  The prevailing methodology for analyzing population games and evolutionary
dynamics in the large population limit assumes that a Poisson process (or
clock) inherent to each agent determines when the agent can revise its
strategy. Hence, such an approach presupposes exponentially distributed
inter-revision intervals, and is inadequate for cases where each strategy
entails a sequence of sub-tasks (sub-strategies) that must be completed before
a new revision time occurs. This article proposes a methodology for such cases
under the premise that a sub-strategy's duration is exponentially-distributed,
leading to Erlang distributed inter-revision intervals. We assume that a
so-called pairwise-comparison protocol captures the agents' revision
preferences to render our analysis concrete. The presence of sub-strategies
brings on additional dynamics that is incompatible with existing models and
results. Our main contributions are twofold, both derived for a deterministic
approximation valid for large populations. We prove convergence of the
population's state to the Nash equilibrium set when a potential game generates
a payoff for the strategies. We use system-theoretic passivity to determine
conditions under which this convergence is guaranteed for contractive games.
