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54
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 281 (30 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.
Network Design with Weighted Players
 In Proceedings of the 18th Annual ACM Symposium on Parallel Algorithms and Architectures (SPAA
, 2006
"... We consider a model of gametheoretic network design initially studied by Anshelevich et al. [2], where selfish players select paths in a network to minimize their cost, which is prescribed by Shapley cost shares. If all players are identical, the cost share incurred by a player for an edge in its p ..."
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Cited by 49 (7 self)
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We consider a model of gametheoretic network design initially studied by Anshelevich et al. [2], where selfish players select paths in a network to minimize their cost, which is prescribed by Shapley cost shares. If all players are identical, the cost share incurred by a player for an edge in its path is the fixed cost of the edge divided by the number of players using it. In this special case, Anshelevich et al. [2] proved that purestrategy Nash equilibria always exist and that the price of stability—the ratio in costs of a minimumcost Nash equilibrium and an optimal solution—is Θ(log k), where k is the number of players. Little was known about the existence of equilibria or the price of stability in the general weighted version of the game. Here, each player i has aweightwi≥1, and its cost share of an edge in its path
Designing networks with good equilibria
 In SODA ’08
, 2007
"... In a network with selfish users, designing and deploying a protocol determines the rules of the game by which end users interact with each other and with the network. We study the problem of designing a protocol to optimize the equilibrium behavior of the induced network game. We consider network co ..."
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Cited by 34 (4 self)
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In a network with selfish users, designing and deploying a protocol determines the rules of the game by which end users interact with each other and with the network. We study the problem of designing a protocol to optimize the equilibrium behavior of the induced network game. We consider network costsharing games, where the set of Nash equilibria depends fundamentally on the choice of an edge costsharing protocol. Previous research focused on the Shapley protocol, in which the cost of each edge is shared equally among its users. We systematically study the design of optimal costsharing protocols for undirected and directed graphs, singlesink and multicommodity networks, different classes of costsharing methods, and different measures of the inefficiency of equilibria. One of our main technical tools is a complete characterization of the uniform costsharing protocols—protocols that are designed without foreknowledge of or assumptions on the network in which they will be deployed. We use this characterization result to identify the optimal uniform protocol in several scenarios: for example, the Shapley protocol is optimal in directed graphs, while the optimal protocol in undirected graphs, a simple priority scheme, has exponentially smaller worstcase price of anarchy than the Shapley protocol. We also provide several matching upper and lower bounds on the bestpossible performance of nonuniform costsharing protocols.
On the Windfall of Friendship: Inoculation Strategies on Social Networks
 EC'08
, 2008
"... This paper studies a virus inoculation game on social networks. A framework is presented which allows the measuring of the windfall of friendship, i.e., how much players benefit if they care about the welfare of their direct neighbors in the social network graph compared to purely selfish environmen ..."
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Cited by 23 (2 self)
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This paper studies a virus inoculation game on social networks. A framework is presented which allows the measuring of the windfall of friendship, i.e., how much players benefit if they care about the welfare of their direct neighbors in the social network graph compared to purely selfish environments. We analyze the corresponding equilibria and show that the computation of the worst and best Nash equilibrium is N Phard. Intriguingly, even though the windfall of friendship can never be negative, the social welfare does not increase monotonically with the extent to which players care for each other. While these phenomena are known on an anecdotal level, our framework allows us to quantify these effects analytically.
Replica placement in p2p storage: Complexity and game theoretic analyses
 In 2010 International Conference on Distributed Computing Systems
, 2010
"... �bstract—In peertopeer storage systems, peers replicate each others ’ data in order to increase availability. If the matching is done centrally, the algorithm can optimize data availability in an equitable manner for all participants. However, if matching is decentralized, the peers ’ selfishness ..."
