Abstract 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.
Hankins et al. (Tue,) studied this question.