ELSEVIER Physica D 75 (1994) 310-327 From genetic evolution to emergence of game strategies Takashi Ikegami 1 zyxwvutsrqponmlkjihgfedcbaZYXWVUTS The Graduate School of Science and Technology, Kobe university, Kobe 657, Japan Abstract Evolution of game strategies is studied in the Erroneous Iterated Prisoner’s Dilemma game, in which a player sometimes decides on an erroneous action contrary to his own strategy. Erroneous games of this kind have been known to lead to the evolution of a variety of strategies. This paper describes genetic fusion modeling as a particular source of new strategies. Successive actions are chosen according to strategies having finite memory capacity, and strategy algorithms are elaborated by genetic fusion. Such a fusion process introduces a rhizome structure in a genealogy tree. Emergence of module strategies functions as innovative source of new strategies. How the extinction of strategies and module evolution leads to ESS-free open-ended evolution is also discussed. 1. Introduction Evolution is a definitive characteristic of life. It is a process that is not just the pattern- changing exhibited in cloud or snowflake for- mation; the evolutionary process demonstrates adaptive improvements and innovations. Exam- ples of the innovations stemming from natural evolution range from the intricate suture lines of ammonite shells and the expression of armor in gastropods [ 1 ] to the evolution of the human brain and immune system. What sort of evolutionary dynamics make in- novation possible? Is the mechanism which was at work in ammonites also at work in the evolu- tion of the human nervous system? These ques- tions cannot be answered experimentally as cau- sation in natural evolution takes too much time. ’ Present address: Institute of Physics, College of Arts and Sciences, University of Tokyo, Komaba 3-8-1, Meguro-ku, Tokyo 153, Japan. E-mail: ikeg@sacral.c.u-tokyo.ac.jp Fossil studies provide the best evidence we have of natural evolution. Research with artificial life, therefore, enables one effective approach to the study of evolu- tionary dynamics. Artificial evolution proceeds in computers, wherein evolutionary mechanisms are studied in-a purely idealized fashion, free from hardware constraints. To be able to describe a system not from with- out, but from within the system itself, charac- terizes research with artificial life. If a system is in an equilibrium state, the effective degrees of freedom of the system can be determined from without the system, but for evolving systems, in which there are hidden interior degrees of free- dom affecting its future evolution, description of the system from without inevitably fails. Hence we must put our descriptive viewpoint inside the system. This means that we try to understand the system not as much by describing it as by synthesizing it. 0167-2789/94/$07.00 @ 1994 Elsevier Science B.V. All rights reserved SSDIO167-2789(94)00081-Z