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847
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. ..."
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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.
On Selfish Routing in InternetLike Environments
, 2004
"... A recent trend in routing research is to avoid inefficiencies in networklevel routing by allowing hosts to either choose routes themselves (e.g., source routing) or use overlay routing networks (e.g., Detour or RON). Such approaches result in selfish routing, because routing decisions are no longe ..."
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Cited by 160 (10 self)
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A recent trend in routing research is to avoid inefficiencies in networklevel routing by allowing hosts to either choose routes themselves (e.g., source routing) or use overlay routing networks (e.g., Detour or RON). Such approaches result in selfish routing, because routing decisions are no longer based on systemwide criteria but are instead designed to optimize hostbased or overlaybased metrics. A series of theoretical results showing that selfish routing can result in suboptimal system behavior have cast doubts on this approach. In this paper, we use a gametheoretic approach to investigate the performance of selfish routing in Internetlike environments, using realistic topologies and traffic demands in our simulations. We show that in contrast to theoretical worst cases, selfish routing achieves close to optimal average latency in such environments. However, such performance benefit comes at the expense of significantly increased congestion on certain links. Moreover, the adaptive nature of selfish overlays can significantly reduce the effectiveness of traffic engineering by making network traffic less predictable.
Nearoptimal network design with selfish agents
, 2003
"... We introduce a simple network design game that models how independent selfish agents can build or maintain a large network. In our game every agent has a specific connectivity requirement, i.e. each agent has a set of terminals and wants to build a network in which his terminals are connected. Possi ..."
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We introduce a simple network design game that models how independent selfish agents can build or maintain a large network. In our game every agent has a specific connectivity requirement, i.e. each agent has a set of terminals and wants to build a network in which his terminals are connected. Possible edges in the network have costs and each agent’s goal is to pay as little as possible. Determining whether or not a Nash equilibrium exists in this game is NPcomplete. However, when the goal of each player is to connect a terminal to a common source, we prove that there is a Nash equilibrium as cheap as the optimal network, and give a polynomial time algorithmtofinda(1+ε)approximate Nash equilibrium that does not cost much more. For the general connection game we prove that there is a 3approximate Nash equilibrium that is as cheap as the optimal network, and give an algorithm to find a (4.65 +ε)approximate Nash equilibrium that does not cost much more.
The price of routing unsplittable flow
 In Proc. 37th Symp. Theory of Computing (STOC
, 2005
"... The essence of the routing problem in real networks is that the traffic demand from a source to destination must be satisfied by choosing a single path between source and destination. The splittable version of this problem is when demand can be satisfied by many paths, namely a flow from source to d ..."
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Cited by 140 (3 self)
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The essence of the routing problem in real networks is that the traffic demand from a source to destination must be satisfied by choosing a single path between source and destination. The splittable version of this problem is when demand can be satisfied by many paths, namely a flow from source to destination. The unsplittable, or discrete version of the problem is more realistic yet is more complex from the algorithmic point of view; in some settings optimizing such unsplittable traffic flow is computationally intractable. In this paper, we assume this more realistic unsplittable model, and investigate the ”price of anarchy”, or deterioration of network performance measured in total traffic latency under the selfish user behavior. We show that for linear edge latency functions the price of anarchy is exactly 2.618 for weighted demand and exactly 2.5 for unweighted demand. These results are easily extended to (weighted or unweighted) atomic ”congestion games”, where paths are replaced by general subsets. We also show that for polynomials of degree d edge latency functions the price of anarchy is dΘ(d). Our results hold also for mixed strategies. Previous results of Roughgarden and Tardos showed that for linear edge latency functions the price of anarchy is exactly 4 3 under the assumption that each user controls only a negligible fraction of the overall traffic (this result also holds for the splittable case). Note that under the assumption of negligible traffic pure and mixed strategies are equivalent and also splittable and unsplittable models are equivalent. 1
Applications of Approximation Algorithms to Cooperative Games
 STOC'01
, 2001
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Market Equilibrium via a PrimalDual Algorithm for a Convex Program
"... We give the first polynomial time algorithm for exactly computing an equilibrium for the linear utilities case of the market model defined by Fisher. Our algorithm uses the primaldual paradigm in the enhanced setting of KKT conditions and convex programs. We pinpoint the added difficulty raised by ..."
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We give the first polynomial time algorithm for exactly computing an equilibrium for the linear utilities case of the market model defined by Fisher. Our algorithm uses the primaldual paradigm in the enhanced setting of KKT conditions and convex programs. We pinpoint the added difficulty raised by this setting and the manner in which our algorithm circumvents it.
Stackelberg scheduling strategies
 In Proceedings of the 33rd Annual ACM Symposium on the Theory of Computing
, 2001
"... AbstractWe study the problem of optimizing the performance of a system shared by selfish, noncooperative users. We consider the concrete setting of scheduling jobs on a set of shared machines with loaddependent latency functions specifying the length of time necessary to complete a job; we measure ..."
