A Nash Bargaining Solution for Cooperative Network Formation Games

Avrachenkov, Konstantin; Elias, J. E.; Martignon, Fabio; Neglia, Giovanni; Petrosyan, Leon A.

doi:10.1007/978-3-642-20757-0_24

Cited by 20 publications

(21 citation statements)

References 21 publications

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“…In [21], the NBS is implemented to improve the fairness and efficiency of traffic engineering and server selection. In [22], network formation is addressed through the use of cooperative game theoretic tools such as the Shapley Value [1] and the NBS. There, it is numerically shown that the NBS permits to allocate costs fairly to users within a reasonable computation time.…”

Section: B Previous Workmentioning

confidence: 99%

How Good is Bargained Routing?

Blocq

Orda

2016

IEEE/ACM Trans. Networking

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Abstract-In the context of networking, research has focused on non-cooperative games, where the selfish agents cannot reach a binding agreement on the way they would share the infrastructure. Many approaches have been proposed for mitigating the typically inefficient operating points. However, in a growing number of networking scenarios selfish agents are able to communicate and reach an agreement. Hence, the degradation of performance should be considered at an operating point of a cooperative game. Accordingly, our goal is to lay foundations for the application of cooperative game theory to fundamental problems in networking. We explain our choice of the Nash Bargaining Scheme (NBS) as the solution concept, and introduce the Price of Selfishness (PoS), which considers the degradation of performance at the worst NBS. We focus on the fundamental load balancing game of routing over parallel links. First, we consider agents with identical performance objectives. We show that, while the PoA here can be large, through bargaining, all agents, and the system, strictly improve their performance. Interestingly, in a two-agent system or when all agents have identical demands, we establish that they reach social optimality. We then consider agents with different performance objectives and demonstrate that the PoS and PoA can be unbounded, yet we explain why both measures are unsuitable. Accordingly, we introduce the Price of Heterogeneity (PoH), as an extension of the PoA. We establish an upper-bound on the PoH and indicate its further motivation for bargaining. Finally, we discuss network design guidelines that follow from our findings.

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Section: B Previous Workmentioning

confidence: 99%

How Good is Bargained Routing?

Blocq

Orda

2016

IEEE/ACM Trans. Networking

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“…The idea of using the Nash bargaining solution in the context of telecommunication networks has been considered in different networking scenarios [19,20,21,22,23,24].…”

Section: Related Workmentioning

confidence: 99%

Cooperative network design: A Nash bargaining solution approach

et al. 2015

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The Network Design problem has received increasing attention in recent years. Previous works have addressed this problem considering almost exclusively networks designed by selfish users, which can be consistently suboptimal. This paper addresses the network design issue using cooperative game theory, which permits to study ways to enforce and sustain cooperation among users. Both the Nash bargaining solution and the Shapley value are widely applicable concepts for solving these games. However, the Shapley value presents several drawbacks in this context.For this reason, we solve the cooperative network design game using the Nash bargaining solution (NBS) concept. More specifically, we extend the NBS approach to the case of multiple players and give an explicit expression for users' cost allocations. We further provide a distributed algorithm for computing the Nash bargaining solution. Then, we compare the NBS to the Shapley value and the Nash equilibrium solution in several network scenarios, including real ISP topologies, showing its advantages and appealing properties in terms of cost allocation to users and computation time to obtain the solution.Numerical results demonstrate that the proposed Nash bargaining solution approach permits to allocate costs fairly to users in a reasonable computation time, thus representing a very effective framework for the design of efficient and stable networks.

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“…Nahir et al [15] have considered similar NFG problems in directed graphs. Coalition and bilateral agreements between players in NFG and game-theory in general have been considered in [18], [5], [19], [2]. In order to evaluate "the goodness" of the equilibria, the prices of anarchy and stability [14], [20] have been used.…”

Section: Related Workmentioning

confidence: 99%

Designing virus-resistant networks: A game-formation approach

Trajanovski

Kuipers

Hayel

et al. 2015

2015 54th IEEE Conference on Decision and Control (CDC)

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Abstract-Designing an optimal network topology while balancing multiple, possibly conflicting objectives like cost, high performance, security and resiliency to viruses is a challenging endeavor in a decentralized network formation as, for example, happens in the Internet. In this paper, we take a game-formation approach to network design where each player, for instance an autonomous system, aims to minimize the cost of installing links, of being infected by a virus and of the connectivity.In the game, minimizing virus risk as well as connectivity costs results in sparse graphs. We show that the Nash Equilibria are trees that, according to the Price of Anarchy (PoA), are close to the global optimum, while the worst-case Nash Equilibrium and the global optimum may significantly differ for small infection rate and installation cost. Moreover, the types of trees, in both the Nash Equilibria and the optimal solution, depend on the virus infection rate, which provides new insights into how viruses spread: for high infection rate τ , the path graph is the worst-and the star graph is the best-case Nash Equilibrium. However, for small and intermediate values of τ , trees different from the path and star graphs may be optimal.

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A Nash Bargaining Solution for Cooperative Network Formation Games

Cited by 20 publications

References 21 publications

How Good is Bargained Routing?

How Good is Bargained Routing?

Cooperative network design: A Nash bargaining solution approach

Designing virus-resistant networks: A game-formation approach

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