Results 1  10
of
506
How bad is selfish routing?
 JOURNAL OF THE ACM
, 2002
"... We consider the problem of routing traffic to optimize the performance of a congested network. We are given a network, a rate of traffic between each pair of nodes, and a latency function for each edge specifying the time needed to traverse the edge given its congestion; the objective is to route t ..."
Abstract

Cited by 516 (27 self)
 Add to MetaCart
We consider the problem of routing traffic to optimize the performance of a congested network. We are given a network, a rate of traffic between each pair of nodes, and a latency function for each edge specifying the time needed to traverse the edge given its congestion; the objective is to route traffic such that the sum of all travel times—the total latency—is minimized. In many settings, it may be expensive or impossible to regulate network traffic so as to implement an optimal assignment of routes. In the absence of regulation by some central authority, we assume that each network user routes its traffic on the minimumlatency path available to it, given the network congestion caused by the other users. In general such a “selfishly motivated ” assignment of traffic to paths will not minimize the total latency; hence, this lack of regulation carries the cost of decreased network performance. In this article, we quantify the degradation in network performance due to unregulated traffic. We prove that if the latency of each edge is a linear function of its congestion, then the total latency of the routes chosen by selfish network users is at most 4/3 times the minimum possible total latency (subject to the condition that all traffic must be routed). We also consider the more general setting in which edge latency functions are assumed only to be continuous and nondecreasing in the edge congestion. Here, the total
The price of stability for network design with fair cost allocation
 In Proceedings of the 45th Annual Symposium on Foundations of Computer Science (FOCS
, 2004
"... Abstract. Network design is a fundamental problem for which it is important to understand the effects of strategic behavior. Given a collection of selfinterested agents who want to form a network connecting certain endpoints, the set of stable solutions — the Nash equilibria — may look quite differ ..."
Abstract

Cited by 208 (28 self)
 Add to MetaCart
Abstract. Network design is a fundamental problem for which it is important to understand the effects of strategic behavior. Given a collection of selfinterested agents who want to form a network connecting certain endpoints, the set of stable solutions — the Nash equilibria — may look quite different from the centrally enforced optimum. We study the quality of the best Nash equilibrium, and refer to the ratio of its cost to the optimum network cost as the price of stability. The best Nash equilibrium solution has a natural meaning of stability in this context — it is the optimal solution that can be proposed from which no user will defect. We consider the price of stability for network design with respect to one of the most widelystudied protocols for network cost allocation, in which the cost of each edge is divided equally between users whose connections make use of it; this fairdivision scheme can be derived from the Shapley value, and has a number of basic economic motivations. We show that the price of stability for network design with respect to this fair cost allocation is O(log k), where k is the number of users, and that a good Nash equilibrium can be achieved via bestresponse dynamics in which users iteratively defect from a starting solution. This establishes that the fair cost allocation protocol is in fact a useful mechanism for inducing strategic behavior to form nearoptimal equilibria. We discuss connections to the class of potential games defined by Monderer and Shapley, and extend our results to cases in which users are seeking to balance network design costs with latencies in the constructed network, with stronger results when the network has only delays and no construction costs. We also present bounds on the convergence time of bestresponse dynamics, and discuss extensions to a weighted game.
Computationally feasible VCG mechanisms
 In Proceedings of the Second ACM Conference on Electronic Commerce (EC’00
, 2000
"... A major achievement of mechanism design theory is a general method for the construction of truthful mechanisms called VCG. When applying this method to complex problems such as combinatorial auctions, a difficulty arises: VCG mechanisms are required to compute optimal outcomes and are therefore comp ..."
Abstract

Cited by 188 (5 self)
 Add to MetaCart
A major achievement of mechanism design theory is a general method for the construction of truthful mechanisms called VCG. When applying this method to complex problems such as combinatorial auctions, a difficulty arises: VCG mechanisms are required to compute optimal outcomes and are therefore computationally infeasible. However, if the optimal outcome is replaced by the results of a suboptimal algorithm, the resulting mechanism (termed VCGbased) is no longer necessarily truthful. The first part of this paper studies this phenomenon in depth and shows that it is near universal. Specifically, we prove that essentially all reasonable approximations or heuristics for combinatorial auctions as well as a wide class of cost minimization problems yield nontruthful VCGbased mechanisms. We generalize these results for affine maximizers. The second part of this paper proposes a general method for circumventing the above problem. We introduce a modification of VCGbased mechanisms in which the agents are given a chance to improve the output of the underlying algorithm. When the agents behave truthfully, the welfare obtained by the mechanism is at least as good as the one obtained by the algorithm’s output. We provide a strong rationale for truthtelling behavior. Our method satisfies individual rationality as well.
On a network creation game
 in Proceedings of the 22nd Annual Symposium on Principles of Distributed Computing
, 2003
"... christos @ cs.berkeley.edu ..."
The price of anarchy is independent of the network topology
 JOURNAL OF COMPUTER AND SYSTEM SCIENCES
, 2002
"... We study the degradation in network performance caused by the selfish behavior of noncooperative network users. We consider a model of selfish routing in which the latency experienced by network traffic on an edge of the network is a function of the edge congestion, and network users are assumed to ..."
Abstract

