In this paper we present a sufficient condition for the existence of a solution for an \mbox{equilibrium} problem on an Hadamard manifold and under suitable assumptions on the sectional curvature, we \mbox{propose} a framework for the convergence analysis of a proximal point algorithm to solve this equilibrium \mbox{problem}. Finally, we offer an application to the necessity for an agent to escape to a succession of temporary traps to be able to reach, at the end, his desires, using a recent “variational rationality” approach of human behavior.