Mathematical Problems in Engineering
Volume 2007 (2007), Article ID 82184, 34 pages
Research Article

Rational Probabilistic Deciders—Part II: Collective Behavior

P. T. Kabamba, W.-C. Lin, and S. M. Meerkov

Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor 48109-2122, MI, USA

Received 7 December 2006; Accepted 23 February 2007

Academic Editor: Jingshan Li

Copyright © 2007 P. T. Kabamba et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper explores the behavior of rational probabilistic deciders (RPDs) in three types of collectives: zero sum matrix games, fractional interactions, and Edgeworth exchange economies. The properties of steady states and transients are analyzed as a function of the level of rationality, N, and, in some cases, the size of the collective, M. It is shown that collectives of RPDs, may or may not behave rationally, depending, for instance, on the relationship between N and M (under fractional interactions) or N and the minimum amount of product exchange (in Edgeworth economies). The results obtained can be useful for designing rational reconfigurable systems that can autonomously adapt to changing environments.