Stability and trembles in extensive-form games |
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| Affiliation: | 1. Université de Franche-Comté, CRESE, 30 Avenue de l’Observatoire, 25009 Besançon, France;2. Université de Saint-Etienne, CNRS UMR 5824 GATE Lyon Saint-Etienne, France;1. Tuberculosis and Infectious Diseases Control Division, Health Service Bureau, Ministry of Health, Labour and Welfare, Tokyo 100-8916, Japan;1. ICEF, NRU Higher School of Economics, Moscow, Russian Federation;2. Saïd Business School and St. Edmund Hall, University of Oxford, United Kingdom;1. Department for Management of Science and Technology Development, Ton Duc Thang University, Ho Chi Minh City, Vietnam;2. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam;3. School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland;1. Institute of Applied Mathematical Research, Karelian Research Center, Russian Academy of Science, Pushkinskaya St. 11, 185910 Petrozavodsk, Russia;2. Department of Computer Science and Engineering, Aalto University, Computer Science building, Konemiehentie 2, 02150 Espoo, Finland |
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| Abstract: | A leading solution concept in the evolutionary study of extensive-form games is Selten (1983) notion of limit ESS. This note demonstrates that a limit ESS does not imply neutral stability, and that it may be dynamically unstable (almost any small perturbation takes the population away). These problems arise due to an implicit assumption that “mutants” are arbitrarily rare relative to “trembling” incumbents. Finally, I present a novel definition that solves this issue and has appealing properties. |
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| Keywords: | Limit ESS Evolutionary stability Extensive-form games |
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