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The Price of Stability for Network Design with Fair Cost Allocation

The Price of Stability for Network Design with Fair Cost Allocation,10.1109/FOCS.2004.68,Elliot Anshelevich,Anirban Dasgupta,Jon M. Kleinberg,Éva Tard

The Price of Stability for Network Design with Fair Cost Allocation   (Citations: 234)
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Network design is a fundamental problem for which it is important to understand the efiects of strategic behavior. Given a collection of self-interested agents who want to form a network connecting certain endpoints, the set of stable solutions | the Nash equilibria | may look quite difierent 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 widely-studied protocols for network cost allocation, in which the cost of each edge is divided equally between users whose connections make use of it; this fair-division 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(logk), where k is the number of users, and that a good Nash equilibrium can be achieved via best-response 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 near-optimal equilibria. We discuss connections to the class of potential games deflned 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 best-response dynamics, and discuss extensions to a weighted game.
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    • ...Congestion games (Rosenthal 1973) are a well-studied model of strategic sharing of resource, and have been used to investigate domains ranging from network design and routing (Kunniyur and Srikant 2003; Anshelevich et al. 2004) to cloud-computing and load-balancing (Suri, T ´ oth, and Zhou 2007; V¨ 2007; Ashlagi, Tennenholtz, and Zohar 2010)...

    Reshef Meiret al. Congestion Games with Agent Failures

    • ...Recent works [1,2,3,4,5] have modeled how independent selfish agents can build or maintain a large network by paying for possible edges...
    • ...The network formation problem has been addressed in several recent works, mainly in the context of non-cooperative games [1,2,6]...
    • ...The so-called Shapley network design game is proposed in [1]...
    • ...This latter is determined in the non-cooperative network formation framework proposed in [1], revised in Section 2, starting from the empty network and using a best response algorithm where each user greedily minimizes its path cost until an equilibrium is reached...

    Konstantin Avrachenkovet al. A Nash Bargaining Solution for Cooperative Network Formation Games

    • ...Central to this area is the notion of the price of anarchy (PoA) [20, 25] and the price of stability (PoS) [3]...
    • ...For example, there are still open problems from the first paper to study the PoS [3] concerning some important cases of network design games (for example undirected networks [2, 18])...

    George Christodoulouet al. On the Performance of Approximate Equilibria in Congestion Games

    • ...Consequently, the collaborative solution proposed by our algorithm approximates the socially best Nash equilibrium (corresponding to the equilibrium used in the Price of Stability [17]), as it optimizes the global makespan with a guarantee that no player has incentive to deviate from the proposed solution...

    Pierre-Francois Dutotet al. Approximation Algorithms for the Multiorganization Scheduling Problem

    • ...Opposite to this, Anshelevich et al. [2] define the price of stability as the ratio of the social value of the best Nash equilibrium and an optimal strategy profile, thus characterizing the minimal loss of optimality that a system has to suffer in presence of selfish users...

    Vittorio Bilòet al. Performance of One-Round Walks in Linear Congestion Games

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