A Game-Theoretic Analysis of Decode-and-Forward Cooperation in Rayleigh Fading Channels

Abstract

A game-theoretic analysis of decode and forward cooperative communications is presented for Rayleigh fading channels. The channel is studied as a two-state Markov model and cooperation is modeled as a repeated game in which selfish user terminals seek to maximize their own payoff, a utility function that monotonically increases with signal-to-noise ratio. Nash equilibria are investigated for both convex and concave utility functions. Results show a mutually cooperative Nash Equilibrium can always be obtained when convex utility functions* are used and users care somewhat about future performance. Concave utility functions may not always support a mutually cooperative Nash Equilibrium, especially under adverse channel conditions. Examinations of two widely-applied concave utility functions, however, demonstrate that mutual cooperation is more likely when users place more value on future performance. Additionally, techniques that improve effective channel conditions, e.g., use of multiple transmit antennas, further encourage cooperation.