Optimality and stability of symmetric evolutionary games with applications in genetic selection
Symmetric evolutionary games, i.e., evolutionary games with symmetric fitness matrices, have important applications in population genetics, where they can be used to model for example the selection and evolution of the genotypes of a given population. In this paper, we review the theory for obtainin...
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| Format: | Article |
| Language: | English |
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AIMS Press
2014-12-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.503 |
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| author | Yuanyuan Huang Yiping Hao Min Wang Wen Zhou Zhijun Wu |
| author_facet | Yuanyuan Huang Yiping Hao Min Wang Wen Zhou Zhijun Wu |
| author_sort | Yuanyuan Huang |
| collection | DOAJ |
| description | Symmetric evolutionary games, i.e., evolutionary games with symmetric fitness matrices, have important applications in population genetics, where they can be used to model for example the selection and evolution of the genotypes of a given population. In this paper, we review the theory for obtaining optimal and stable strategies for symmetric evolutionary games, and provide some new proofs and computational methods. In particular, we review the relationship between the symmetric evolutionary game and the generalized knapsack problem, and discuss the first and second order necessary and sufficient conditions that can be derived from this relationship for testing the optimality and stability of the strategies. Some of the conditions are given in different forms from those in previous work and can be verified more efficiently. We also derive more efficient computational methods for the evaluation of the conditions than conventional approaches. We demonstrate how these conditions can be applied to justifying the strategies and their stabilities for a special class of genetic selection games including some in the study of genetic disorders. |
| format | Article |
| id | doaj-art-8c56cd1e39ad45249308589ff4ad85b4 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2014-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-8c56cd1e39ad45249308589ff4ad85b42025-01-24T02:31:53ZengAIMS PressMathematical Biosciences and Engineering1551-00182014-12-0112350352310.3934/mbe.2015.12.503Optimality and stability of symmetric evolutionary games with applications in genetic selectionYuanyuan Huang0Yiping Hao1Min Wang2Wen Zhou3Zhijun Wu4Department of Mathematics, Iowa State University, Ames, IA 50011Department of Mathematics, Iowa State University, Ames, IA 50011Department of Mathematics, Iowa State University, Ames, IA 50011Department of Statistics, Iowa State University, Ames, IA 50011Department of Mathematics, Iowa State University, Ames, IA 50011Symmetric evolutionary games, i.e., evolutionary games with symmetric fitness matrices, have important applications in population genetics, where they can be used to model for example the selection and evolution of the genotypes of a given population. In this paper, we review the theory for obtaining optimal and stable strategies for symmetric evolutionary games, and provide some new proofs and computational methods. In particular, we review the relationship between the symmetric evolutionary game and the generalized knapsack problem, and discuss the first and second order necessary and sufficient conditions that can be derived from this relationship for testing the optimality and stability of the strategies. Some of the conditions are given in different forms from those in previous work and can be verified more efficiently. We also derive more efficient computational methods for the evaluation of the conditions than conventional approaches. We demonstrate how these conditions can be applied to justifying the strategies and their stabilities for a special class of genetic selection games including some in the study of genetic disorders.https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.503evolutionary gamesgenetic selectionpopulation geneticsevolutionary stability.evolutionary biologygeneralized knapsack problems |
| spellingShingle | Yuanyuan Huang Yiping Hao Min Wang Wen Zhou Zhijun Wu Optimality and stability of symmetric evolutionary games with applications in genetic selection Mathematical Biosciences and Engineering evolutionary games genetic selection population genetics evolutionary stability. evolutionary biology generalized knapsack problems |
| title | Optimality and stability of symmetric evolutionary games with applications in genetic selection |
| title_full | Optimality and stability of symmetric evolutionary games with applications in genetic selection |
| title_fullStr | Optimality and stability of symmetric evolutionary games with applications in genetic selection |
| title_full_unstemmed | Optimality and stability of symmetric evolutionary games with applications in genetic selection |
| title_short | Optimality and stability of symmetric evolutionary games with applications in genetic selection |
| title_sort | optimality and stability of symmetric evolutionary games with applications in genetic selection |
| topic | evolutionary games genetic selection population genetics evolutionary stability. evolutionary biology generalized knapsack problems |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.503 |
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