A game theoretic approach to network coding

We introduce a game theoretic framework for studying a restricted form of network coding in a general wireless network. The network is fixed and known, and the system performance is measured as the number of wireless transmissions required to meet n unicast demands. Game theory is here employed as a tool for improving distributed network coding solutions. We propose a framework that allows each unicast session to independently adjust his routing decision in response to local information. Specifically, we model the unicast sessions as self-interested decision makers in a noncooperative game. This approach involves designing both local cost functions and decision rules for the unicast sessions so that the resulting collective behavior achieves a desirable system performance in a shared network environment. We compare the performance of the resulting distributed algorithms to the best performance that could be found and implemented using a centralized controller. We focus on the performance of stable solutions - where stability here refers to a form of Nash equilibrium defined below. Results include bounds on the best- and worst-case stable solutions as compared to the optimal centralized solution. We show that our bounds on the best- and worst-case stable performance cannot be improved using cost functions that are independent of the network structure. Results in learning in games prove that the best-case stable solution can be learned by self-interested players with probability approaching 1.