Abstract
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.