Population dynamics and games of variable size

Bibliographic Details
Main Author: Hansen, Matheus
Publication Date: 2024
Other Authors: Chalub, Fábio Augusto da Costa Carvalho
Format: Article
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: http://hdl.handle.net/10362/178635
Summary: Funding Information: FACCC and MH thanks C. Gokhale for suggesting applying the ideas from Chalub and Souza (2019) to a non-fixed number of players. This idea is at the origin of the present work. MH and FACCC are funded by national funds through the FCT \u2013 Funda\u00E7\u00E3o para a Ci\u00EAncia e a Tecnologia , I.P., under the scope of the projects UIDB/00297/2020 ( https://doi.org/10.54499/UIDB/00297/2020 ) and UIDP/00297/2020 ( https://doi.org/10.54499/UIDP/00297/2020 ) (Center for Mathematics and Applications). FACCC also acknowledges the support of the project Mathematical Modelling of Multi-scale Control Systems: applications to human diseases 2022.03091.PTDC ( https://doi.org/10.54499/2022.03091.PTDC ), supported by national funds (OE), through FCT/MCTES . (CoSysM3). MH and FACCC contributed equally to the development of the work\u2019s ideas, computational codes, data analysis, discussions, and writing of the final version of the manuscript. We also thank both referees for many suggestions that helped to improve this work, and Renata Ramalho (Universidade NOVA de Lisboa) for helping in the language editing of the manuscript. Funding Information: FACCC and MH thanks C. Gokhale for suggesting applying the ideas from Chalub and Souza (2019) to a non-fixed number of players. This idea is at the origin of the present work. MH and FACCC are funded by national funds through the FCT \u2013 Funda\u00E7\u00E3o para a Ci\u00EAncia e a Tecnologia, I.P. under the scope of the projects UIDB/00297/2020 ( https://doi.org/10.54499/UIDB/00297/2020) and UIDP/00297/2020 ( https://doi.org/10.54499/UIDP/00297/2020) (Center for Mathematics and Applications). FACCC also acknowledges the support of the project Mathematical Modelling of Multi-scale Control Systems: applications to human diseases 2022.03091.PTDC ( https://doi.org/10.54499/2022.03091.PTDC), supported by national funds (OE), through FCT/ MCTES. (CoSysM3). MH and FACCC contributed equally to the development of the work's ideas, computational codes, data analysis, discussions, and writing of the final version of the manuscript. We also thank both referees for many suggestions that helped to improve this work, and Renata Ramalho (Universidade NOVA de Lisboa) for helping in the language editing of the manuscript. Publisher Copyright: © 2024 The Authors
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spelling Population dynamics and games of variable sizeEpidemic modelsEvolution of eusocialityFixationGame theorySpeciationStatistics and ProbabilityModelling and SimulationBiochemistry, Genetics and Molecular Biology(all)Immunology and Microbiology(all)Agricultural and Biological Sciences(all)Applied MathematicsFunding Information: FACCC and MH thanks C. Gokhale for suggesting applying the ideas from Chalub and Souza (2019) to a non-fixed number of players. This idea is at the origin of the present work. MH and FACCC are funded by national funds through the FCT \u2013 Funda\u00E7\u00E3o para a Ci\u00EAncia e a Tecnologia , I.P., under the scope of the projects UIDB/00297/2020 ( https://doi.org/10.54499/UIDB/00297/2020 ) and UIDP/00297/2020 ( https://doi.org/10.54499/UIDP/00297/2020 ) (Center for Mathematics and Applications). FACCC also acknowledges the support of the project Mathematical Modelling of Multi-scale Control Systems: applications to human diseases 2022.03091.PTDC ( https://doi.org/10.54499/2022.03091.PTDC ), supported by national funds (OE), through FCT/MCTES . (CoSysM3). MH and FACCC contributed equally to the development of the work\u2019s ideas, computational codes, data analysis, discussions, and writing of the final version of the manuscript. We also thank both referees for many suggestions that helped to improve this work, and Renata Ramalho (Universidade NOVA de Lisboa) for helping in the language editing of the manuscript. Funding Information: FACCC and MH thanks C. Gokhale for suggesting applying the ideas from Chalub and Souza (2019) to a non-fixed number of players. This idea is at the origin of the present work. MH and FACCC are funded by national funds through the FCT \u2013 Funda\u00E7\u00E3o para a Ci\u00EAncia e a Tecnologia, I.P. under the scope of the projects UIDB/00297/2020 ( https://doi.org/10.54499/UIDB/00297/2020) and UIDP/00297/2020 ( https://doi.org/10.54499/UIDP/00297/2020) (Center for Mathematics and Applications). FACCC also acknowledges the support of the project Mathematical Modelling of Multi-scale Control Systems: applications to human diseases 2022.03091.PTDC ( https://doi.org/10.54499/2022.03091.PTDC), supported by national funds (OE), through FCT/ MCTES. (CoSysM3). MH and FACCC contributed equally to the development of the work's ideas, computational codes, data analysis, discussions, and writing of the final version of the manuscript. We also thank both referees for many suggestions that helped to improve this work, and Renata Ramalho (Universidade NOVA de Lisboa) for helping in the language editing of the manuscript. Publisher Copyright: © 2024 The AuthorsThis work introduces the concept of Variable Size Game Theory (VSGT), in which the number of players in a game is a strategic decision made by the players themselves. We start by discussing the main examples in game theory: dominance, coexistence, and coordination. We show that the same set of pay-offs can result in coordination-like or coexistence-like games depending on the strategic decision of each player type. We also solve an inverse problem to find a d-player game that reproduces the same fixation pattern of the VSGT. In the sequel, we