Network congestion games are robust to variable demand

Correa, José R.; Hoeksma, Ruben; Schröder, Marc

doi:10.1016/j.trb.2018.11.010

Cited by 11 publications

(13 citation statements)

References 21 publications

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“…Roughgarden (2015) showed that whenever player types are independent, the inefficiency bounds for complete information games extend to Bayesian Nash equilibria of the incomplete information game. Wang et al (2014) and Correa et al (2019) looked at similar questions for nonatomic routing games. This trend does not only include congestion games: Stidham (2014) studied the efficiency of some classical queueing models on various networks, whereas Hassin et al (2018) examined a queueing model with heterogeneous agents and studied how the inefficiency of equilibria varies with the intensity function.…”

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confidence: 99%

Approximation and Convergence of Large Atomic Congestion Games

Cominetti¹,

Scarsini²,

Schröder³

et al. 2020

Preprint

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A. We study the convergence of sequences of atomic unsplittable congestion games with an increasing number of players. We consider two situations. In the first setting, each player has a weight that tends to zero, in which case the mixed equilibria of the finite games converge to the set of Wardrop equilibria of the corresponding nonatomic limit game. In the second case, players have unit weights, but participate in the game with a probability that tends to zero. In this case, the mixed equilibria converge to the set of Wardrop equilibria of another nonatomic game with suitably defined costs, which can be seen as a Poisson game in the sense of Myerson (1998b). In both settings we show that the price of anarchy of the sequence of games converges to the price of anarchy of the nonatomic limit. Beyond the case of congestion games, we establish a general result on the convergence of large games with random players towards a Poisson game.

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confidence: 99%

Approximation and Convergence of Large Atomic Congestion Games

Cominetti¹,

Scarsini²,

Schröder³

et al. 2020

Preprint

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“…His framework for incomplete information games is very robust, but requires a smoothness de nition that holds across di erent types (see Roughgarden, 2015b, De nition 3.1 and Remark 3.2). A result in the same spirit appears in Correa et al (2019), where it is shown that the bound of 5/2 holds for the PoA of ACGSDs with a ne costs even if the events of players being active are not i.i.d. These authors consider a class of games and an information structure that makes these objects games of incomplete information; then they compute bounds for the PoA of games in this class over all possible probabilities that characterize the incomplete information.…”

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confidence: 58%

“…However, because Roughgarden's bounds are more robust, they are not as sharp as ours. Recently, Correa et al (2019) proved a similar result for smooth games with stochastic demand and arbitrary correlations in the participation probability, but again their bounds are not tight for a xed p ∈ (0, 1). Wrede (2019) considers the same model as ours, but restricts attention to games with a small number of players.…”

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confidence: 99%

Price of Anarchy in Stochastic Atomic Congestion Games with Affine Costs

Cominetti

Scarsini

Schröder

et al. 2019

Proceedings of the 2019 ACM Conference on Economics and Computation

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A. We consider atomic congestion games with stochastic demands. The game captures the fact that players may end up not being able to participate. Participation happens independently and with exogenous probabilities p i ∈ [0, 1] that are common knowledge. Conversely, exclusion happens with probability 1−p i , in which case players incur no cost. We prove that this is a potential game, and that the price of anarchy parameterized by the probabilities is a nondecreasing function of p = max i p i . The worst case is attained for players with the same probabilities p i ≡ p. In the case of a ne costs we provide an analytic expression for the parameterized price of anarchy as a function of p. This function is continuous on (0, 1], it is equal to 4/3 for 0 < p ≤ 1/4, and increases towards the known atomic bound of 5/2 when p → 1. The result follows using the (λ, µ)smoothness framework and optimizing the parameters to get sharp bounds. We show that these bounds are tight and are attained on routing games with purely linear costs (i.e., without constant terms). Additionally, we derive tight bounds for the price of stability for all values of p ∈ [0, 1].

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“…For example, Harsanyi (1967Harsanyi ( , 1968 proposed Bayesian games that consider the incomplete information of payoffs, Ordóñez and Stier-Moses (2010) modeled the risk-averse behavior of travelers by padding the expected travel time along paths with a safety margin, Watling (2006) proposed an equilibrium based on the optimality measure of minimizing the probability of being late or maximizing the probability of being on time, Szeto, O'Brien, and O'Mahony (2006) associated a cost with the travel time uncertainty based on travelers' risk-averse behavior, Chen and Zhou (2010) proposed an equilibrium based on the optimality measure of minimizing the conditional expectation of travel time beyond a travel time budget, and Bell and Cassir (2002) proposed to play out all possible scenarios before making a choice. For more details in the context of traffic networks, we refer readers to (Aashtiani and Magnanti 1981, Aghassi and Bertsimas 2006, Altman et al 2006, Hayashi, Yamashita, and Fukushima 2005, Mirchandani and Soroush 1987, Nie 2011, Connors and Sumalee 2009, Schmöcker et al 2009, Fonzone et al 2012, Angelidakis, Fotakis, and Lianeas 2013, Nikolova and Stier-Moses 2011, and (Correa, Hoeksma, and Schröder 2019). A feasible assignment m := {m p : p ∈ P} allocates a non-negative number of players to every path p ∈ P such that p∈P k m p = n k for all k ∈ K. As a result, the number of players along link e ∈ E denoted by m e is given by m e = {p∈P:e∈p} m p .…”

Section: Related Workmentioning

confidence: 99%

Risk-Averse Equilibrium for Autonomous Vehicles in Stochastic Congestion Games

Yekkehkhany,

Nagi

2020

Preprint

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The fast-growing market of autonomous vehicles, unmanned aerial vehicles, and fleets in general necessitates the design of smart and automatic navigation systems considering the stochastic latency along different paths in the traffic network. The longstanding shortest path problem in a deterministic network, whose counterpart in a congestion game setting is Wardrop equilibrium, has been studied extensively, but it is well known that finding the notion of an optimal path is challenging in a traffic network with stochastic arc delays. In this work, we propose three classes of risk-averse equilibria for an atomic stochastic congestion game in its general form where the arc delay distributions are load dependent and not necessarily independent of each other. The three classes are risk-averse equilibrium (RAE), mean-variance equilibrium (MVE), and conditional value at risk level α equilibrium (CVaRαE) whose notions of risk-averse best responses are based on maximizing the probability of taking the shortest path, minimizing a linear combination of mean and variance of path delay, and minimizing the expected delay at a specified risky quantile of the delay distributions, respectively.We prove that for any finite stochastic atomic congestion game, the risk-averse, mean-variance, and CVaRα equilibria exist. We show that for risk-averse travelers, the Braess paradox may not occur to the extent presented originally since players do not necessarily travel along the shortest path in expectation, but they take the uncertainty of travel time into consideration as well. We show through some examples that the price of anarchy can be improved when players are risk-averse and travel according to one of the three classes of risk-averse equilibria rather than the Wardrop equilibrium.

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Network congestion games are robust to variable demand

Cited by 11 publications

References 21 publications

Approximation and Convergence of Large Atomic Congestion Games

Approximation and Convergence of Large Atomic Congestion Games

Price of Anarchy in Stochastic Atomic Congestion Games with Affine Costs

Risk-Averse Equilibrium for Autonomous Vehicles in Stochastic Congestion Games

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