  It has been well recognized that channel state information (CSI) feedback is
of great importance for dowlink transmissions of closed-loop wireless networks.
However, the existing work typically researched the CSI feedback problem for
each individual mobile station (MS), and thus, cannot efficiently model the
interactions among self-interested mobile users in the network level. To this
end, in this paper, we propose an alternative approach to investigate the CSI
feedback rate control problem in the analytical setting of a game theoretic
framework, in which a multiple-antenna base station (BS) communicates with a
number of co-channel MSs through linear precoder. Specifically, we first
present a non-cooperative feedback-rate control game (NFC), in which each MS
selects the feedback rate to maximize its performance in a distributed way. To
improve efficiency from a social optimum point of view, we then introduce
pricing, called the non-cooperative feedback-rate control game with price
(NFCP). The game utility is defined as the performance gain by CSI feedback
minus the price as a linear function of the CSI feedback rate. The existence of
the Nash equilibrium of such games is investigated, and two types of feedback
protocols (FDMA and CSMA) are studied. Simulation results show that by
adjusting the pricing factor, the distributed NFCP game results in close
optimal performance compared with that of the centralized scheme.
