An Analysis of the Replicator Dynamics for an Asymmetric Hawk-Dove Game
We analyze, using a dynamical systems approach, the replicator dynamics for the asymmetric Hawk-Dove game in which there is a set of four pure strategies with arbitrary payoffs. We give a full account of the equilibrium points and their stability and derive the Nash equilibria. We also give a detail...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2017-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2017/8781570 |
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| _version_ | 1832568428403097600 |
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| author | Ikjyot Singh Kohli Michael C. Haslam |
| author_facet | Ikjyot Singh Kohli Michael C. Haslam |
| author_sort | Ikjyot Singh Kohli |
| collection | DOAJ |
| description | We analyze, using a dynamical systems approach, the replicator dynamics for the asymmetric Hawk-Dove game in which there is a set of four pure strategies with arbitrary payoffs. We give a full account of the equilibrium points and their stability and derive the Nash equilibria. We also give a detailed account of the local bifurcations that the system exhibits based on choices of the typical Hawk-Dove parameters v and c. We also give details on the connections between the results found in this work and those of the standard two-strategy Hawk-Dove game. We conclude the paper with some examples of numerical simulations that further illustrate some global behaviours of the system. |
| format | Article |
| id | doaj-art-53172017e40743f8afe0aeaa28b9f90e |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-53172017e40743f8afe0aeaa28b9f90e2025-02-03T00:59:08ZengWileyInternational Journal of Differential Equations1687-96431687-96512017-01-01201710.1155/2017/87815708781570An Analysis of the Replicator Dynamics for an Asymmetric Hawk-Dove GameIkjyot Singh Kohli0Michael C. Haslam1Department of Mathematics and Statistics, York University, Toronto, ON, CanadaDepartment of Mathematics and Statistics, York University, Toronto, ON, CanadaWe analyze, using a dynamical systems approach, the replicator dynamics for the asymmetric Hawk-Dove game in which there is a set of four pure strategies with arbitrary payoffs. We give a full account of the equilibrium points and their stability and derive the Nash equilibria. We also give a detailed account of the local bifurcations that the system exhibits based on choices of the typical Hawk-Dove parameters v and c. We also give details on the connections between the results found in this work and those of the standard two-strategy Hawk-Dove game. We conclude the paper with some examples of numerical simulations that further illustrate some global behaviours of the system.http://dx.doi.org/10.1155/2017/8781570 |
| spellingShingle | Ikjyot Singh Kohli Michael C. Haslam An Analysis of the Replicator Dynamics for an Asymmetric Hawk-Dove Game International Journal of Differential Equations |
| title | An Analysis of the Replicator Dynamics for an Asymmetric Hawk-Dove Game |
| title_full | An Analysis of the Replicator Dynamics for an Asymmetric Hawk-Dove Game |
| title_fullStr | An Analysis of the Replicator Dynamics for an Asymmetric Hawk-Dove Game |
| title_full_unstemmed | An Analysis of the Replicator Dynamics for an Asymmetric Hawk-Dove Game |
| title_short | An Analysis of the Replicator Dynamics for an Asymmetric Hawk-Dove Game |
| title_sort | analysis of the replicator dynamics for an asymmetric hawk dove game |
| url | http://dx.doi.org/10.1155/2017/8781570 |
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