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36
Basic Network Creation Games
, 2010
"... We study a natural network creation game, in which each node locally tries to minimize its local diameter or its local average distance to other nodes, by swapping one incident edge at a time. The central question is what structure the resulting equilibrium graphs have, in particular, how well they ..."
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Cited by 22 (1 self)
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We study a natural network creation game, in which each node locally tries to minimize its local diameter or its local average distance to other nodes, by swapping one incident edge at a time. The central question is what structure the resulting equilibrium graphs have, in particular, how well they globally minimize diameter. For the localaveragedistance version, we prove an upper bound of 2 O( √ lg n), a lower bound of 3, a tight bound of exactly 2 for trees, and give evidence of a general polylogarithmic upper bound. For the localdiameter version, we prove a lower bound of Ω ( √ n), and a tight upper bound of 3 for trees. All of our upper bounds apply equally well to previously extensively studied network creation games, both in terms of the diameter metric described above and the previously studied price of anarchy (which are related by constant factors). In surprising contrast, our model has no parameter α for the link creation cost, so our results automatically apply for all values of α without additional effort; furthermore, equilibrium can be checked in polynomial time in our model, unlike previous models. Our perspective enables simpler and more general proofs that get at the heart of network creation games.
Cost Sharing and Strategyproof Mechanisms for Set Cover Games
"... We develop for set cover games several general costsharing methods that are approximately budgetbalanced, core, and/or groupstrategyproof. We first study the cost sharing for a single set cover game, which does not have a budgetbalanced core. We show that there is no cost allocation method that ..."
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Cited by 13 (3 self)
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We develop for set cover games several general costsharing methods that are approximately budgetbalanced, core, and/or groupstrategyproof. We first study the cost sharing for a single set cover game, which does not have a budgetbalanced core. We show that there is no cost allocation method that can of the total cost if we require the cost sharing being a core. Here n is the number of all players to be served. We give an efficient cost 1 allocation method that always recovers of the total cost, where dmax is ln dmax the maximum size of all sets. We then study the cost allocation scheme for all induced subgames. It is known that no cost sharing scheme can always recover more than 1 of the total cost for every subset of players. We give an efficient cost n sharing scheme that always recovers at least 1 of the total cost for every subset 2n of players and furthermore, our scheme is crossmonotone. When the elements to be covered are selfish agents with privately known valuations, we present a strategyproof charging mechanism, under the assumption that all sets are simple sets, such that each element maximizes its profit when it reports its valuation truthfully; further, the total cost of the set cover is no more than ln dmax times that of an optimal solution. When the sets are selfish agents with privately known costs, we present a strategyproof payment mechanism in which each set maximizes its profit when it reports its cost truthfully. We also show how to fairly share the payments to all sets among the elements. always recover more than 1 ln n 1
THE PRICE OF ANARCHY IN COOPERATIVE NETWORK CREATION GAMES
, 2009
"... We analyze the structure of equilibria and the price of anarchy in the family of network creation games considered extensively in the past few years, which attempt to unify the network design and network routing problems by modeling both creation and usage costs. In general, the games are played o ..."
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Cited by 11 (1 self)
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We analyze the structure of equilibria and the price of anarchy in the family of network creation games considered extensively in the past few years, which attempt to unify the network design and network routing problems by modeling both creation and usage costs. In general, the games are played on a host graph, where each node is a selfish independent agent (player) and each edge has a fixed link creation cost α. Together the agents create a network (a subgraph of the host graph) while selfishly minimizing the link creation costs plus the sum of the distances to all other players (usage cost). In this paper, we pursue two important facets of the network creation game. First, we study extensively a natural version of the game, called the cooperative model, where nodes can collaborate and share the cost of creating any edge in the host graph. We prove the first nontrivial bounds in this model, establishing that the price of anarchy is polylogarithmic in n for all values of α in complete host graphs. This bound is the first result of this type for any version of the network creation game; most previous general upper bounds are polynomial in n. Interestingly, we also show that equilibrium graphs have polylogarithmic diameter for the most natural range of α (at most n polylg n). Second,
SociallyAware Network Design Games
 IN PROC. OF INFOCOM 2010
, 2010
"... In many scenarios network design is not enforced by a central authority, but arises from the interactions of several selfinterested agents. This is the case of the Internet, where connectivity is due to Autonomous Systems ’ choices, but also of overlay networks, where each user client can decide th ..."
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Cited by 10 (4 self)
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In many scenarios network design is not enforced by a central authority, but arises from the interactions of several selfinterested agents. This is the case of the Internet, where connectivity is due to Autonomous Systems ’ choices, but also of overlay networks, where each user client can decide the set of connections to establish. Recent works have used game theory, and in particular the concept of Nash Equilibrium, to characterize stable networks created by a set of selfish agents. The majority of these works assume that users are completely noncooperative, leading, in most cases, to inefficient equilibria. To improve efficiency, in this paper we propose two novel sociallyaware network design games. In the first game we incorporate a sociallyaware component in the users ’ utility functions, while in the second game we use additionally a Stackelberg (leaderfollower) approach, where a leader (e.g., the network administrator) architects the desired network buying an appropriate subset of network’s links, driving in this way the users to overall efficient Nash equilibria. We provide bounds on the Price of Anarchy and other efficiency measures, and study the performance of the proposed schemes in several network scenarios, including realistic topologies where players build an overlay on top of real Internet Service Provider networks. Numerical results demonstrate that (1) introducing some incentives to make users more sociallyaware is an effective solution to achieve stable and efficient networks in a distributed way, and (2) the proposed Stackelberg approach permits to achieve dramatic performance improvements, designing almost always the socially optimal network.
