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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.
The Social Cost of Cheap Pseudonyms
 Journal of Economics and Management Strategy
, 2000
"... We consider the problems of societal norms for cooperation and reputation when it is possible to obtain "cheap pseudonyms", something which is becoming quite common in a wide variety of interactions on the Internet. This introduces opportunities to misbehave without paying reputational con ..."
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Cited by 273 (10 self)
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We consider the problems of societal norms for cooperation and reputation when it is possible to obtain "cheap pseudonyms", something which is becoming quite common in a wide variety of interactions on the Internet. This introduces opportunities to misbehave without paying reputational consequences. A large degree of cooperation can still emerge, through a convention in which newcomers "pay their dues" by accepting poor treatment from players who have established positive reputations. One might hope for an open society where newcomers are treated well, but there is an inherent social cost in making the spread of reputations optional. We prove that no equilibrium can sustain significantly more cooperation than the duespaying equilibrium in a repeated random matching game with a large number of players in which players have finite lives and the ability to change their identities, and there is a small but nonvanishing probability of mistakes. Although one could remove the ineffici...
Pricing in Computer Networks: Reshaping the Research Agenda
 ACM Computer Communication Review
, 1996
"... As the Internet makes the transition from research testbed to commercial enterprise, the topic of pricing in computer networks has suddenly attracted great attention. Much of the discussion in the network design community and the popular press centers on the usagebased vs. fiat pricing debate. The ..."
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Cited by 236 (2 self)
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As the Internet makes the transition from research testbed to commercial enterprise, the topic of pricing in computer networks has suddenly attracted great attention. Much of the discussion in the network design community and the popular press centers on the usagebased vs. fiat pricing debate. The more academic literature has largely focused on devising optimal pricing policies; achieving optimal welfare requires charging marginal congestion costs for usage. In this paper we critique this optimality paradigm on three grounds: (1) marginal cost prices may not produce sufficient revenue to fully recover costs and so are perhaps of limited relevance, (2) congestion costs are inherently inaccessible to the network and so cannot reliably form the basis for pricing, and (3) there are other, more structural, goals besides optimality, and some of these goals are incompatible with the global uniformity required for optimal pricing schemes. For these reasons, we contend that the research agenda on pricing in computer network should shift away from the optimality paradigm and focus more on structural and architectural issues. Such issues include allowing local control of pricing policies,
Strategyproof Sharing of Submodular Costs: budget balance versus efficiency
, 1999
"... A service is produced for a set of agents. The service is binary, each agent either receives service or not, and the total cost of service is a submodular function of the set receiving service. We investigate strategyproof mechanisms that elicit individual willingness to pay, decide who is served ..."
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Cited by 201 (19 self)
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A service is produced for a set of agents. The service is binary, each agent either receives service or not, and the total cost of service is a submodular function of the set receiving service. We investigate strategyproof mechanisms that elicit individual willingness to pay, decide who is served, and then share the cost among them. If such a mechanism is budget balanced (covers cost exactly), it cannot be efficient (serve the surplus maximizing set of users) and viceversa. We characterize the rich family of budget balanced and group strategyproof mechanisms; they correspond to the family of cost sharing formulae where an agent's cost share does not decrease when the set of users expand. The mechanism associated with the Shapley value cost sharing formula is characterized by the property that its worst welfare loss is minimal. When we require efficiency rather than budget balance  the more common route in the literature  we find that there is a single ClarkeGroves mech...
Pricing Multicast Communication: A CostBased Approach
 Telecommunication Systems
, 2001
"... Multicast and unicast traffic share and compete for network resources. A costbased approach to multicast pricing, based on accurate characterization of multicast scalability, will facilitate the efficient and equitable resource allocation between traffic types. Through the quantification of link us ..."
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Cited by 78 (0 self)
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Multicast and unicast traffic share and compete for network resources. A costbased approach to multicast pricing, based on accurate characterization of multicast scalability, will facilitate the efficient and equitable resource allocation between traffic types. Through the quantification of link usage, this paper establishes a multicast scaling relationship: the cost of a multicast distribution tree varies at the 0.8 power of the multicast group size. This result is validated with both real and generated networks, and is robust across topological styles and network sizes. Since multicast cost can be accurately predicted given the membership size, there is strong motivation to price multicast according to membership size. Furthermore, a price ceiling should be set to account for the effect of tree saturation. This tariff structure is superior to either a purely membershipbased or a flatrate pricing scheme, since it reflects the actual tree cost at all group membership levels. Keywords: multicast pricing, multicast scaling 1.
Approximation and Collusion in Multicast Cost Sharing
, 2004
"... in Proceedings of the 3rd ACM Conference on Electronic Commerce, Tampa FL, October 2001. This work was supported by the DoD University Research Initiative (URI) program administered by the Oce of Naval Research under Grant N000140110795. ..."
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Cited by 52 (3 self)
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in Proceedings of the 3rd ACM Conference on Electronic Commerce, Tampa FL, October 2001. This work was supported by the DoD University Research Initiative (URI) program administered by the Oce of Naval Research under Grant N000140110795.
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 40 (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.
On the Value of Coordination in Network Design
"... We study network design games where n selfinterested agents have to form a network by purchasing links from a given set of edges. We consider Shapley cost sharing mechanisms that split the cost of an edge in a fair manner among the agents using the edge. It is well known that the price of anarchy o ..."
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Cited by 36 (0 self)
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We study network design games where n selfinterested agents have to form a network by purchasing links from a given set of edges. We consider Shapley cost sharing mechanisms that split the cost of an edge in a fair manner among the agents using the edge. It is well known that the price of anarchy of these games is as high as n. Therefore, recent research has focused on evaluating the price of stability, i.e. the cost of the best Nash equilibrium relative to the social optimum. In this paper we investigate to which extent coordination among agents can improve the quality of solutions. We resort to the concept of strong Nash equilibria, which were introduced by Aumann and are resilient to deviations by coalitions of agents. We analyze the price of anarchy of strong Nash equilibria and develop lower and upper bounds for unweighted and weighted games in both directed and undirected graphs. These bounds are tight or nearly tight for many scenarios. It shows that using coordination, the price of anarchy drops from linear to logarithmic bounds. We complement these results by also proving the first superconstant lower bound on the price of stability of standard equilibria (without coordination) in undirected graphs. More specifically, we show a lower bound of Ω(log W / log log W) for weighted games, where W is the total weight of all the agents. This almost matches the known upper bound of O(log W). Our results imply that, for most settings, the worstcase performance ratios of strong coordinated equilibria are essentially always as good as the performance ratios of the best equilibria achievable without coordination. These settings include unweighted games in directed graphs as well as weighted games in both directed and undirected graphs.
Hardness results for multicast cost sharing
 Theoretical Computer Science
, 2002
"... We continue the study of multicast cost sharing from the viewpoints of both computational complexity and economic mechanism design. We provide fundamental lower bounds on the network complexity of groupstrategyproof, budgetbalanced mechanisms. We also extend a classical impossibility result in gam ..."
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Cited by 31 (3 self)
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We continue the study of multicast cost sharing from the viewpoints of both computational complexity and economic mechanism design. We provide fundamental lower bounds on the network complexity of groupstrategyproof, budgetbalanced mechanisms. We also extend a classical impossibility result in game theory to show that no strategyproof mechanism can be both approximately efficient and approximately budgetbalanced. Our results show that one important and natural case of multicast cost sharing is an example of a canonical hard problem in distributed, algorithmic mechanism design; in this sense, they represent progress toward the development of a complexity theory of Internet computation.