A Game of Ages for Slotted ALOHA With Capture

Within a recent line of research, age of information is supported as an alternate network performance metric with respect to throughput or delay, to evaluate the performance of medium access techniques, especially for remote sensing applications. Analytical investigations based on game theory have shown how selfish players can behave efficiently in random access systems if they are driven by AoI-based objectives. We extend this kind of reasoning to the case of a slotted ALOHA system with capture. We present a fully analytical derivation of the general framework and its main results. We provide a quantitative characterization for the strength of capture in relation to the efficiency of the resulting Nash equilibrium, which provides extremely useful insights for a distributed system management. We apply our analysis to some scenarios of interest, in particular the case of exponentially distributed powers, for which we obtain a closed-form relationship. We highlight the impact of the system parameters, specifically the cost coefficient and the capture threshold, towards achieving an efficient allocation that represents an equilibrium for the network management. It is ultimately shown that, when capture is strong, as quantified through precise conditions (the system is driven towards a Nash equilibrium achieving near-optimal performance).