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Population dynamics and games of variable size
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Resumo(s)
This 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.
Descrição
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
Palavras-chave
Epidemic models Evolution of eusociality Fixation Game theory Speciation Statistics and Probability Modelling and Simulation General Biochemistry,Genetics and Molecular Biology General Immunology and Microbiology General Agricultural and Biological Sciences Applied Mathematics