Strong and Pareto Price of Anarchy in Congestion Games
, 2008
"... Strong Nash equilibria and Paretooptimal Nash equilibria are natural and important strengthenings of the Nash equilibrium concept. We study these stronger notions of equilibrium in congestion games, focusing on the relationships between the price of anarchy for these equilibria and that for standar ..."
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Cited by 9 (0 self)
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Strong Nash equilibria and Paretooptimal Nash equilibria are natural and important strengthenings of the Nash equilibrium concept. We study these stronger notions of equilibrium in congestion games, focusing on the relationships between the price of anarchy for these equilibria and that for standard Nash equilibria (which is well understood). For symmetric congestion games with polynomial or exponential latency functions, we show that the price of anarchy for strong and Paretooptimal equilibria is much smaller than the standard price of anarchy. On the other hand, for asymmetric congestion games with polynomial latencies the strong and Pareto prices of anarchy are essentially as large as the standard price of anarchy; while for asymmetric games with exponential latencies the Pareto and standard prices of anarchy are the same but the strong price of anarchy is substantially smaller. Finally, in the special case of linear latencies, we show that the strong and Pareto prices of anarchy coincide exactly with the known value 5 2 for standard Nash, but are strictly smaller for symmetric games.
On the performance of approximate equilibria in congestion games
, 2008
"... We study the performance ..."
Approximate Strong Equilibrium in Job Scheduling Games
, 2009
"... A Nash Equilibrium (NE) is a strategy profile resilient to unilateral deviations, and is predominantly used in the analysis of multiagent systems. A downside of NE is that it is not necessarily stable against deviations by coalitions. Yet, as we show in this paper, in some cases, NE does exhibit sta ..."
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Cited by 9 (0 self)
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A Nash Equilibrium (NE) is a strategy profile resilient to unilateral deviations, and is predominantly used in the analysis of multiagent systems. A downside of NE is that it is not necessarily stable against deviations by coalitions. Yet, as we show in this paper, in some cases, NE does exhibit stability against coalitional deviations, in that the benefits from a joint deviation are bounded. In this sense, NE approximates strong equilibrium. Coalition formation is a key issue in multiagent systems. We provide a framework for quantifying the stability and the performance of various assignment policies and solution concepts in the face of coalitional deviations. Within this framework we evaluate a given configuration according to three measures: (i) IRmin: the maximal number α, such that there exists a coalition in which the minimal improvement ratio among the coalition members is α, (ii) IRmax: the maximal number α, such that there exists a coalition in which the maximal improvement ratio among the coalition members is α, and (iii) DRmax: the maximal possible damage ratio of an agent outside the coalition. We analyze these measures in job scheduling games on identical machines. In particular, we provide upper and lower bounds for the above three measures for both NE and the wellknown assignment rule Longest Processing Time (LPT). Our results indicate that LPT performs better than a general NE. However, LPT is not the best possible approximation. In particular, we present a polynomial time approximation scheme (PTAS) for the makespan minimization problem which provides a schedule with IRmin of 1 + ε for any given ɛ. With respect to computational complexity, we show that given an NE on m ≥ 3 identical machines or m ≥ 2 unrelated machines, it is NPhard to determine whether a given coalition can deviate such that every member decreases its cost.
Noncooperative Facility Location and Covering Games
"... We consider a general class of noncooperative games related to combinatorial covering and facility location problems. A game is based on an integer programming formulation of the corresponding optimization problem, and each of the k players wants to satisfy a subset of the constraints. For that pur ..."
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Cited by 7 (1 self)
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We consider a general class of noncooperative games related to combinatorial covering and facility location problems. A game is based on an integer programming formulation of the corresponding optimization problem, and each of the k players wants to satisfy a subset of the constraints. For that purpose, resources available in integer units must be bought, and their cost can be shared arbitrarily between players. We consider the existence and cost of exact and approximate purestrategy Nash equilibria. In general, prices of anarchy and stability are in Θ(k) and deciding the existence of a pure Nash equilibrium is NPhard. Under certain conditions, however, cheap Nash equilibria exist, in particular if the integrality gap of the underlying integer program is 1, or in the case of single constraint players. We also present algorithms that compute simultaneously nearstable and nearoptimal approximate Nash equilibria in polynomial time.
An O(log n/ log log n) upper bound on the price of stability for undirected Shapley network design games
 Information Processing Letters
, 2009
"... log n ..."