A game-theoretic analysis of decode-and-forward user cooperation

A game-theoretic analysis of decode and forward cooperative communications is presented for additive white Gaussian noise (AWGN) and Rayleigh fading channels. Cooperative communications is modeled as a repeated game in which the two participating terminals are selfish and seek to maximize their own payoff, a general utility function that monotonically increases with signal-to-noise ratio. Results show a Nash Equilibrium in which users mutually cooperate can be obtained for AWGN channels when strict power control is enforced and users care about future payoff. However, such power control may not be necessary to achieve cooperative Nash Equilibrium when the game is played in Rayleigh fading channels. We study the Rayleigh fading channel as a two state Markov model in this paper. In this case, a mutually cooperative Nash Equilibrium 1) always exists when the utility function is convex and users care somewhat about future payoff; and 2) may not always exist when the utility function is concave, especially in adverse channel conditions. Examinations of several widely-used concave functions, however, demonstrate that mutual cooperation is more likely when users increase their value on future payoff. Additionally, it is shown that improving the effective uplink channel conditions of users, e.g., by using multiple transmit antennas, further encourages cooperation.