  We analyze the stability of a nonlinear dynamical model describing the
noncooperative strategic interactions among the agents of a finite collection
of populations. Each agent selects one strategy at a time and revises it
repeatedly according to a protocol that typically prioritizes strategies whose
payoffs are either higher than that of the current strategy or exceed the
population average. The model is predicated on well-established research in
population and evolutionary games, and has two sub-components. The first is the
payoff dynamics model (PDM), which ascribes the payoff to each strategy
according to the proportions of every population adopting the available
strategies. The second sub-component is the evolutionary dynamics model (EDM)
that accounts for the revision process. In our model, the social state at
equilibrium is a best response to the payoff, and can be viewed as a Nash-like
solution that has predictive value when it is globally asymptotically stable
(GAS). We present a systematic methodology that ascertains GAS by checking
separately whether the EDM and PDM satisfy appropriately defined
system-theoretic dissipativity properties. Our work generalizes pioneering
methods based on notions of contractivity applicable to memoryless PDMs, and
more general system-theoretic passivity conditions. As demonstrated with
examples, the added flexibility afforded by our approach is particularly useful
when the contraction properties of the PDM are unequal across populations.
