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Roy S, Nag Chowdhury S, Kundu S, Sar GK, Banerjee J, Rakshit B, Mali PC, Perc M, Ghosh D. Time delays shape the eco-evolutionary dynamics of cooperation. Sci Rep 2023; 13:14331. [PMID: 37653103 PMCID: PMC10471784 DOI: 10.1038/s41598-023-41519-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/16/2023] [Accepted: 08/28/2023] [Indexed: 09/02/2023] Open
Abstract
We study the intricate interplay between ecological and evolutionary processes through the lens of the prisoner's dilemma game. But while previous studies on cooperation amongst selfish individuals often assume instantaneous interactions, we take into consideration delays to investigate how these might affect the causes underlying prosocial behavior. Through analytical calculations and numerical simulations, we demonstrate that delays can lead to oscillations, and by incorporating also the ecological variable of altruistic free space and the evolutionary strategy of punishment, we explore how these factors impact population and community dynamics. Depending on the parameter values and the initial fraction of each strategy, the studied eco-evolutionary model can mimic a cyclic dominance system and even exhibit chaotic behavior, thereby highlighting the importance of complex dynamics for the effective management and conservation of ecological communities. Our research thus contributes to the broader understanding of group decision-making and the emergence of moral behavior in multidimensional social systems.
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Affiliation(s)
- Sourav Roy
- Department of Mathematics, Jadavpur University, Kolkata, 700032, India
| | - Sayantan Nag Chowdhury
- Department of Environmental Science and Policy, University of California, Davis, CA, 95616, USA
| | - Srilena Kundu
- Department of Ecology & Evolution, University of Chicago, Chicago, IL, 60637, USA
| | - Gourab Kumar Sar
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata, 700108, India
| | - Jeet Banerjee
- BYJU'S, Think & Learn Pvt. Ltd., IBC Knowledge Park, 4/1 Bannerghatta Main Road, Bangalore, 560029, India
| | - Biswambhar Rakshit
- Department of Mathematics, Amrita School of Physical Sciences, Amrita Vishwa Vidyapeetham, Coimbatore, 641112, India
| | | | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000, Maribor, Slovenia
- Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 404332, Taiwan
- Alma Mater Europaea, Slovenska ulica 17, 2000, Maribor, Slovenia
- Complexity Science Hub Vienna, Josefstädterstraße 39, 1080, Vienna, Austria
- Department of Physics, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul, Republic of Korea
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata, 700108, India.
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Roy S, Nag Chowdhury S, Mali PC, Perc M, Ghosh D. Eco-evolutionary dynamics of multigames with mutations. PLoS One 2022; 17:e0272719. [PMID: 35944035 PMCID: PMC9362954 DOI: 10.1371/journal.pone.0272719] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2022] [Accepted: 07/25/2022] [Indexed: 11/30/2022] Open
Abstract
Most environments favor defection over cooperation due to natural selection. Nonetheless, the emergence of cooperation is omnipresent in many biological, social, and economic systems, quite contrary to the well-celebrated Darwinian theory of evolution. Much research has been devoted to better understanding how and why cooperation persists among self-interested individuals despite their competition for limited resources. Here we go beyond a single social dilemma since individuals usually encounter various social challenges. In particular, we propose and study a mathematical model incorporating both the prisoner’s dilemma and the snowdrift game. We further extend this model by considering ecological signatures like mutation and selfless one-sided contribution of altruist free space. The nonlinear evolutionary dynamics that results from these upgrades offer a broader range of equilibrium outcomes, and it also often favors cooperation over defection. With the help of analytical and numerical calculations, our theoretical model sheds light on the mechanisms that maintain biodiversity, and it helps to explain the evolution of social order in human societies.
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Affiliation(s)
- Sourav Roy
- Department of Mathematics, Jadavpur University, Kolkata, West Bengal, India
| | - Sayantan Nag Chowdhury
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata, West Bengal, India
| | | | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Maribor, Slovenia
- Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
- Alma Mater Europaea, Maribor, Slovenia
- Complexity Science Hub Vienna, Vienna, Austria
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata, West Bengal, India
- * E-mail:
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Chowdhury SN, Kundu S, Perc M, Ghosh D. Complex evolutionary dynamics due to punishment and free space in ecological multigames. Proc Math Phys Eng Sci 2021. [DOI: 10.1098/rspa.2021.0397] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Abstract
The concurrence of ecological and evolutionary processes often arises as an integral part of various biological and social systems. We here study eco-evolutionary dynamics by adopting two paradigmatic metaphors of social dilemmas with contrasting outcomes. We use the Prisoner’s Dilemma and Snowdrift games as the backbone of the proposed mathematical model. Since cooperation is a costly proposition in the face of the Darwinian theory of evolution, we go beyond the traditional framework by introducing punishment as an additional strategy. Punishers bare an additional cost from their own resources to try and discourage or prohibit free-riding from selfish defectors. Our model also incorporates the ecological signature of free space, which has an altruistic-like impact because it allows others to replicate and potentially thrive. We show that the consideration of these factors has broad implications for better understanding the emergent complex evolutionary dynamics. In particular, we report the simultaneous presence of different subpopulations through the spontaneous emergence of cyclic dominance, and we determine various stationary points using traditional game-theoretic concepts and stability analysis.