Cited by 178 (14 self)
 Add to MetaCart
We study the degradation in network performance caused by the selfish behavior of noncooperative network users. We consider a model of selfish routing in which the latency experienced by network traffic on an edge of the network is a function of the edge congestion, and network users are assumed to selfishly route traffic on minimumlatency paths. The quality of a routing of traffic is measured by the sum of travel times, also called the total latency. The outcome of selfish routing—a Nash equilibrium—does not in general minimize the total latency; hence, selfish behavior carries the cost of decreased network performance. We quantify this degradation in network performance via the price of anarchy, the worstpossible ratio between the total latency of a Nash equilibrium and of an optimal routing of the traffic. We show the price of anarchy is determined only by the simplest of networks. Specifically, we prove that under weak hypotheses on the class of allowable edge latency functions, the worstcase ratio between the total latency of a Nash equilibrium and of a minimumlatency routing for any multicommodity flow network is achieved by a singlecommodity
Tight bounds for worstcase equilibria
 Proc. 13th SODA
, 2002
"... We study the problem of traffic routing in noncooperative networks. In such networks, users may follow selfish strategies to optimize their own performance measure and therefore their behavior does not have to lead to optimal performance of the entire network. In this paper we investigate the worst ..."
Abstract

Cited by 160 (6 self)
 Add to MetaCart
We study the problem of traffic routing in noncooperative networks. In such networks, users may follow selfish strategies to optimize their own performance measure and therefore their behavior does not have to lead to optimal performance of the entire network. In this paper we investigate the worstcase coordination ratio, which is a game theoretic measure aiming to reflect the price of selfish routing. Following a line of previous work, we focus on the most basic networks consisting of parallel links with linear latency functions. Our main result is that the worstcase coordination ratio on m parallel links of possibly different speeds is logm Θ log log logm In fact, we are able to give an exact description of the worstcase coordination ratio depending on the number of links and the ratio of the speed of the fastest link over the speed of the slowest link. For example, for the special case in which all m parallel links have the same speed, we can prove that the worstcase coordination ratio is Γ (−1) (m) + Θ(1) with Γ denoting the Gamma (factorial) function. Our bounds entirely resolve an open problem posed recently by Koutsoupias and Papadimitriou [KP99].
Tsitsiklis. Efficiency loss in a network resource allocation game
 Mathematics of Operations Research
"... We consider a resource allocation problem where individual users wish to send data across a network to maximize their utility, and a cost is incurred at each link that depends on the total rate sent through the link. It is known that as long as users do not anticipate the effect of their actions on ..."
Abstract

Cited by 144 (10 self)
 Add to MetaCart
We consider a resource allocation problem where individual users wish to send data across a network to maximize their utility, and a cost is incurred at each link that depends on the total rate sent through the link. It is known that as long as users do not anticipate the effect of their actions on prices, a simple proportional pricing mechanism can maximize the sum of users’ utilities minus the cost (called aggregate surplus). Continuing previous efforts to quantify the effects of selfish behavior in network pricing mechanisms, we consider the possibility that users anticipate the effect of their actions on link prices. Under the assumption that the links’ marginal cost functions are convex, we establish existence of a Nash equilibrium. We show that the aggregate surplus at a Nash equilibrium is no worse than a factor of 4 √ 2 − 5 times the optimal aggregate surplus; thus, the efficiency loss when users are selfish is no more than approximately 34%. The current Internet is used by a widely heterogeneous population of users; not only are different types of traffic sharing the same network, but different end users place different values on their perceived network performance. This has led to a surge of interest in congestion pricing, where
Algorithms, Games, and the Internet
 In STOC
, 2001
"... If the Internet is the next great subject for Theoretical Computer Science to model and illuminate mathematically, then Game Theory, and Mathematical Economics more generally, are likely to prove useful tools. In this talk I survey some opportunities and challenges in this important frontier. 1. ..."
Abstract

Cited by 135 (0 self)
 Add to MetaCart
If the Internet is the next great subject for Theoretical Computer Science to model and illuminate mathematically, then Game Theory, and Mathematical Economics more generally, are likely to prove useful tools. In this talk I survey some opportunities and challenges in this important frontier. 1.
Complexity Results about Nash Equilibria
, 2002
"... Noncooperative game theory provides a normative framework for analyzing strategic interactions. ..."
Abstract

Cited by 130 (10 self)
 Add to MetaCart
Noncooperative game theory provides a normative framework for analyzing strategic interactions.