Violations Of Monotonicity In Evolutionary Models With Sample Based Beliefs
by
Richard Ball
Haverford College

This paper shows that an important class of evolutionary game-theoretic models--those in which agents form beliefs about the behavior of others on the basis of samples they observe from the population--violate a property--monotonicity--that many authors have argued any well-specified evolutionary model should possess. A stripped down evolutionary model that closely follows Young's (1993) pioneering model is developed, and a theorem based on the Central Limit Theorem is presented, showing that the sampling process on which beliefs are based necessarily generates a violation of monotonicity. (Loosely, a violation of monotonicity means that the population proportion of a "less fit" strategy grows more quickly than the population proportion of a "more fit" strategy.) A numerical example illustrating this violation is also presented. This violation does not imply that models with sampling-based beliefs are defective or implausible in any way. On the contrary, these models are built on carefully articulated and justified microfoundations. What this paper demonstrates is that analyses that begin with an assumption of monotonicity, without the>specifics of the dynamic process explicitly stated, are not applicable to>all evolutionary models.

REFERENCE: Young, H.P. 1993. "The Evolution of Conventions." ECONOMETRICA 61:57-84.

http://www.haverford.edu/economics/ball/home.html

Date received: June 9, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafi-38.