  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.
