0 . For games with at least three players, we prove that is consistent if and only if exactly one of the following cases holds: (a) contains only affine functions; (b) contains only exponential functions such that c x = a c e x + b c for some a c b c ∈ , where a c and b c may depend on c, while must be equal for every c ∈ . The latter characterization is even valid for three-player games. Finally, we derive several characterizations of consistency of cost functions for games with restricted strategy spaces, such as weighted network congestion games or weighted congestion games with singleton strategies.

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Section: 2mentioning

confidence: 94%

On the Existence of Pure Nash Equilibria in Weighted Congestion Games

Harks

Klimm

2010

Automata, Languages and Programming

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“…For example, in a network context, players could have different durations of resource usage, different bandwidth requirements, or different contracts with the network provider. Almost all research to date has modeled non-uniform players in congestion-type games through proportional cost sharing [1,2,3,4,5,8,11,12,17,18]. The first assumption in proportional cost sharing is that each player i has a positive weight w i , with larger weights indicating larger resource usage.…”

mentioning

confidence: 99%

Restoring Pure Equilibria to Weighted Congestion Games

Kollias

Roughgarden

2015

ACM Trans. Econ. Comput.

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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 pure-strategy 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 cost-sharing and weighted routing games with Shapley value-based cost shares, we prove tight bounds on the worst-case inefficiency of equilibria. For weighted network cost-sharing games, we precisely calculate the price of stability for any given player weight vector, while for weighted routing games, we precisely calculate the price of anarchy, as a parameter of the set of allowable cost functions.

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“…non-sequential) price of anarchy of symmetric network routing games with linear costs and show that it equals 5/2. This resolves an open question posed by Bhawalkar et al [18] regarding the price of anarchy of congestion games. Surprisingly, the lower bound that we provide is conceptually simpler than the one previously provided for the more general class of (non-network) affine congestion games by Christodoulou and Koutsoupias [29].…”

Section: Price Of Anarchysupporting

confidence: 64%

“…Moreover, Christodoulou and Koutsoupias [29] also obtained a tight bound of 5n−2 2n+1 on the price of anarchy for affine symmetric congestion games. Interestingly, obtaining a tight lower bound on the price of anarchy for the symmetric network case was an open problem [18]. In this chapter, next to resolving this open problem for linear cost functions (Section 4.5), we analyze the sequential version of network congestion games.…”

Section: Sequential Price Of Anarchy For Affine Symmetric Network Conmentioning

confidence: 99%

Quality of equilibria in resource allocation games

Jong

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Weighted Congestion Games: Price of Anarchy, Universal Worst-Case Examples, and Tightness

Cited by 52 publications

References 21 publications

On the Existence of Pure Nash Equilibria in Weighted Congestion Games

On the Existence of Pure Nash Equilibria in Weighted Congestion Games

Restoring Pure Equilibria to Weighted Congestion Games

Quality of equilibria in resource allocation games

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