An ALOHA multi-user game with tradeoff between throughput and transmission proportional fairness

The paper considers an ALOHA type communication, where several users send data, and investigates the problem in a game-theoretic framework. We show that in such ALOHA type communication, the throughput metric leads to a continuum of equilibria. Moreover, its traditional extension via adding a transmission cost, which might collapse such a continuum to a finite number of equilibria, actually remains a multi equilibria situation, and that this might potentially destabilize users communication. Also we show that in contrast to the flat-fading multiple access communication (MAC) networks, in an ALOHA network, users' communication might not be stabilized via switching from throughput to latency communication utility. This phenomena puts forward a question of which metric might lead to a unique equilibrium, and thus to stability in multi user ALOHA type communication. Here for multi user ALOHA type communication we suggest an advanced communication metric reflecting tradeoff between throughput and the transmission's fairness. Such metric might be also interpreted as a trade-off for a user between its selfish and cooperative behavior. We prove that, in contrast to the throughput metric, such an advanced metric always lead to a unique equilibrium, and thus to communication stability under the corresponding transmission protocol. The other proven advantage is that it supports uninterrupted communication between the users. The equilibrium is derived in closed form. Finally, it is shown how to optimize weights of throughput and transmission's fairness in the suggested trade-off metric.