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AbstractWe study the problem of optimizing the performance of a system shared by selfish, noncooperative users. We consider the concrete setting of scheduling jobs on a set of shared machines with loaddependent latency functions specifying the length of time necessary to complete a job; we measure system performance by the total latency of the system. Assigning jobs according to the selfish interests of individual users (who wish to minimize only the latency that their own jobs experience) typically results in suboptimal system performance. However, in many systems of this type there is a mixture of &quot;selfishly controlled &quot; and &quot;centrally controlled &quot; jobs; as the assignment of centrally controlled jobs will influence the subsequent actions by selfish users, we aspire to contain the degradation in system performance due to selfish behavior by scheduling the centrally controlled jobs in the best possible way. We formulate this goal as an optimization problem via Stackelberg games, games in which one player acts a leader (here, the centralized authority interested in optimizing system performance) and the rest as followers (the selfish users). The problem is then to compute a strategy for the leader (a Stackelberg strategy) that induces the followers to react in a way that (at least approximately) minimizes the total latency in the system. In this paper, we prove that it is NPhard to compute the optimal Stackelberg strategy and present simple strategies with provable performance guarantees. More precisely, we give a simple algorithm that computes a strategy inducing a job assignment with total latency no more than a constant times that of the optimal assignment of all of the jobs; in the absence of centrally controlled jobs and a Stackelberg strategy, no result of this type is possible. We also prove stronger performance guarantees in the special case where every machine latency function is linear in the machine load.
Nash Equilibria in Competitive Societies, with Applications to Facility Location, Traffic Routing and Auction
, 2002
"... We consider the following class of problems. The value of an outcome to a society is measured via a submodular utility function (submodularity has a natural economic interpretation: decreasing marginal utility). Decisions, however are controlled by noncooperative agents who seek to maximise their ..."
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Cited by 124 (6 self)
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We consider the following class of problems. The value of an outcome to a society is measured via a submodular utility function (submodularity has a natural economic interpretation: decreasing marginal utility). Decisions, however are controlled by noncooperative agents who seek to maximise their own private utility. We present, under some basic assumptions, guarantees on the social performance of Nash equilibria. For submodular utility functions, any Nash equilibrium gives an expected social utility within a factor 2 of optimal, subject to a functiondependent additive term. For nondecreasing, submodular utility functions, any Nash equilibrium gives an expected social utility within a factor 1 + of optimal, where 0 1 is a number based upon the discrete curvature of the function. A condition under which all sets of social and private utility functions induce pure strategy Nash equilibria is presented. The case in which agents, themselves, make use of approximation algorithms in decision making is discussed and performance guarantees given. Finally we present some specific problems that fall into our framework. These include the competitive versions of the facility location problem and kmedian problem, a maximisation version of the traffic routing problem of Roughgarden and Tardos [16], and multipleitem auctions.
On ProfitMaximizing Envyfree Pricing
"... We study the problem of pricing items for sale to consumers so as to maximize the seller’s revenue. We assume that for each consumer, we know the maximum amount he would be willing to pay for each bundle of items, and want to find pricings of the items with corresponding allocations that maximize se ..."
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Cited by 122 (12 self)
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We study the problem of pricing items for sale to consumers so as to maximize the seller’s revenue. We assume that for each consumer, we know the maximum amount he would be willing to pay for each bundle of items, and want to find pricings of the items with corresponding allocations that maximize seller profit and at the same time are envyfree, which is a natural fairness criterion requiring that consumers are maximally happy with the outcome they receive given the pricing. We study this problem for two important classes of inputs: unit demand consumers, who want to buy at most one item from among a selection they are interested in, and singleminded consumers, who want to buy one particular subset, but only if they can afford it. We show that computing envyfree prices to maximize the seller’s revenue is APXhard in both of these cases, and give a logarithmic approximation algorithm for them. For several interesting special cases, we derive polynomialtime algorithms. Furthermore, we investigate some connections with the corresponding mechanism design problem, in which the consumer’s preferences are private values: for this case, we give a logcompetitive truthful mechanism.
The Structure and Complexity of Nash Equilibria for a Selfish Routing Game
, 2002
"... In this work, we study the combinatorial structure and the computational complexity of Nash equilibria for a certain game that models sel sh routing over a network consisting of m parallel links. We assume a collection of n users, each employing a mixed strategy, which is a probability distribu ..."
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In this work, we study the combinatorial structure and the computational complexity of Nash equilibria for a certain game that models sel sh routing over a network consisting of m parallel links. We assume a collection of n users, each employing a mixed strategy, which is a probability distribution over links, to control the routing of its own assigned trac. In a Nash equilibrium, each user sel shly routes its trac on those links that minimize its expected latency cost, given the network congestion caused by the other users. The social cost of a Nash equilibrium is the expectation, over all random choices of the users, of the maximum, over all links, latency through a link.