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209
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 ..."
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Cited by 279 (27 self)
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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.
Selfish Routing and the Price of Anarchy
 MATHEMATICAL PROGRAMMING SOCIETY NEWSLETTER
, 2007
"... Selfish routing is a classical mathematical model of how selfinterested users might route traffic through a congested network. The outcome of selfish routing is generally inefficient, in that it fails to optimize natural objective functions. The price of anarchy is a quantitative measure of this in ..."
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Cited by 252 (11 self)
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Selfish routing is a classical mathematical model of how selfinterested users might route traffic through a congested network. The outcome of selfish routing is generally inefficient, in that it fails to optimize natural objective functions. The price of anarchy is a quantitative measure of this inefficiency. We survey recent work that analyzes the price of anarchy of selfish routing. We also describe related results on bounding the worstpossible severity of a phenomenon called Braess’s Paradox, and on three techniques for reducing the price of anarchy of selfish routing. This survey concentrates on the contributions of the author’s PhD thesis, but also discusses several more recent results in the area.
Network Coding with a Cost Criterion
 in Proc. 2004 International Symposium on Information Theory and its Applications (ISITA 2004
, 2004
"... We consider applying network coding in settings where there is a cost associated with network use. ..."
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Cited by 87 (17 self)
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We consider applying network coding in settings where there is a cost associated with network use.
Network optimization and control
 Foundations and Trends in Networking
"... We study how protocol design for various functionalities within a communication network architecture can be viewed as a distributed resource allocation problem. This involves understanding what resources are, how to allocate them fairly, and perhaps most importantly, how to achieve this goal in a di ..."
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Cited by 66 (4 self)
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We study how protocol design for various functionalities within a communication network architecture can be viewed as a distributed resource allocation problem. This involves understanding what resources are, how to allocate them fairly, and perhaps most importantly, how to achieve this goal in a distributed and stable fashion. We start with ideas of a centralized optimization framework and show how congestion control, routing and scheduling in wired and wireless networks can be thought of as fair resource allocation. We then move to the study of controllers that allow a decentralized solution of this problem. These controllers are the analytical equivalent of protocols in use on the Internet today, and we describe existing protocols as realizations of such controllers. The Internet is a dynamic system with feedback delays and flows that arrive and depart, which means that stability of the system cannot be taken for granted. We show how to incorporate
Optimal Allocation of a Divisible Good to Strategic Buyers
 Proceedings of the 43d IEEE conference on Decision and Control
, 2004
"... We address the problem of allocating a divisible resource to buyers who value the quantity they receive, but strategize to maximize their net payoff (value minus payment). An allocation mechanism is used to allocate the resource based on bids declared by the buyers. The bids are equal to the payment ..."
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Cited by 50 (2 self)
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We address the problem of allocating a divisible resource to buyers who value the quantity they receive, but strategize to maximize their net payoff (value minus payment). An allocation mechanism is used to allocate the resource based on bids declared by the buyers. The bids are equal to the payments, and the buyers are assumed to be in Nash equilibrium. For two buyers such an allocation mechanism is found that guarantees that the aggregate value is always greater than of the maximum possible, and it is shown that no other mechanism achieves a larger ratio. For a general finite number of buyers an allocation mechanism is given and an expression is given for its worst case efficiency. For three buyers the expression evaluates to 0.8737, for four buyers to 0.8735 and numerical computations suggest that the numerical value does not decrease when the number of buyers is increased beyond four. A potential application of this work is the allocation of communication bandwidth on a single link.
A PriceAnticipating Resource Allocation Mechanism for Distributed Shared
 Clusters”, 6th ACM Conference on Electronic Commerce
, 2005
"... In this paper we formulate the fixed budget resource allocation game to understand the performance of a distributed marketbased resource allocation system. Multiple users decide how to distribute their budget (bids) among multiple machines according to their individual preferences to maximize their ..."
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Cited by 45 (8 self)
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In this paper we formulate the fixed budget resource allocation game to understand the performance of a distributed marketbased resource allocation system. Multiple users decide how to distribute their budget (bids) among multiple machines according to their individual preferences to maximize their individual utility. We look at both the efficiency and the fairness of the allocation at the equilibrium, where fairness is evaluated through the measures of utility uniformity and envyfreeness. We show analytically and through simulations that despite being highly decentralized, such a system converges quickly to an equilibrium and unlike the social optimum that achieves high efficiency but poor fairness, the proposed allocation scheme achieves a nice balance of high degrees of efficiency and fairness at the equilibrium. 1.
VCGKelly mechanisms for allocation of divisible goods: Adapting VCG mechanisms to onedimensional signals
 in Proc. of CISS
, 2006
"... Abstract — The VCGKelly mechanism is proposed, which is obtained by composing the communication efficient, onedimensional signaling idea of Kelly with the VCG mechanism, providing efficient allocation for strategic buyers at Nash equilibrium points. It is shown that the revenue to the seller can be ..."
