Designing Network Protocols for Good Equilibria

Abstract

Designing and deploying a network protocol determines the rules by which end users interact with each other and with the network. We consider the problem of designing a protocol to optimize the equilibrium behavior of a network with selfish users. We consider network costsharing games, where the set of Nash equilibria depends fundamentally on the choice of an edge cost-sharing protocol. Previous research focused on the Shapley protocol, in which the cost of each edge is shared equally among its users.We systematically study the design of optimal cost-sharing protocols for undirected and directed graphs, single-sink and multicommodity networks, and different measures of the inefficiency of equilibria. Our primary technical tool is a precise characterization of the cost-sharing protocols that only induce network games with pure-strategy Nash equilibria. We use this characterization to prove, among other results, that the Shapley protocol is optimal in directed graphs, and that simple priority protocols are essentially optimal in undirected graphs.

Implementing efficient graphs in connection networks

“…This means that the strong price of anarchy (SPoA) of the EG equals the strong price of stability of EG, and they equal H(k). This earmarks another advantage of EG over Sh, since we know that Sh does not always admit Strong NE [3,4] and therefore, SPoA does not exist for Sh.…”

“…[19] finds a new upper bound of O(log k/ log log k) for single source networks when steiner nodes are allowed. [4] shows that the upper bound in two player case with single source is 4 3 . [18] finds out that 4 3 is also the upper bound in general multi commodity case.…”

“…The Shapley mechanism (Sh, [4]), which divides the cost of every edge equally among its users, has become focal in this setup. Even though Shapley looks like a natural mechanism in this setting, there are serious problems associated with it.…”

“…Alternative separable mechanisms can be constructed by considering different cost-sharing rules for the links, for instance, by giving priority across all users. Nevertheless, Sh is the optimal mechanism (using the price of stability measure; see below) across all separable mechanism ( [4]). Sh can be computed in polynomial time.…”

“…For example, [4] studies the equilibrium behavior of separable mechanisms, a class of decentralized mechanisms that divides the cost of each edge among its users. The PoS of separable mechanisms with a linear cost-sharing function is at least H(k) (which is O(log k)), where k is the number of agents [4]. H(k) is the upper bound on PoS(Sh) in general graphs, [3].…”