ON THE LIMIT POINTS OF DISCRETE SELECTION DYNAMICS

This paper provides an analog to the aggregate monotonicity condition introduced by Samuelson and Zhang [J. Econ. Theory, 1992] in a study of continuous dynamics. Our condition guarantees that limit points of discrete selection dynamics are rationalizable strategies. We show that the condition will be satisfied by the discrete replicator dynamic if the population does not change rapidly. These results reconcile the Samuelson-Zhang theorem, which implies that limit points of continuous replicator dynamics must be rationalizable, with an example of Dekel and Scotchmer [J. Econ. Theory, 1992], which shows that limit points of the discrete replicator dynamic may place positive probability on strictly dominated stategies. © 1992.