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Affiliation(s)
- Sayantan Nag Chowdhury
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Srilena Kundu
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000 Maribor, Slovenia
- Alma Mater Europaea, Slovenska ulica, 17, 2000 Maribor, Slovenia
- Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
- Complexity Science Hub Vienna, Josefstädterstraße 39, 1080 Vienna, Austria
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
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Nag Chowdhury S, Kundu S, Banerjee J, Perc M, Ghosh D. Eco-evolutionary dynamics of cooperation in the presence of policing. J Theor Biol 2021; 518:110606. [PMID: 33582077 DOI: 10.1016/j.jtbi.2021.110606] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2020] [Revised: 12/31/2020] [Accepted: 01/24/2021] [Indexed: 11/15/2022]
Abstract
Ecology and evolution are inherently linked, and studying a mathematical model that considers both holds promise of insightful discoveries related to the dynamics of cooperation. In the present article, we use the prisoner's dilemma (PD) game as a basis for long-term apprehension of the essential social dilemma related to cooperation among unrelated individuals. We upgrade the contemporary PD game with an inclusion of evolution-induced act of punishment as a third competing strategy in addition to the traditional cooperators and defectors. In a population structure, the abundance of ecologically-viable free space often regulates the reproductive opportunities of the constituents. Hence, additionally, we consider the availability of free space as an ecological footprint, thus arriving at a simple eco-evolutionary model, which displays fascinating complex dynamics. As possible outcomes, we report the individual dominance of cooperators and defectors as well as a plethora of mixed states, where different strategies coexist followed by maintaining the diversity in a socio-ecological framework. These states can either be steady or oscillating, whereby oscillations are sustained by cyclic dominance among different combinations of cooperators, defectors, and punishers. We also observe a novel route to cyclic dominance where cooperators, punishers, and defectors enter a coexistence via an inverse Hopf bifurcation that is followed by an inverse period doubling route.
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Affiliation(s)
- Sayantan Nag Chowdhury
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Srilena Kundu
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Jeet Banerjee
- BYJU'S, Think & Learn Pvt. Ltd., IBC Knowledge Park, 4/1 Bannerghatta Main Road, Bangalore 560029, India.
| | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000 Maribor, Slovenia; Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan; Complexity Science Hub Vienna, Josefstädterstraße 39, 1080 Vienna, Austria.
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India.
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Braha D. Patterns of ties in problem-solving networks and their dynamic properties. Sci Rep 2020; 10:18137. [PMID: 33093552 PMCID: PMC7582982 DOI: 10.1038/s41598-020-75221-3] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2020] [Accepted: 10/13/2020] [Indexed: 11/09/2022] Open
Abstract
Understanding the functions carried out by network subgraphs is important to revealing the organizing principles of diverse complex networks. Here, we study this question in the context of collaborative problem-solving, which is central to a variety of domains from engineering and medicine to economics and social planning. We analyze the frequency of all three- and four-node subgraphs in diverse real problem-solving networks. The results reveal a strong association between a dynamic property of network subgraphs-synchronizability-and the frequency and significance of these subgraphs in problem-solving networks. In particular, we show that highly-synchronizable subgraphs are overrepresented in the networks, while poorly-synchronizable subgraphs are underrepresented, suggesting that dynamical properties affect their prevalence, and thus the global structure of networks. We propose the possibility that selective pressures that favor more synchronizable subgraphs could account for their abundance in problem-solving networks. The empirical results also show that unrelated problem-solving networks display very similar local network structure, implying that network subgraphs could represent organizational routines that enable better coordination and control of problem-solving activities. The findings could also have potential implications in understanding the functionality of network subgraphs in other information-processing networks, including biological and social networks.
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Affiliation(s)
- Dan Braha
- New England Complex Systems Institute, Cambridge, MA, 02139, USA.
- University of Massachusetts Dartmouth, Dartmouth, MA, 02747-2300, USA.
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Cooperation on Interdependent Networks by Means of Migration and Stochastic Imitation. ENTROPY 2020; 22:e22040485. [PMID: 33286258 PMCID: PMC7516967 DOI: 10.3390/e22040485] [Citation(s) in RCA: 34] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/19/2020] [Revised: 04/12/2020] [Accepted: 04/21/2020] [Indexed: 11/17/2022]
Abstract
Evolutionary game theory in the realm of network science appeals to a lot of research communities, as it constitutes a popular theoretical framework for studying the evolution of cooperation in social dilemmas. Recent research has shown that cooperation is markedly more resistant in interdependent networks, where traditional network reciprocity can be further enhanced due to various forms of interdependence between different network layers. However, the role of mobility in interdependent networks is yet to gain its well-deserved attention. Here we consider an interdependent network model, where individuals in each layer follow different evolutionary games, and where each player is considered as a mobile agent that can move locally inside its own layer to improve its fitness. Probabilistically, we also consider an imitation possibility from a neighbor on the other layer. We show that, by considering migration and stochastic imitation, further fascinating gateways to cooperation on interdependent networks can be observed. Notably, cooperation can be promoted on both layers, even if cooperation without interdependence would be improbable on one of the layers due to adverse conditions. Our results provide a rationale for engineering better social systems at the interface of networks and human decision making under testing dilemmas.
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