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Cited by 20 (5 self)
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�bstract—In peertopeer storage systems, peers replicate each others ’ data in order to increase availability. If the matching is done centrally, the algorithm can optimize data availability in an equitable manner for all participants. However, if matching is decentralized, the peers ’ selfishness can greatly alter the results, leading to performance inequities that can render the system unreliable and thus ultimately unusable. We analyze the problem using both theoretical approaches �complexity analysis for the centralized system, game theory for the decentralized one) and simulation. We prove that the problem of optimizing availability in a centralized system is NPhard. In decentralized settings, we show that the rational behavior of selfish peers will be to replicate only with similarlyavailable peers. Compared to the sociallyoptimal solution, highly available peers have their data availability increased at the expense of decreased data availability for less available peers. The price of anarchy is high: unbounded in one model, and linear with the number of time slots in the second model. We also propose centralized and decentralized heuristics that, according to our experiments, converge fast in the average case. The high price of anarchy means that a completely decentralized system could be too hostile for peers with low availability, who could never achieve satisfying replication parameters. Moreover, we experimentally show that even explicit consideration and exploitation of diurnal patterns of peer availability has a small effect on the data availability—except when the system has truly global scope. Yet a fully centralized system is infeasible, not only because of problems in information gathering, but also the complexity of optimizing availability. The solution to this dilemma is to create systemwide cooperation rules that allow a decentralized algorithm, but also limit the selfishness of the participants. Index Terms—price of anarchy, equitable optimization, distributed storage I.
Bounded budget connection (BBC) games or how to make friends and influence people, on a budget
 in Proceedings of the 27th ACM Symposium on Principles of Distributed Computing
"... Motivated by applications in social networks, peertopeer and overlay networks, we define and study the Bounded Budget Connection (BBC) game we have a collection of n players or nodes each of whom has a budget for purchasing links; each link has a cost as well as a length and each node has a set o ..."
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Cited by 19 (2 self)
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Motivated by applications in social networks, peertopeer and overlay networks, we define and study the Bounded Budget Connection (BBC) game we have a collection of n players or nodes each of whom has a budget for purchasing links; each link has a cost as well as a length and each node has a set of preference weights for each of the remaining nodes; the objective of each node is to use its budget to buy a set of outgoing links so as to minimize its sum of preferenceweighted distances to the remaining nodes. We study the structural and complexitytheoretic properties of pure Nash equilibria in BBC games. We show that determining the existence of a pure Nash equilibrium in general BBC games is NPhard. We counterbalance this result by considering a natural variant, fractional BBC games where it is permitted to buy fractions of links and show that a pure Nash equilibrium always exists in such games. A major focus is the study of (n, k)uniform BBC games those in which all link costs, link lengths and preference weights are equal (to 1) and all budgets are equal (to k). We show that a pure Nash equilibrium or stable graph exists for all (n, k)uniform BBC games and that all stable graphs are essentially fair (i.e. all nodes have similar costs). We provide an explicit construction of a family of stable graphs that spans the spectrum from minimum total social cost to maximum total social cost. To be precise we show that that the price of stability is Θ(1) and the price of anarchy is Ω( n/k) and O( logk n
Designing Network Protocols for Good Equilibria
, 2009
"... Designing and deploying a network protocol determines the rules by which end users interact with each other and with the network. We consider the problem of designing a protocol to optimize the equilibrium behavior of a network with selfish users. We consider network costsharing games, where the set ..."
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Cited by 13 (1 self)
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Designing and deploying a network protocol determines the rules by which end users interact with each other and with the network. We consider the problem of designing a protocol to optimize the equilibrium behavior of a network with selfish users. We consider network costsharing games, where the set of Nash equilibria depends fundamentally on the choice of an edge costsharing protocol. Previous research focused on the Shapley protocol, in which the cost of each edge is shared equally among its users. We systematically study the design of optimal costsharing protocols for undirected and directed graphs, singlesink and multicommodity networks, and different measures of the inefficiency of equilibria. Our primary technical tool is a precise characterization of the costsharing protocols that only induce network games with purestrategy Nash equilibria. We use this characterization to prove, among other results, that the Shapley protocol is optimal in directed graphs, and that simple priority protocols are essentially optimal in undirected graphs.
