A dynamic game model for Amplify-and-Forward cooperative communications

Cooperative wireless communication protocols are designed with the assumption that users always behave in a socially efficient manner. This assumption may not be valid in commercial wireless networks where users may violate rules of cooperation to reap benefits of cooperation at no cost. Disobeying the rules of cooperation creates a social-dilemma where well-behaved users exhibit uncertainty about intention of other users. Cooperation in social-dilemma is characterized by a non-cooperative Nash equilibrium which indicates the difficulty of maintaining a socially optimal cooperation without establishing a mechanism to detect and mitigates effects of misbehavior. In this paper, we formulate interaction of users in cooperative Amplify-and-Forward as a dynamic game with incomplete information. We show the existence of a perfect Bayesian equilibrium.