Transmission Probability Control Game with Limited Energy

Due to limited batteries in mobile communications, network participants are confronted with a trade-off between transmitting more often or with more power. In this paper, we examine the situation arising from selfish utilization of the spectrum game theoretically. We design a game, called Transmission Probability Control Game with Limited Energy. Players optimize their probabilistic throughput selfishly while being restricted in their available energy. Each device can adjust the transmission probability and the transmission power. We examine Nash equilibria in this game. We prove that mixed Nash equilibria always exist whereas pure ones do not. By analyzing their structure and the existence of pure Nash equilibria in a restricted case, we determine how much performance is lost when Nash equilibria are applied in comparison to an optimal choice of sending probabilities and powers.