Equilibrium selection under evolutionary game dynamics with optimizing behavior

The purpose of this paper is to investigate equilibrium selection in a heterogeneous population composed of both optimizing and programmed agents using an evolutionary game-theoretic framework. Under the Smith dynamic, we are able to identify a class of games in which any programmed behavior will become extinct ultimately starting from any initial state, as well as a class of games in which all programmed agents can get wiped out eventually, as long as there are not enough initially. Besides, the long-run behavior is characterized under a variety of well-behaved dynamics such as the Brown–von Neumann–Nash dynamic.