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