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117
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 557 (28 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 97 (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
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 73 (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
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 ..."
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Cited by 64 (9 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].
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 48 (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 27 (4 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 25 (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: ..."
Decentralized Information and the Walrasian Outcome: A Pairwise Meetings Market with Private Values
, 1996
"... I study a onetime entry market for a single indivisible good, where buyers and sellers, privately informed regarding their valuation for the good, are randomly matched, bargain, and in the event of agreement, trade and exit the market. Each agent’s search procedure is modeled as a sequence of discr ..."
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Cited by 16 (1 self)
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I study a onetime entry market for a single indivisible good, where buyers and sellers, privately informed regarding their valuation for the good, are randomly matched, bargain, and in the event of agreement, trade and exit the market. Each agent’s search procedure is modeled as a sequence of discrete double auctions. For each value of the discount factor, the equilibrium behavior of traders satisfies a certain property of monotonicity within each side of the market—the lower a trader’s potential surplus the tougher his market position. As discounting is removed, equilibria with Walrasian and nonWalrasian features persist, although sufficient conditions are identified to single out the Walrasian outcome.
Generic uniqueness of equilibrium in large crowding games
 Math. Oper. Res
, 2000
"... A crowding game is a noncooperative game in which the payo ¤ of each player depends only on the players action and the size of the set of players choosing that particular action: The larger the set, the smaller the payo¤. Finite, nplayer crowding games often have multiple equilibria. However, a lar ..."
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Cited by 16 (1 self)
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A crowding game is a noncooperative game in which the payo ¤ of each player depends only on the players action and the size of the set of players choosing that particular action: The larger the set, the smaller the payo¤. Finite, nplayer crowding games often have multiple equilibria. However, a large crowding game generically has just one equilibrium, and the equilibrium payo¤s in such a game are always unique. Moreover, the sets of equilibria of the mreplicas of a
nite crowding game generically converge to a singleton as m tends to in
nity. This singleton consists of the unique equilibrium of the limit large crowding game. This equilibrium generically has the following graphtheoretic property: The bipartite graph, in which each player in the original,
nite crowding game is joined with all bestresponse actions for (copies of) that player, does not contain cycles.