Communication games on the generalized Gaussian relay channel

Relaying is often seen as one of the means of increasing capacity of wireless networks [?]. Thus, various cooperative communication schemes for relaying have been proposed that achieve close to the information-theoretic network capacity. The premise behind such schemes is cooperative behavior of users. This, however, cannot be taken for granted. Users may be selfish and care only about their own rates. They might even strategically deviate from their agreed role in such cooperative communication schemes leading to a possible degradation for all. In this paper, we look at the generalized Gaussian relay channel model with two selfish users. A capacity-achieving communication scheme for such channel models was proposed by Sendonaris, et al. [?]. We show that under certain channel conditions, operating on a part of the Pareto-optimal boundary of the achievable rate region with this scheme is a Nash equilibrium, and in fact these are the only Nash equilibria. We establish the results for the one-way Gaussian relay channel, and then extend it to the two-way Gaussian relay channel model. These results may be seen as being in the same spirit as the recent results of Berry and Tse for the Gaussian interference channel [?], [?].