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The replicator equation on graphs
https://ir.soken.ac.jp/records/3663
https://ir.soken.ac.jp/records/3663dbffe8b3-a9d8-4043-86b1-d5158e048f19
| 名前 / ファイル | ライセンス | アクション |
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nihms51830 (1.9 MB)
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| Item type | 学術雑誌論文 / Journal Article(1) | |||||||||
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| 公開日 | 2013-06-27 | |||||||||
| タイトル | ||||||||||
| タイトル | The replicator equation on graphs | |||||||||
| タイトル | ||||||||||
| タイトル | The replicator equation on graphs | |||||||||
| 言語 | en | |||||||||
| 言語 | ||||||||||
| 言語 | eng | |||||||||
| 資源タイプ | ||||||||||
| 資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||||||
| 資源タイプ | journal article | |||||||||
| 著者 |
OHTSUKI, Hisashi
× OHTSUKI, Hisashi
× NOWAK, Martin A
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| 著者別名 |
大槻, 久
× 大槻, 久
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| 抄録 | ||||||||||
| 内容記述タイプ | Abstract | |||||||||
| 内容記述 | We study evolutionary games on graphs. Each player is represented by a vertex of the graph. The edges denote who meets whom. A player can use any one of n strategies. Players obtain a payoff from interaction with all their immediate neighbors. We consider three different update rules, called ‘birth-death’, ‘death-birth’ and ‘imitation’. A fourth update rule, ‘pairwise comparison’, is shown to be equivalent to birth-death updating in our model. We use pair-approximation to describe the evolutionary game dynamics on regular graphs of degree k. In the limit of weak selection, we can derive a differential equation which describes how the average frequency of each strategy on the graph changes over time. Remarkably, this equation is a replicator equation with a transformed payoff matrix. Therefore, moving a game from a well-mixed population (the complete graph) onto a regular graph simply results in a transformation of the payoff matrix. The new payoff matrix is the sum of the original payoff matrix plus another matrix, which describes the local competition of strategies. We discuss the application of our theory to four particular examples, the Prisoner’s Dilemma, the Snow-Drift game, a coordination game and the Rock-Scissors-Paper game. | |||||||||
| 書誌情報 |
Journal of Theoretical Biology en : Journal of Theoretical Biology 巻 243, 号 1, p. 86-97, 発行日 2006-11-07 |
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| 出版者 | ||||||||||
| 出版者 | Elsevier | |||||||||
| ISSN | ||||||||||
| 収録物識別子タイプ | ISSN | |||||||||
| 収録物識別子 | 00225193 | |||||||||
| PubMed番号 | ||||||||||
| 関連タイプ | isVersionOf | |||||||||
| 識別子タイプ | PMID | |||||||||
| 関連識別子 | 2430083 | |||||||||
| DOI | ||||||||||
| 関連タイプ | isVersionOf | |||||||||
| 識別子タイプ | DOI | |||||||||
| 関連識別子 | http://doi.org/10.1016/j.jtbi.2006.06.004 | |||||||||
| 関連名称 | 10.1016/j.jtbi.2006.06.004 | |||||||||
| 権利 | ||||||||||
| 権利情報 | © 2006 Elsevier Ltd. | |||||||||
| 関連サイト | ||||||||||
| 識別子タイプ | URI | |||||||||
| 関連識別子 | http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2430083/ | |||||||||
| 関連名称 | NIH Public Access | |||||||||
| 関連サイト | ||||||||||
| 識別子タイプ | URI | |||||||||
| 関連識別子 | http://www.ncbi.nlm.nih.gov/About/disclaimer.html | |||||||||
| 関連名称 | Copyright | |||||||||
| フォーマット | ||||||||||
| 内容記述タイプ | Other | |||||||||
| 内容記述 | application/pdf | |||||||||
| 著者版フラグ | ||||||||||
| 出版タイプ | AM | |||||||||
| 出版タイプResource | http://purl.org/coar/version/c_ab4af688f83e57aa | |||||||||
