Dept. Math, Hokkaido Univ. EPrints Server

Stability and Diversity in Collective Adaptation

Preprint Series # 662
Sato, Yuzuru and Akiyama, Eizo and Crutchfield, James P. Stability and Diversity in Collective Adaptation. (2004);

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Abstract

We derive a class of macroscopic differential equations that describe collective adaptation, starting from a discrete-time stochastic microscopic model. The behavior of each agent is a dynamic balance between adaptation that locally achieves the best action and memory loss that leads to randomized behavior. We show that, although individual agents interact with their environment and other agents in a purely self-interested way, macroscopic behavior can be interpreted as game dynamics. Application to several familiar, explicit game interactions shows that the adaptation dynamics exhibits a diversity of collective behaviors, including stable limit cycles, quasiperiodicity, intermittency, and deterministic chaos. The simplicity of the assumptions underlying the macroscopic equations suggests that these behaviors should be expected broadly in collective adaptation. We also analyze the adaptation dynamics from an information-theoretic viewpoint and discuss self-organization induced by information flux between agents, giving a novel view of collective adaptation.

Item Type:Preprint
Additional Information:21 pages, 23 figures, arxiv/abs/nlin.AO/0408039, SFI working paper 04-08-025
Uncontrolled Keywords:collective adaptation, evolutionary dynamics, game theory, information theory, dynamical systems
Subjects:92-xx BIOLOGY AND OTHER NATURAL SCIENCES
91-xx GAME THEORY, ECONOMICS, SOCIAL AND BEHAVIORAL SCIENCES
37-xx DYNAMICAL SYSTEMS AND ERGODIC THEORY
ID Code:428