Coalitional Games for Transmitter Cooperation in Wireless Networks

Cooperation between nodes in a wireless network will increasingly become necessary to achieve performance goals when nodes employ the same resource spectrum. The question of feasibility of cooperation between rational nodes in a wireless network and whether there exists a fair division of the benefits of cooperation is unknown even for simple multi-terminal networks such as multiple access and broadcast channels, much less for a large wireless network. This paper addresses the stability of the grand coalition of transmitters (TXs) signaling over a multiple access channel using the framework of cooperative game theory. By modeling the game in partition form, each coalition’s utility can be accurately characterized by accounting for external interference. Single user decoding (SUD) and successive interference cancellation (SIC) receivers are considered and it is shown that the grand coalition maximizes the obtainable sum utility for both the decoding schemes. The grand coalition is stable if the core of the game, the set of all divisions of utility which cannot be achieved by any smaller coalition of TXs, is nonempty. For an SUD receiver, TX cooperation is shown to be stable at both high and low SNRs, while for an SIC receiver with a fixed decoding order, the cooperation is stable only at very low SNRs. However, for an SIC receiver which allows time-sharing between decoding orders, it is shown using an approximate utility function that TX cooperation is also stable at high SNRs. Finally, using numerical simulations, it is observed that the core is nonempty, in general, for an SUD receiver and an SIC receiver with time-sharing between decoding orders, thus showing that ideal zero cost TX cooperation over a MAC channel improves achievable rates for each individual user in every coalition.