Applicability of the Analytical Solution to N-Person Social Dilemma Games
The purpose of this study is to present an analysis of the applicability of an analytical solution to the N−person social dilemma game. Such solution has been earlier developed for Pavlovian agents in a cellular automaton environment with linear payoff functions and also been verified using agent ba...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2018-05-01
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| Series: | Frontiers in Applied Mathematics and Statistics |
| Subjects: | |
| Online Access: | https://www.frontiersin.org/article/10.3389/fams.2018.00015/full |
| _version_ | 1811197511496368128 |
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| author | Ugo Merlone Daren R. Sandbank Ferenc Szidarovszky |
| author_facet | Ugo Merlone Daren R. Sandbank Ferenc Szidarovszky |
| author_sort | Ugo Merlone |
| collection | DOAJ |
| description | The purpose of this study is to present an analysis of the applicability of an analytical solution to the N−person social dilemma game. Such solution has been earlier developed for Pavlovian agents in a cellular automaton environment with linear payoff functions and also been verified using agent based simulation. However, no discussion has been offered for the applicability of this result in all Prisoners' Dilemma game scenarios or in other N−person social dilemma games such as Chicken or Stag Hunt. In this paper it is shown that the analytical solution works in all social games where the linear payoff functions are such that each agent's cooperating probability fluctuates around the analytical solution without cooperating or defecting with certainty. The social game regions where this determination holds are explored by varying payoff function parameters. It is found by both simulation and a special method that the analytical solution applies best in Chicken when the payoff parameter S is slightly negative and then the analytical solution slowly degrades as S becomes more negative. It turns out that the analytical solution is only a good estimate for Prisoners' Dilemma games and again becomes worse as S becomes more negative. A sensitivity analysis is performed to determine the impact of different initial cooperating probabilities, learning factors, and neighborhood size. |
| first_indexed | 2024-04-12T01:16:08Z |
| format | Article |
| id | doaj.art-008bfc648cc04586b7914a82d4d10a90 |
| institution | Directory Open Access Journal |
| issn | 2297-4687 |
| language | English |
| last_indexed | 2024-04-12T01:16:08Z |
| publishDate | 2018-05-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Applied Mathematics and Statistics |
| spelling | doaj.art-008bfc648cc04586b7914a82d4d10a902022-12-22T03:53:57ZengFrontiers Media S.A.Frontiers in Applied Mathematics and Statistics2297-46872018-05-01410.3389/fams.2018.00015344624Applicability of the Analytical Solution to N-Person Social Dilemma GamesUgo Merlone0Daren R. Sandbank1Ferenc Szidarovszky2Department of Psychology, Center for Logic, Language, and Cognition, University of Torino, Turin, ItalySystems and Industrial Engineering Department, University of Arizona, Tucson, AZ, United StatesDepartment of Applied Mathematics, University of Pécs, Pécs, HungaryThe purpose of this study is to present an analysis of the applicability of an analytical solution to the N−person social dilemma game. Such solution has been earlier developed for Pavlovian agents in a cellular automaton environment with linear payoff functions and also been verified using agent based simulation. However, no discussion has been offered for the applicability of this result in all Prisoners' Dilemma game scenarios or in other N−person social dilemma games such as Chicken or Stag Hunt. In this paper it is shown that the analytical solution works in all social games where the linear payoff functions are such that each agent's cooperating probability fluctuates around the analytical solution without cooperating or defecting with certainty. The social game regions where this determination holds are explored by varying payoff function parameters. It is found by both simulation and a special method that the analytical solution applies best in Chicken when the payoff parameter S is slightly negative and then the analytical solution slowly degrades as S becomes more negative. It turns out that the analytical solution is only a good estimate for Prisoners' Dilemma games and again becomes worse as S becomes more negative. A sensitivity analysis is performed to determine the impact of different initial cooperating probabilities, learning factors, and neighborhood size.https://www.frontiersin.org/article/10.3389/fams.2018.00015/fullagent-based simulationN−person gamescellular automatonpavlovian agentskinnerian agentequilibrium |
| spellingShingle | Ugo Merlone Daren R. Sandbank Ferenc Szidarovszky Applicability of the Analytical Solution to N-Person Social Dilemma Games Frontiers in Applied Mathematics and Statistics agent-based simulation N−person games cellular automaton pavlovian agent skinnerian agent equilibrium |
| title | Applicability of the Analytical Solution to N-Person Social Dilemma Games |
| title_full | Applicability of the Analytical Solution to N-Person Social Dilemma Games |
| title_fullStr | Applicability of the Analytical Solution to N-Person Social Dilemma Games |
| title_full_unstemmed | Applicability of the Analytical Solution to N-Person Social Dilemma Games |
| title_short | Applicability of the Analytical Solution to N-Person Social Dilemma Games |
| title_sort | applicability of the analytical solution to n person social dilemma games |
| topic | agent-based simulation N−person games cellular automaton pavlovian agent skinnerian agent equilibrium |
| url | https://www.frontiersin.org/article/10.3389/fams.2018.00015/full |
| work_keys_str_mv | AT ugomerlone applicabilityoftheanalyticalsolutiontonpersonsocialdilemmagames AT darenrsandbank applicabilityoftheanalyticalsolutiontonpersonsocialdilemmagames AT ferencszidarovszky applicabilityoftheanalyticalsolutiontonpersonsocialdilemmagames |