Darwinian evolution in games with perfect information
type: Item
instance of: scholarly article
title: Darwinian evolution in games with perfect information
zbMATH Open document ID: 0618.92012
DOI: 10.1007/BF02281974
author: Petr Kůrka
published in: Biological Cybernetics
publication date: 1987-01-01T00:00:00Z
review text: The author considers a model of Darwinian evolution in games with perfect information like chess or checkers. The evolution is viewed as a sequence of strategies, each of which wins over its immediate predecessor. If strategy q wins over p, there is an evolutionary transition from p to q (denoted \(p\to q)\). There is an evolutionary path from p to q (denoted \(p\to^{*}q)\) if there is a sequence of strategies such that \(p=r_ 0\to r_ 1\to...\to r_ n=q.\) A strategy p is optimal [resp. pessimal; resp. quasipessimal] if there is no q with \(p\to q\) [resp. if there is no q with \(q\to p\); resp. if p is not pessimal and \(q\to p\) only for q pessimal]. A strategy p is normal if it is neither optimal nor pessimal nor quasipessimal. It is shown that between these four evolutionary levels (pessimal, quasipessimal, normal, optimal) there are evolutionary transitions from lower to higher levels and within the set of normal strategies, but there are no others. Every normal strategy may evolve (in several steps) from every other normal strategy. Moreover, if the admissible strategies are restricted by some given upper bound on their computational complexity, no optimal strategies need exist, but otherwise the results remain true. In contrast to this, if the additional restriction is imposed that when \(p\to q\), then p and q should differ only slightly (random mutation), degenerative evolutionary sequences become possible, i.e. paths leading form higher intelligence levels to lower ones. This is illustrated by a simple computer program for \(8\times 8\) checkers.
Mathematics Subject Classification ID: 92D15
Mathematics Subject Classification ID: 91A40
Mathematics Subject Classification ID: 91A80
zbMATH DE Number: 4003967
zbMATH Keywords: model of Darwinian evolution
zbMATH Keywords: games with perfect information
zbMATH Keywords: sequence of strategies
zbMATH Keywords: evolutionary transition
zbMATH Keywords: evolutionary path
zbMATH Keywords: pessimal
zbMATH Keywords: quasipessimal
zbMATH Keywords: normal strategies
zbMATH Keywords: admissible strategies
zbMATH Keywords: computational complexity
zbMATH Keywords: optimal strategies
zbMATH Keywords: random mutation
zbMATH Keywords: degenerative evolutionary sequences
reviewed by: Manfred Nermuth
MaRDI profile type: Publication
cites work: Evolution of replicators playing a strategic game
cites work: Game dynamics and evolutionary transitions
cites work: Q4745305
cites work: Q3040961
cites work: Theory of games and economic behavior.
cites work: N by N Checkers is Exptime Complete
full work available at URL: https://doi.org/10.1007/bf02281974
OpenAlex ID: W4233870607
description: scientific article; zbMATH DE number 4003967