Bargaining and Price-of-Anarchy in Repeated Inter-Session Network Coding Games

Abstract

Most of the previous work on network coding has assumed that the users are not selfish and always follow the designed coding schemes. However, recent results have shown that selfish users do not have the incentive to participate in inter-session network coding in a static non-cooperative game setting. As a result, the worst-case network efficiency (i.e., the price-of-anarchy) can be as low as 22%. In this paper, we show that if the same game is played repeatedly, then the price-of-anarchy can be significantly improved to 48%. We propose a grim-trigger strategy that encourages users to cooperate and participate in the inter-session network coding. A key challenge is to determine a common cooperative coding rate that the users should mutually agree on. We propose to resolve the conflict of interest among the users through a bargaining process. We derive a tight upper bound for the price-of-anarchy which is valid for any bargaining scheme. Moreover, we propose a simple and efficient min-max bargaining solution that can achieve this upper bound. Our results represent one of the first steps towards designing practical inter-session network coding schemes that can achieve reasonable performance for selfish users.