Cellular Games: An Introduction
Lenore Levine
Department of Mathematics, University of Illinois,
273 Altgeld Hall, 1409 W. Green St., Urbana, IL 61801, USA
Abstract
A cellular game is a dynamical system in which cells, placed in some discrete structure, are regarded as playing a game with their immediate neighbors. Individual strategies may be either deterministic or stochastic. Strategy success is measured according to some universal and unchanging criterion. Successful strategies persist and spread; unsuccessful ones disappear.
In this paper, two cellular game models are formally defined, and are compared to cellular automata. Computer simulations of these models are presented.
Conditions providing maximal average cell success, on one- and two-dimensional lattices, are examined. It is shown that these conditions are not necessarily stable; and an example of such instability is analyzed. It is also shown that Nash equilibrium strategies are not necessarily stable.
