An Evolutionary Model with Myopic Learning

We examine a dynamical system consisting of two distinct, but interactive, subsystems, namely population dynamics and learning dynamics. The population dynamics formalize that the population shares of fitter groups increase relatively to those of less fit groups. The learning dynamics describe that each subgroup adapts its strategy, by placing more weight on activities contributing more than average to its fitness, meanwhile decreasing weights on activities contributing less than average. A saturated equilibrium is a dynamic equilibrium where no subgroup has aboveaverage fitness, and all subgroups employ best-reply strategies to the population share weighted average strategy. We demonstrate that if a trajectory converges from the interior of the state space, then its limit point is a saturated equilibrium. An evolutionary stable equilibrium is a saturated equilibrium attracting all trajectories starting in a certain neighborhood of it. The properties of the saturated equilibrium and the evolutionary stable equilibrium suggest that these concepts are adequate dynamic generalizations of the Nashequilibrium and the evolutionary stable strategy of the standard models. Maastricht Economic Research Institute on Innovation and Technology University of Limburg, P.O. Box 616, NL-6200 MD Maastricht, The Netherlands tel (31) (0)43 883875, fax (31) (0)43 216518, Email [email protected] 1 Maastricht Economic Research Institute on Innovation and Technology, and Department of Mathematics, University of Limburg, P.O. Box 616, 6200 MD Maastricht, The Netherlands. 2 Participants in a game theory meeting at the University of Limburg are thanked for comments.