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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.

No abstract

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.

We investigate a routing game that allows for the creation of coalitions, within the framework of cooperative game theory. Specifically, we describe the cost of each coalition as its maximin value. This represents the performance that the coalition can guarantee itself, under any (including worst) conditions. We then investigate fundamental solution concepts of the considered cooperative game, namely the core and a variant of the min-max fair nucleolus. We consider two types of routing games based on the agents' Performance Objectives, namely bottleneck routing games and additive routing games. For bottleneck games we establish that the core includes all system-optimal flow profiles and that the nucleolus is system-optimal or disadvantageous for the smallest agent in the system. Moreover, we describe an interesting set of scenarios for which the nucleolus is always system-optimal. For additive games, we focus on the fundamental load balancing game of routing over parallel links. We establish that, in contrary to bottleneck games, not all system-optimal flow profiles lie in the core. However, we describe a specific system-optimal flow profile that does lie in the core and, under assumptions of symmetry, is equal to the nucleolus.