On the limit points of discrete selection dynamics

https://doi.org/10.1016/0022-0531(92)90043-HGet rights and content

Abstract

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.

References (11)

There are more references available in the full text version of this article.

Cited by (73)

  • A coevolution model of defensive medicine, litigation and medical malpractice insurance

    2023, Communications in Nonlinear Science and Numerical Simulation
    Citation Excerpt :

    Patients may sue the physicians for medical malpractice when adverse events occur. The adoption process of choices by patients and physicians is modeled by a three-dimensional discrete-time dynamic system based on the exponential replicator dynamics proposed in [27], augmented by an equation describing the time evolution of the assurance premium. This way we describe bifurcations of the system, in particular Neimark–Sacker bifurcations, as well as is ruled out the period doubling bifurcation.

  • Evolutionary dynamics in club goods binary games

    2018, Journal of Economic Dynamics and Control
  • Emergence of competition and cooperation in an evolutionary resource war model

    2018, Communications in Nonlinear Science and Numerical Simulation
View all citing articles on Scopus

We thank Tilman Börgers, Richard Boylan, Vincent Crawford, Eddie Dekel-Tabak, George Mailath (who found an error in our first attempt to prove Proposition 2), Larry Samuelson, Jianbo Zhang, and referees for helpful comments. Cabrales thanks Spain's Ministry of Education and Sobel thanks the NSF for financial support.

View full text