Continuous Stability and Evolutionary Convergence

✍ Scribed by Ilan Eshel; Uzi Motro; Emilia Sansone

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 209 KB
• Volume: 185
• Category: Article
• ISSN: 0022-5193
• DOI: 10.1006/jtbi.1996.0312

✦ Synopsis

A stochastic process of long-term evolution due to mutation and selection is defined over an asexually reproducing population, with selection according to a population game with a one-dimensional continuity of pure strategies. Limiting the analysis to mutations of small effect, it is shown that long-term dynamic stability in such a process is equivalent to continuous stability in the relevant population game. In the case of a one-dimensional strategy set (but not necessarily if the strategy set is multi-dimensional), this result is virtually independent of the distribution of mutations.