consider a game involving prosocial and antisocial players, i.e., individuals who tend to play with large groups and small groups, respectively. In this game, a certain task should be performed, that will benefit one of the participants at the expense of the other players. We show that individuals able to gather large groups to perform the task may prevail, even if this task is costly, providing a possible scenario for the evolution of eusociality. The next example shows that different strategies regarding game size may lead to spontaneous separation of different types, a possible scenario for speciation without physical separation (sympatric speciation). In the last example, we generalize to three types of populations from the previous analysis and study compartmental epidemic models: in particular, we recast the SIRS model into the VSGT framework: Susceptibles play 2-player games, while Infectious and Removed play a 1-player game. The SIRS epidemic model is then obtained as the replicator equation of the VSGT. We finish with possible applications of VSGT to be addressed in the future.CMA - Centro de Matemática e AplicaçõesDM - Departamento de MatemáticaRUNHansen, MatheusChalub, Fábio Augusto da Costa Carvalho2025-02-07T21:13:53Z2024-07-212024-07-21T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10362/178635eng0022-5193PURE: 106546350https://doi.org/10.1016/j.jtbi.2024.111842info:eu-repo/semantics/openAccessreponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2025-02-24T01:40:37Zoai:run.unl.pt:10362/178635Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T19:46:57.092278Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
dc.title.none.fl_str_mv Population dynamics and games of variable size
title Population dynamics and games of variable size
spellingShingle Population dynamics and games of variable size
Hansen, Matheus
Epidemic models
Evolution of eusociality
Fixation
Game theory
Speciation
Statistics and Probability
Modelling and Simulation
Biochemistry, Genetics and Molecular Biology(all)
Immunology and Microbiology(all)
Agricultural and Biological Sciences(all)
Applied Mathematics
title_short Population dynamics and games of variable size
title_full Population dynamics and games of variable size
title_fullStr Population dynamics and games of variable size
title_full_unstemmed Population dynamics and games of variable size
title_sort Population dynamics and games of variable size
author Hansen, Matheus
author_facet Hansen, Matheus
Chalub, Fábio Augusto da Costa Carvalho
author_role author
author2 Chalub, Fábio Augusto da Costa Carvalho
author2_role author
dc.contributor.none.fl_str_mv CMA - Centro de Matemática e Aplicações
DM - Departamento de Matemática
RUN
dc.contributor.author.fl_str_mv Hansen, Matheus
Chalub, Fábio Augusto da Costa Carvalho
dc.subject.por.fl_str_mv Epidemic models
Evolution of eusociality
Fixation
Game theory
Speciation
Statistics and Probability
Modelling and Simulation
Biochemistry, Genetics and Molecular Biology(all)
Immunology and Microbiology(all)
Agricultural and Biological Sciences(all)
Applied Mathematics
topic Epidemic models
Evolution of eusociality
Fixation
Game theory
Speciation
Statistics and Probability
Modelling and Simulation
Biochemistry, Genetics and Molecular Biology(all)
Immunology and Microbiology(all)
Agricultural and Biological Sciences(all)
Applied Mathematics
description Funding Information: FACCC and MH thanks C. Gokhale for suggesting applying the ideas from Chalub and Souza (2019) to a non-fixed number of players. This idea is at the origin of the present work. MH and FACCC are funded by national funds through the FCT \u2013 Funda\u00E7\u00E3o para a Ci\u00EAncia e a Tecnologia , I.P., under the scope of the projects UIDB/00297/2020 ( https://doi.org/10.54499/UIDB/00297/2020 ) and UIDP/00297/2020 ( https://doi.org/10.54499/UIDP/00297/2020 ) (Center for Mathematics and Applications). FACCC also acknowledges the support of the project Mathematical Modelling of Multi-scale Control Systems: applications to human diseases 2022.03091.PTDC ( https://doi.org/10.54499/2022.03091.PTDC ), supported by national funds (OE), through FCT/MCTES . (CoSysM3). MH and FACCC contributed equally to the development of the work\u2019s ideas, computational codes, data analysis, discussions, and writing of the final version of the manuscript. We also thank both referees for many suggestions that helped to improve this work, and Renata Ramalho (Universidade NOVA de Lisboa) for helping in the language editing of the manuscript. Funding Information: FACCC and MH thanks C. Gokhale for suggesting applying the ideas from Chalub and Souza (2019) to a non-fixed number of players. This idea is at the origin of the present work. MH and FACCC are funded by national funds through the FCT \u2013 Funda\u00E7\u00E3o para a Ci\u00EAncia e a Tecnologia, I.P. under the scope of the projects UIDB/00297/2020 ( https://doi.org/10.54499/UIDB/00297/2020) and UIDP/00297/2020 ( https://doi.org/10.54499/UIDP/00297/2020) (Center for Mathematics and Applications). FACCC also acknowledges the support of the project Mathematical Modelling of Multi-scale Control Systems: applications to human diseases 2022.03091.PTDC ( https://doi.org/10.54499/2022.03091.PTDC), supported by national funds (OE), through FCT/ MCTES. (CoSysM3). MH and FACCC contributed equally to the development of the work's ideas, computational codes, data analysis, discussions, and writing of the final version of the manuscript. We also thank both referees for many suggestions that helped to improve this work, and Renata Ramalho (Universidade NOVA de Lisboa) for helping in the language editing of the manuscript. Publisher Copyright: © 2024 The Authors
publishDate 2024
dc.date.none.fl_str_mv 2024-07-21
2024-07-21T00:00:00Z
2025-02-07T21:13:53Z
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