Population Games with Sub-Strategies and Evolutionary Nash Equilibrium Learning

We establish a modified notion of Nash equilibrium learning—convergence of the population state to the Nash equilibria set—in a generalization of the standard population games and evolutionary dynamics framework using system-theoretic passivity methods. In this setting, we allow each strategy to involve a sequence of sub-tasks that must be completed before strategy revision so long as the durations of the sub-tasks can be modeled with Erlang or exponential distributions. Furthermore, several canonical classes of natural learning rules are established and useful properties are derived.