Selfish Users in Graph-Based Random Access

Recent advances in random access (RA) have highlighted the performance improvement yield by the joint use of proactive replication of packets and successive interference cancellation (SIC). Users send multiple replicas and collisions are resolved via iterative cancellation of the interference. The optimal choice for the number of replicas is drawn from a properly designed probability mass function (PMF). Selfish uncoordinated users are prone to choose the maximum number of replicas and diverge from the designed PMF. Exploiting game theoretic tools, we describe such scenario as a non-cooperative game. Properly setting the cost per replica transmission, we are able to drive the Nash equilibrium to the designed PMF and thus hinder the users to diverge. Numerical results complement the study, showing the practical impact of the proposed solution.