  This letter establishes a novel relationship between a class of recurrent
neural networks and certain evolutionary dynamics that emerge in the context of
population games. Specifically, it is shown that the output of a recurrent
neural network, in the context of classification problems, coincides with the
evolution of the population state in a population game. This connection is
established with dynamic payoffs and under replicator evolutionary dynamics.
The connection provides insights into the neural network's behavior from both
dynamical systems and game-theoretical perspectives, aligning with recent
literature that suggests that neural network outputs may resemble the Nash
equilibria of suitable games. It also uncovers potential connections between
the neural network classification problem and mechanism design. To illustrate
our results, we present different numerical experiments in the context of
classification problems.