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Cited by 42 (0 self)
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Abstract — The VCGKelly mechanism is proposed, which is obtained by composing the communication efficient, onedimensional signaling idea of Kelly with the VCG mechanism, providing efficient allocation for strategic buyers at Nash equilibrium points. It is shown that the revenue to the seller can be maximized or minimized using a particular onedimensional family of surrogate valuation functions. Index Terms— I.
NonCooperative Multicast and Facility Location Games
"... We consider a multicast game with selfish noncooperative players. There is a special source node and each player is interested in connecting to the source by making a routing decision that minimizes its payment. The mutual influence of the players is determined by a cost sharing mechanism, which in ..."
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Cited by 41 (2 self)
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We consider a multicast game with selfish noncooperative players. There is a special source node and each player is interested in connecting to the source by making a routing decision that minimizes its payment. The mutual influence of the players is determined by a cost sharing mechanism, which in our case evenly splits the cost of an edge among the players using it. We consider two different models: an integral model, where each player connects to the source by choosing a single path, and a fractional model, where a player is allowed to split the flow it receives from the source between several paths. In both models we explore the overhead incurred in network cost due to the selfish behavior of the users, as well as the computational complexity of finding a Nash equilibrium. The existence of a Nash equilibrium for the integral model was previously established by the means of a potential function. We prove that finding a Nash equilibrium that minimizes the potential function is NPhard. We focus on the price of anarchy of a Nash equilibrium resulting from the bestresponse dynamics of a game course, where the players join the game sequentially. For a game with n players, we establish an upper bound of O ( √ n log 2 n) on the price of anarchy, and a lower bound of Ω(log n/log log n). For the fractional model, we prove the existence of a Nash equilibrium via a potential function and give a polynomial time algorithm for computing an equilibrium that minimizes the potential function. Finally, we consider a weighted extension of the multicast game, and prove that in the fractional model, the game always has a Nash equilibrium.
Equilibrium of Heterogeneous Congestion Control: Existence and Uniqueness
 IEEE/ACM Transactions on Networking
, 2007
"... member, IEEE Abstract—When heterogeneous congestion control protocols that react to different pricing signals (They could be different types of signals such as packet loss, queueing delay etc. or different values of the same type of signal such as different ECN marking values based on the same actua ..."
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Cited by 38 (9 self)
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member, IEEE Abstract—When heterogeneous congestion control protocols that react to different pricing signals (They could be different types of signals such as packet loss, queueing delay etc. or different values of the same type of signal such as different ECN marking values based on the same actual link congestion level) share the same network, the current theory based on utility maximization fails to predict the network behavior. Unlike in a homogeneous network, the bandwidth allocation now depends on router parameters and flow arrival patterns. It can be nonunique, suboptimal and unstable. In [36], existence and uniqueness of equilibrium of heterogeneous protocols are investigated. This paper extends the study with two objectives: analyze the optimality and stability of such networks and design control schemes to improve them. First, we demonstrate the intricate behavior of a heterogeneous network through simulations and present a framework to help understand its equilibrium properties. Second, we propose a simple sourcebased algorithm to decouple bandwidth allocation from router parameters and flow arrival patterns by only updating a linear parameter in the sources ’ algorithms on a slow timescale. It is used to steer a network to the unique optimal equilibrium. The scheme can be deployed incrementally as the existing protocol needs no change and only the new protocols need to adopt the slow timescale adaption. I.
Wireless channel allocation using an auction algorithm
 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS
, 2003
"... We develop a novel auctionbased algorithm to allow users to fairly compete for a wireless fading channel. We use the secondprice auction mechanism whereby user bids for the channel, during each time slot, based on the fade state of the channel, and the user that makes the highest bid wins use of ..."
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Cited by 33 (0 self)
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We develop a novel auctionbased algorithm to allow users to fairly compete for a wireless fading channel. We use the secondprice auction mechanism whereby user bids for the channel, during each time slot, based on the fade state of the channel, and the user that makes the highest bid wins use of the channel by paying the second highest bid. Under the assumption that each user has a limited budget for bidding, we show the existence of a Nash equilibrium strategy, and the Nash equilibrium leads to a unique allocation for certain channel state distribution, such as the exponential distribution and the uniform distribution over [0, 1]. For uniformly distributed channel state, we establish that the aggregate throughput received by the users using the Nash equilibrium strategy is at least 3/4 of what can be obtained using an optimal centralized allocation that does not take fairness into account. We also show that the Nash equilibrium strategy leads to an allocation that is Pareto optimal (i.e., it is impossible to make some users better off without making some other users worse off). Based on the Nash equilibrium strategies of the secondprice auction with money constraint, we further propose a centralized opportunistic scheduler that does not suffer the shortcomings associated with the proportional fair scheduler.