A Game-Theoretic Analysis of Inter-Session Network Coding

Abstract

A common assumption in the network coding literature is that the users are cooperative and will not pursue their own interests. However, this assumption can be violated in practice. In this paper, we analyze inter-session network coding in a wired network, assuming that the users are selfish and act as strategic players to maximize their own utility. We prove the existence of Nash equilibria for a wide range of utility functions. The number of Nash equilibria can be large (even infinite) under certain conditions, which is in sharp contrast to a similar game setting with traditional packet forwarding. We then characterize the worst-case efficiency bounds, i.e., the price-of-anarchy (PoA), compared to an optimal and cooperative network design. We show that by using a novel discriminatory pricing scheme that charges encoded and forwarded packets differently, we can improve PoA in comparison with the case where a single pricing scheme is being used. However, PoA is still worse than the case when network coding is not applied. This implies that intersession network coding is more sensitive to strategic behavior. For example, for the case where only two network coding flows share a single bottleneck link, the efficiency at certain Nash equilibria can be as low as 48%. These results generalize the well-known result of guaranteed 67% efficiency bounds shown by Johari and Tsitsiklis for traditional packet forwarding networks.