Dynamic conjectures in random access networks using bio-inspired learning

Inspired by the biological entities\´ ability to achieve reciprocity in the course of evolution, this paper considers a conjecture-based distributed learning approach that enables autonomous nodes to independently optimize their transmission probabilities in random access networks. We model the interaction among multiple self-interested nodes as a game. It is well-known that the Nash equilibria in this game result in zero throughput for all the nodes if they take myopic best-response, thereby leading to a network collapse. This paper enables nodes to behave as intelligent entities which can proactively gather information, form internal conjectures on how their competitors would react to their actions, and update their beliefs according to their local observations. In this way, nodes are capable to autonomously "learn" the behavior of their competitors, optimize their own actions, and eventually cultivate reciprocity in the random access network. To characterize the steady-state outcome of this "evolution", the conjectural equilibrium is introduced. Inspired by the biological phenomena of "derivative action" and "gradient dynamics", two distributed conjecture-based action update mechanisms are proposed to stabilize the random access network. The sufficient conditions that guarantee the proposed conjecture-based learning algorithms to converge are derived. Moreover, it is analytically shown that all the achievable operating points in the throughput region are stable conjectural equilibria corresponding to different conjectures. We also investigate how the conjectural equilibrium can be selected in heterogeneous networks and how the proposed methods can be extended to ad-hoc networks. Numerical simulations verify that the system performance significantly outperforms existing protocols, such as IEEE 802.11 Distributed Coordination Function (DCF) protocol and priority-based fair medium access control (P-MAC) protocol, in terms of throughput, fairness, convergence, and st- - ability.