Darwinian evolution in games with perfect information
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.
scientific article; zbMATH DE number 4003967