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Titlebook: Game Theoretical Foundations of Evolutionary Stability; Immanuel M. Bomze,Benedikt M. P?tscher Book 1989 Springer-Verlag Berlin Heidelberg

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書目名稱Game Theoretical Foundations of Evolutionary Stability
編輯Immanuel M. Bomze,Benedikt M. P?tscher
視頻videohttp://file.papertrans.cn/381/380472/380472.mp4
叢書名稱Lecture Notes in Economics and Mathematical Systems
圖書封面Titlebook: Game Theoretical Foundations of Evolutionary Stability;  Immanuel M. Bomze,Benedikt M. P?tscher Book 1989 Springer-Verlag Berlin Heidelberg
描述These Lecture Notes arose from discussions we had over a working paper written by the first author in fall 1987. We decided then to write a short paper about the basic structure of evolutionary stability and found ourselves ending up with a book manuscript. Parts of the material contained herein were presented in a seminar at the Department of Mathematics at the University of Vienna, as well as at a workshop on evolutionary game theory in Bielefeld. The final version of the manuscript has certainly benefitted from critical comments and suggestions by the participants of both the seminar and the workshop. Thanks are also due to S. Bomze-de Barba, R. Burger, G. Danninger, J. Hofbauer, R. Selten, K. Sigmund, G. Stiastny and F. Weising. The co-operation of W. Muller from Springer Verlag, Heidelberg, is gratefully acknowledged. Vienna, November 1988 Immanuel M. Bomze Benedikt M. Potscher III Contents 1. Introduction 1 2. Strategies and payoffs 5 2. 1. A general setting for evolutionary game theory 6 2. 2. Mixed strategies and population games 8 2. 3. Finite number of strategies . . . . . 13 2. 4. Infinitely many (pure) strategies 15 2. 5. Structured populations: asymmetric contests and
出版日期Book 1989
關(guān)鍵詞dynamics; foundation; mathematics; population; stability; strategy
版次1
doihttps://doi.org/10.1007/978-3-642-45660-2
isbn_softcover978-3-540-50766-6
isbn_ebook978-3-642-45660-2Series ISSN 0075-8442 Series E-ISSN 2196-9957
issn_series 0075-8442
copyrightSpringer-Verlag Berlin Heidelberg 1989
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Mixed strategies, ., . ∈ .. Here .: .→?. maps a distribution . to the vector .(.) of mean payoffs to the pure strategies against members of a population in state .. Using these relations, we have .∈ε.if and only if for all . ∈ ., . ≠ ., . holds whenever 0<ε<ε(.). Similarly, .∈ξ. if and only if
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Replicator dynamics,, uninvadability implies dynamical stability (defined below), whereas evolutionary stability neither implies nor is implied by the dynamical stability concept; see, e.g. [. 1987, p.226, Fig.9.4.4b], and Example 18 below.
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Introduction,racting individuals and to explain why certain states of a given population are — in course of the selection process — stable against perturbations induced by mutations. In particular, an explanation is sought how stable polymorphisms of behaviour can arise in a population, as is observed, e.g., in certain mammal societies.
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