Responsive and strong responsive evolutionary dynamics

We extend Relative Monotonic Dynamics to Responsive Dynamics (RDs) to permit the response of the population to be history dependent, discontinuous and delayed. We introduce Strong Responsive Dynamics (SRDs) to model populations that are a little more responsive than in RDs, and define a relationship called quasi-strict dominance which characterizes the strategies that eventually die out under SRDs. These non-surviving strategies include the strategies that are weakly dominated by a pure strategy. If the game is quasi-strict-dominance solvable, then a SRD will converge to the quasi-strict-dominance solution, which is a weak proper NE. If the game is “quasi-strict-dominance ordered”, then a SRD will converge to a proper NE.