Linearly Coupled Communication Games

This paper discusses a special type of multi-user communication scenario, in which users' utilities are linearly impacted by their competitors' actions. First, we explicitly characterize the Nash equilibrium and Pareto boundary of the achievable utility region. Second, the price of anarchy incurred by the non-collaborative Nash strategy is quantified. Third, to improve the performance in the non-cooperative scenarios, we investigate the properties of an alternative solution concept named conjectural equilibrium, in which individual users compensate for their lack of information by forming internal beliefs about their competitors. The global convergence of the best response and Jacobi update dynamics that achieve various conjectural equilibria are analyzed. It is shown that the Pareto boundaries of the investigated linearly coupled games can be sustained as stable conjectural equilibria if the belief functions are properly initialized. The investigated models apply to a variety of realistic applications encountered in the multiple access design, including wireless random access and flow control.