Computing Nash equilibria and evolutionarily stable states of evolutionary games
Stability analysis is an important research direction in evolutionary game theory. Evolutionarily stable states have a close relationship with Nash equilibria of repeated games, which are characterized by the folk theorem. When applying the folk theorem, one needs to compute the minimax profile of t...
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| Format: | Article |
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Institute of Electrical and Electronics Engineers
2015
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| Online Access: | https://eprints.nottingham.ac.uk/30423/ |
| _version_ | 1848793982661820416 |
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| author | Li, Jiawei Kendall, Graham John, Robert |
| author_facet | Li, Jiawei Kendall, Graham John, Robert |
| author_sort | Li, Jiawei |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | Stability analysis is an important research direction in evolutionary game theory. Evolutionarily stable states have a close relationship with Nash equilibria of repeated games, which are characterized by the folk theorem. When applying the folk theorem, one needs to compute the minimax profile of the game in order to find Nash equilibria. Computing the minimax profile is an NP-hard problem. In this paper we investigate a new methodology to compute evolutionary stable states based on the level-k equilibrium, a new refinement of Nash equilibrium in repeated games. A level-k equilibrium is implemented by a group of players who adopt reactive strategies and who have no incentive to deviate from their strategies simultaneously. Computing the level-k equilibria is tractable because the minimax payoffs and strategies are not needed. As an application, this paper develops a tractable algorithm to compute the evolutionarily stable states and the Pareto front of n-player symmetric games. Three games, including the iterated prisoner’s dilemma, are analyzed by means of the proposed methodology. |
| first_indexed | 2025-11-14T19:08:57Z |
| format | Article |
| id | nottingham-30423 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:08:57Z |
| publishDate | 2015 |
| publisher | Institute of Electrical and Electronics Engineers |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-304232020-05-04T17:19:50Z https://eprints.nottingham.ac.uk/30423/ Computing Nash equilibria and evolutionarily stable states of evolutionary games Li, Jiawei Kendall, Graham John, Robert Stability analysis is an important research direction in evolutionary game theory. Evolutionarily stable states have a close relationship with Nash equilibria of repeated games, which are characterized by the folk theorem. When applying the folk theorem, one needs to compute the minimax profile of the game in order to find Nash equilibria. Computing the minimax profile is an NP-hard problem. In this paper we investigate a new methodology to compute evolutionary stable states based on the level-k equilibrium, a new refinement of Nash equilibrium in repeated games. A level-k equilibrium is implemented by a group of players who adopt reactive strategies and who have no incentive to deviate from their strategies simultaneously. Computing the level-k equilibria is tractable because the minimax payoffs and strategies are not needed. As an application, this paper develops a tractable algorithm to compute the evolutionarily stable states and the Pareto front of n-player symmetric games. Three games, including the iterated prisoner’s dilemma, are analyzed by means of the proposed methodology. Institute of Electrical and Electronics Engineers 2015-10-12 Article PeerReviewed Li, Jiawei, Kendall, Graham and John, Robert (2015) Computing Nash equilibria and evolutionarily stable states of evolutionary games. IEEE Transactions on Evolutionary Computation, 20 (3). pp. 460-469. ISSN 1089-778X Evolutionary game theory evolutionary stability folk theorem iterated prisoner’s dilemma Nash equilibrium http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=7296643 doi:10.1109/TEVC.2015.2490076 doi:10.1109/TEVC.2015.2490076 |
| spellingShingle | Evolutionary game theory evolutionary stability folk theorem iterated prisoner’s dilemma Nash equilibrium Li, Jiawei Kendall, Graham John, Robert Computing Nash equilibria and evolutionarily stable states of evolutionary games |
| title | Computing Nash equilibria and evolutionarily stable states of evolutionary games |
| title_full | Computing Nash equilibria and evolutionarily stable states of evolutionary games |
| title_fullStr | Computing Nash equilibria and evolutionarily stable states of evolutionary games |
| title_full_unstemmed | Computing Nash equilibria and evolutionarily stable states of evolutionary games |
| title_short | Computing Nash equilibria and evolutionarily stable states of evolutionary games |
| title_sort | computing nash equilibria and evolutionarily stable states of evolutionary games |
| topic | Evolutionary game theory evolutionary stability folk theorem iterated prisoner’s dilemma Nash equilibrium |
| url | https://eprints.nottingham.ac.uk/30423/ https://eprints.nottingham.ac.uk/30423/ https://eprints.nottingham.ac.uk/30423/ |