Designing SocioTechnical Systems: From Stakeholder Goals to Social Networks
 REQUIREMENTS ENGINEERING
, 2009
"... Software systems are becoming an integral part of everyday life influencing organizational and social activities. This aggravates the need for a sociotechnical perspective for requirements engineering, which allows for modelling and analyzing the composition and interaction of hardware and softwar ..."
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Cited by 9 (5 self)
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Software systems are becoming an integral part of everyday life influencing organizational and social activities. This aggravates the need for a sociotechnical perspective for requirements engineering, which allows for modelling and analyzing the composition and interaction of hardware and software components with human and organizational actors. In this setting, alternative requirements models have to be evaluated and selected finding a right tradeoff between the technical and social dimensions. To address this problem, we propose a toolsupported process of requirements analysis for sociotechnical systems, which adopts planning techniques for exploring the space of requirements alternatives and a number of social criteria for their evaluation. We illustrate the proposed approach with the help of a case study, conducted within the context of an EU project.
A BoundedDegree Network Formation Game
 In PODC ’08
"... Motivated by applications in peertopeer and overlay networks we define and study the Bounded Degree Network Formation (BDNF) game. In an (n, k)BDNF game, we are given n nodes, a bound k on the outdegree of each node, and a weight wvu for each ordered pair (v, u) representing the traffic rate fro ..."
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Cited by 7 (6 self)
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Motivated by applications in peertopeer and overlay networks we define and study the Bounded Degree Network Formation (BDNF) game. In an (n, k)BDNF game, we are given n nodes, a bound k on the outdegree of each node, and a weight wvu for each ordered pair (v, u) representing the traffic rate from node v to node u. Each node v uses up to k directed links to connect to other nodes with an objective to minimize its average distance, using weights wvu, to all other destinations. We study the existence of pure Nash equilibria for (n, k)BDNF games. We show that if the weights are arbitrary, then a pure Nash wiring may not exist. Furthermore, it is NPhard to determine whether a pure Nash wiring exists for a given (n, k)BDNF instance. A major focus of this paper is on uniform (n, k)BDNF games, in which all weights are 1. We describe how to construct a pure Nash equilibrium wiring given any n and k, and establish that in all pure Nash wirings the cost of individual nodes cannot differ by more than a factor of nearly 2, whereas the diameter cannot exceed O ( p nlog k n). We also analyze bestresponse walks on the configuration space defined by the uniform game, and show that starting from any initial configuration, strong connectivity is reached within Θ(n 2) rounds. Convergence to a pure Nash equilibrium, however, is not guaranteed. We present simulation results that suggest that loopfree bestresponse walks always exist, but may not be polynomially bounded. We also study a special family of regular wirings, the class of Abelian Cayley graphs, in which all nodes imitate the same wiring pattern, and show that if n is sufficiently large no such regular wiring can be a pure Nash equilibrium. 1
A Game Theoretic Approach to the Formation of Clustered Overlay Networks (Extended Version)
"... In many largescale content sharing applications, participants or peers are grouped together forming clusters based on their content or interests. In this paper, we deal with the maintenance of such clusters in the presence of updates. We model the evolution of the system as a game, where peers dete ..."
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Cited by 7 (0 self)
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In many largescale content sharing applications, participants or peers are grouped together forming clusters based on their content or interests. In this paper, we deal with the maintenance of such clusters in the presence of updates. We model the evolution of the system as a game, where peers determine their cluster membership based on a utility function of the query recall. Peers are guided either by selfish or altruistic motives: selfish peers aim at improving the recall of their own queries, whereas altruistic peers aim at improving the recall of the queries of other peers. We study the evolution of such clusters both theoretically and experimentally under a variety of conditions. We show that, in general, local decisions made independently by each peer enable the system to adapt to changes and maintain the overall recall of the query workload. 1