Relating maximum entropy, resilient behavior and game-theoretic equilibrium feedback operators in multi-channel systems

摘要

In this paper, we first draw a connection between the existence of astationary density function (which corresponds to an equilibrium state in thesense of statistical mechanics) and a set of feedback operators in amulti-channel system that strategically interacts in a game-theoreticframework. In particular, we show that there exists a set of (game-theoretic)equilibrium feedback operators such that the composition of the multi-channelsystem with this set of equilibrium feedback operators, when described bydensity functions, will evolve towards an equilibrium state in such a way thatthe entropy of the whole system is maximized. As a result of this, we are ledto study, by a means of a stationary density function (i.e., a commonfixed-point) for a family of Frobenius-Perron operators, how the dynamics ofthe system together with the equilibrium feedback operators determine theevolution of the density functions, and how this information translates intothe maximum entropy behavior of the system. Later, we use such results toexamine the resilient behavior of this set of equilibrium feedback operators,when there is a small random perturbation in the system.