Cooperative network design: A Nash bargaining solution approach

Abstract

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.

Game-Theoretic Multi-Agent Control and Network Cost Allocation Under Communication Constraints

“…Several approaches to fair payoff allocation have been proposed in the literature [16], [17], [29], [30]. We employ the Nash Bargaining Solution (NBS) due to its computational efficiency in NFGs [16], [17]. The NBS payoff allocation algorithm proceeds in three steps based on [17]:…”

“…using the above algorithms, we apply cooperative NFG theory [15] and the Nash Bargaining Solution (NBS) [16], [17] to allocate the costs of communication among the agents proportionally to the benefits they derive from sparsity-constrained feedback and cooperation. This network cost allocation method improves on our previous WAC cost allocation approaches [18], [19], which employed heuristics, relied on the centralized optimization in [8], and extrapolated the costs of a dense network [5] to sparse scenarios.…”

Distributed multi-step power scheduling and cost allocation for cooperative microgrids

“…Several approaches to fair cost allocation for cooperative games have been proposed in the literature [9], [17]- [19]. We employ Nash Bargaining Solution (NBS) due to its computational efficiency [9]. The proposed cost allocation is unique and fair as discussed below.…”

“…Consider a system with r players and a system-wide cost function J. The NBS cost allocation algorithm proceeds in three steps [9]:…”

“…Nash Bargaining Solution (NBS) [9] to fairly allocate the costs of power provided by the grid. Game theory was utilized for microgrid energy storage optimization in e.g., [4]- [6] while cost allocation for power industry was addressed in [10]- [12] as well as our recent work [13], [14].…”