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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 ..."
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Cited by 516 (27 self)
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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
Pricing network edges for heterogeneous selfish users
 Proc. of STOC
, 2003
"... We study the negative consequences of selfish behavior in a congested network and economic means of influencing such behavior. We consider the model of selfish routing defined by Wardrop [30] and studied in a computer science context by Roughgarden and Tardos [26]. In this model, the latency experie ..."
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Cited by 88 (10 self)
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We study the negative consequences of selfish behavior in a congested network and economic means of influencing such behavior. We consider the model of selfish routing defined by Wardrop [30] and studied in a computer science context by Roughgarden and Tardos [26]. In this model, 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 (the total latency). It is well known that the outcome of selfish routing (a Nash equilibrium) does not minimize the total latency and can be improved upon with coordination. An ancient strategy for improving the selfish solution is the principle of marginal cost pricing, which asserts that on each edge of the network, each network user on the edge should pay a tax offsetting the congestion effects caused by its presence. By pricing network edges according to this principle, the inefficiency of selfish routing can always be eradicated. This result, while fundamental, assumes a very strong homogeneity property: all network users are assumed to trade off time and money in an identical way. The guarantee also ignores both the algorithmic
Bounding the Inefficiency of Equilibria in Nonatomic Congestion Games
 Games and Economic Behavior
, 2002
"... Equilibria in noncooperative games are typically inefficient, as illustrated by the Prisoner's Dilemma. In this paper, we quantify this inefficiency by comparing the payoffs of equilibria to the payoffs of a "best possible" outcome. We study a nonatomic version of the congestion games defined by Ros ..."
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Cited by 61 (8 self)
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Equilibria in noncooperative games are typically inefficient, as illustrated by the Prisoner's Dilemma. In this paper, we quantify this inefficiency by comparing the payoffs of equilibria to the payoffs of a "best possible" outcome. We study a nonatomic version of the congestion games defined by Rosenthal [15], and identify games in which equilibria are approximately optimal in the sense that no other outcome achieves a significantly larger total payoff to the players  games in which optimization by individuals approximately optimizes the social good, in spite of the lack of coordination between players. Our results extend previous work on traffic routing games [16, 17, 18].
Evolutionary Games in Economics
 Econometrica
, 1991
"... Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at ..."
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Cited by 61 (3 self)
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Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at
Routing without regret: On convergence to nash equilibria of regretminimizing algorithms in routing games
 In PODC
, 2006
"... Abstract There has been substantial work developing simple, efficient noregret algorithms for a wideclass of repeated decisionmaking problems including online routing. These are adaptive strategies an individual can use that give strong guarantees on performance even in adversariallychanging envi ..."
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Cited by 47 (6 self)
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Abstract There has been substantial work developing simple, efficient noregret algorithms for a wideclass of repeated decisionmaking problems including online routing. These are adaptive strategies an individual can use that give strong guarantees on performance even in adversariallychanging environments. There has also been substantial work on analyzing properties of Nash equilibria in routing games. In this paper, we consider the question: if each player in a routing game uses a noregret strategy, will behavior converge to a Nash equilibrium? In general games the answer to this question is known to be no in a strong sense, but routing games havesubstantially more structure. In this paper we show that in the Wardrop setting of multicommodity flow and infinitesimalagents, behavior will approach Nash equilibrium (formally, on most days, the cost of the flow will be close to the cost of the cheapest paths possible given that flow) at a rate that dependspolynomially on the players ' regret bounds and the maximum slope of any latency function. We also show that priceofanarchy results may be applied to these approximate equilibria, and alsoconsider the finitesize (noninfinitesimal) loadbalancing model of Azar [2].
A Decentralized Market with Common Values Uncertainty: NonSteady States
, 2001
"... We analyze a market where (i) trade proceeds by random and anonymous pairwise meetings with bargaining; (ii) agents are asymmetrically informed about the value of the traded good; and (iii) no new entrants are allowed once the market is open. We show that information revelation and e±ciency never ob ..."
