The price of anarchy for non-atomic congestion games with symmetric cost maps and elastic demands

Chau, Chi-Kin; Sim, Kwang Mong

doi:10.1016/s0167-6377(03)00030-0

Cited by 97 publications

(71 citation statements)

References 7 publications

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“…Several authors analyzed the bound on the inefficiency of equilibria for more general classes of cost functions and model features such as toll pricing (e.g. Chau and Sim, 2003;Correa et al, 2004;Roughgarden and Tardos, 2004;Yang et al, 2008). Roughgarden (2005) summarized the latest developments of this research subject.…”

Section: Bounding the Inefficiency Of Logit-based Stochastic User Equmentioning

confidence: 99%

Bounding the inefficiency of logit-based stochastic user equilibrium

Guo

Yang

Liu

2010

European Journal of Operational Research

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Abstract. Bounding the inefficiency of selfish routing has become an emerging research subject. A central result obtained in the literature is that the inefficiency of deterministic User Equilibrium (UE) is bounded and the bound is independent of network topology. This paper makes a contribution to the literature by bounding the inefficiency of the logit-based Stochastic User Equilibrium (SUE). In a stochastic environment there are two different definitions of system optimization: one is the traditional System Optimum (SO) which minimizes the total actual system travel time, and the other is the Stochastic System Optimum (SSO) which minimizes the total perceived travel time of all users. Thus there are two ways to define the inefficiency of SUE, i.e. to compare SUE with SO in terms of total actual system travel time, or to compare SUE with SSO in terms of total perceived travel time.We establish upper bounds on the inefficiency of SUE in both situations.

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Section: Bounding the Inefficiency Of Logit-based Stochastic User Equmentioning

confidence: 99%

Bounding the inefficiency of logit-based stochastic user equilibrium

Guo

Yang

Liu

2010

European Journal of Operational Research

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“…Constrained system optima can be generalized without difficulty given that they have the same structure as system optima. Although bounds on the efficiency of user equilibria with the more general latency functions were previously given [5,17], it is an interesting open question to determine the price of anarchy with respect to constrained system optima. It is clear that under user equilibrium normal lengths, (3.3) is still valid because any user equilibrium remains feasible for the constrained system optimum problem.…”

Section: Discussionmentioning

confidence: 99%

“…They proposed to measure the inefficiency of equilibria in a network consisting of two nodes and multiple parallel arcs by computing the worst-case ratio of the social cost of an equilibrium to that of a system optimum. Later, a series of papers studied the efficiency of user equilibria in traffic networks, under less and less restrictive assumptions: affine latency functions [23], convex and differentiable latency functions [21], general latency functions in networks with side constraints [7], nonseparable symmetric latency functions [5], nonseparable asymmetric latency functions [17], and networks with a fixed congestion level and arbitrary latency functions [8]. For additional references, see also [22].…”

Section: The Price Of Anarchymentioning

confidence: 99%

Efficiency and fairness of system‐optimal routing with user constraints

Schulz

Stier-Moses

2006

Networks

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We study the route-guidance system proposed by Jahn, Möhring, Schulz, and Stier-Moses [Operations Research 53 (2005), 600-616] from a theoretical perspective. As system-optimal guidance is known to be problematic, this approach computes a traffic pattern that minimizes the total travel time subject to user constraints. These constraints are designed to ensure that routes suggested to users are not much longer than shortest paths for the prevailing network conditions. To calibrate the system, a certain measure-called normal length-must be selected. We show that when this length is defined as the travel time at equilibrium, the resulting traffic assignment is provably efficient and close to fair. To measure efficiency, we compare the output to the best solution without guidance and to user equilibria. To measure unfairness, we compare travel times of different users, and show that they do not differ too much. Inefficient or unfair traffic assignments cause users to travel too long or discourage people from accepting the system; either consequence would jeopardize the potential impact of a route-guidance system.

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“…Despite these bounds for specific classes of latency functions, it is known that the price of anarchy in routing games with general latency functions is unbounded even on simple parallel-arc networks (Roughgarden and Tardos 2002). Chau and Sim (2003) studied the price of anarchy for nonatomic network games with elastic demands and general cost functions. They obtain bounds for the more general case of separable cost functions and elastic demands.…”

Section: Related Workmentioning

confidence: 99%

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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The price of anarchy for non-atomic congestion games with symmetric cost maps and elastic demands

Cited by 97 publications

References 7 publications

Bounding the inefficiency of logit-based stochastic user equilibrium

Bounding the inefficiency of logit-based stochastic user equilibrium

Efficiency and fairness of system‐optimal routing with user constraints

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

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