  We use system-theoretic passivity methods to study evolutionary Nash
equilibria learning in large populations of agents engaged in strategic,
non-cooperative interactions. The agents follow learning rules (rules for
short) that capture their strategic preferences and a payoff mechanism ascribes
payoffs to the available strategies. The population's aggregate strategic
profile is the state of an associated evolutionary dynamical system.
Evolutionary Nash equilibrium learning refers to the convergence of this state
to the Nash equilibria set of the payoff mechanism. Most approaches consider
memoryless payoff mechanisms, such as potential games. Recently, methods using
$\delta$-passivity and equilibrium independent passivity (EIP) have introduced
dynamic payoff mechanisms. However, $\delta$-passivity does not hold when
agents follow rules exhibiting ``imitation" behavior, such as in replicator
dynamics. Conversely, EIP applies to the replicator dynamics but not to
$\delta$-passive rules. We address this gap using counterclockwise
dissipativity (CCW). First, we prove that continuous memoryless payoff
mechanisms are CCW if and only if they are potential games. Subsequently, under
(possibly dynamic) CCW payoff mechanisms, we establish evolutionary Nash
equilibrium learning for any rule within a convex cone spanned by imitation
rules and continuous $\delta$-passive rules.