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Cited by 22 (3 self)
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We analyze a market where (i) trade proceeds by random and anonymous pairwise meetings with bargaining; (ii) agents are asymmetrically informed about the value of the traded good; and (iii) no new entrants are allowed once the market is open. We show that information revelation and e±ciency never obtain in equilibrium, even as discounting is removed. This holds whether the asymmetry is twosided or onesided. In some cases there exist equilibria where a substantial amount goes untraded. This contrasts with the earlier literature, which was based on the steadystate equilibria of a model where agents enter the market every period.
A model of financial crises in emerging markets
 Quarterly Journal of Economics
, 2001
"... We develop a model in which financial crises in emerging markets may occur when domestic banks are internationally illiquid. Runs on domestic deposits may interact with foreign creditor panics, depending on the maturity of the foreign debt and the possibility of international default. Financial libe ..."
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Cited by 16 (2 self)
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We develop a model in which financial crises in emerging markets may occur when domestic banks are internationally illiquid. Runs on domestic deposits may interact with foreign creditor panics, depending on the maturity of the foreign debt and the possibility of international default. Financial liberalization and increased inflows of foreign capital, especially if short term, can aggravate the illiquidity of banks and increase their vulnerability. The primary role of illiquidity is consistent with the existence of asset price booms and crashes and of government distortions.
Lectures on Young Measure Theory and its Applications in Economics
 Rend. Istit. Mat. Univ. Trieste
, 1998
"... this paper we work with the following hypothesis: ..."
Genericity and congestion control in selfish routing
 In Proceedings of the 43rd Annual IEEE Conference on Decision and Control (CDC
, 2004
"... In this paper we consider the problem of selfish routing in a congested data network, such as the Internet. While previous analyses (e.g., [RT00, Rou01])have discussed the possibility of large losses due to selfish routing, we present several reasons why one could expect typical losses to be small. ..."
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Cited by 12 (0 self)
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In this paper we consider the problem of selfish routing in a congested data network, such as the Internet. While previous analyses (e.g., [RT00, Rou01])have discussed the possibility of large losses due to selfish routing, we present several reasons why one could expect typical losses to be small. The first is based on a “generic analysis ” where we consider worst case topologies and latency functions, but ignore a small set of “transmission demands. ” We show that one can bound these “generic losses ” by the log of the network’s “criticallity factor, ” a reasonably natural parameter. Our second reason is based on the near universal use of TCP or some other congestion control mechanism in networks. We show that for a specific model of TCP, the losses due to selfish routing are quite small and suggest that this is true in general. Both of these results are also shown to hold for the (nonlinear) latency functions which commonly arise on the Internet. Lastly, we provide some nongametheoretic justifications for this analysis, which may be applicable to current networks, in which routing is not selfish. We show that in certain cases, common routing algorithms, such as OSPF, generate the same routes as selfish routing.
The Multiunit Assignment Problem: Theory and Evidence from Course Allocation at Harvard. Working Paper
, 2010
"... We use theory and field data to study the draft mechanism used to allocate courses at Harvard Business School. We show that the draft is manipulable in theory, manipulated in practice, and that these manipulations cause significant welfare loss. Nevertheless, we find that welfare is higher than unde ..."
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Cited by 12 (2 self)
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We use theory and field data to study the draft mechanism used to allocate courses at Harvard Business School. We show that the draft is manipulable in theory, manipulated in practice, and that these manipulations cause significant welfare loss. Nevertheless, we find that welfare is higher than under its widely studied strategyproof alternative. We identify a new link between fairness and welfare that explains why the draft performs well despite the costs of strategic behavior, and then design a new draft that reduces these costs. We draw several broader lessons for market design, regarding Pareto efficiency, fairness, and strategyproofness. (JEL D63, D82, I23) Educational institutions commonly place limits on the number of students in any particular class. These classsize limits create an instance of the multiunit assignment problem: if it is not possible for all students to take their most desired schedule of courses, then how should seats in courses be allocated? 1 Other examples of multiunit assignment problems include the assignment of tasks or shifts to workers, players to sports teams, shared scientific resources to their users, and airport takeoffandlanding slots to airlines. Perhaps the central difference between how practitioners and economists have approached multiunit assignment and other similar market design problems is the attention paid to incentives. Practitioners often design mechanisms that would lead to economically desirable outcomes if agents told the truth about their preferences, but which fail to provide agents with an incentive to do so. Economists try where possible to design mechanisms where truthful reporting not only leads