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Zimmaro F, Miranda M, Fernández JMR, Moreno López JA, Reddel M, Widler V, Antonioni A, Han TA. Emergence of cooperation in the one-shot Prisoner's dilemma through Discriminatory and Samaritan AIs. J R Soc Interface 2024; 21:20240212. [PMID: 39317332 DOI: 10.1098/rsif.2024.0212] [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: 03/28/2024] [Revised: 06/10/2024] [Accepted: 07/11/2024] [Indexed: 09/26/2024] Open
Abstract
As artificial intelligence (AI) systems are increasingly embedded in our lives, their presence leads to interactions that shape our behaviour, decision-making and social interactions. Existing theoretical research on the emergence and stability of cooperation, particularly in the context of social dilemmas, has primarily focused on human-to-human interactions, overlooking the unique dynamics triggered by the presence of AI. Resorting to methods from evolutionary game theory, we study how different forms of AI can influence cooperation in a population of human-like agents playing the one-shot Prisoner's dilemma game. We found that Samaritan AI agents who help everyone unconditionally, including defectors, can promote higher levels of cooperation in humans than Discriminatory AI that only helps those considered worthy/cooperative, especially in slow-moving societies where change based on payoff difference is moderate (small intensities of selection). Only in fast-moving societies (high intensities of selection), Discriminatory AIs promote higher levels of cooperation than Samaritan AIs. Furthermore, when it is possible to identify whether a co-player is a human or an AI, we found that cooperation is enhanced when human-like agents disregard AI performance. Our findings provide novel insights into the design and implementation of context-dependent AI systems for addressing social dilemmas.
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Affiliation(s)
- Filippo Zimmaro
- Department of Mathematics, University of Bologna , Bologna, Italy
- Department of Computer Science, University of Pisa , Pisa, Italy
| | - Manuel Miranda
- Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB) , Palma de Mallorca, Spain
| | | | - Jesús A Moreno López
- Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB) , Palma de Mallorca, Spain
| | - Max Reddel
- International Center for Future Generations , Brussels, Belgium
| | - Valeria Widler
- Institut für Mathematik, Freie Universität Berlin , Berlin, Germany
| | - Alberto Antonioni
- GISC, Department of Mathematics, Carlos III University of Madrid , Leganés, Spain
| | - The Anh Han
- School of Computing, Engineering and Digital Technologies, Teesside University , Middlesbrough, UK
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2
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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: 2] [Impact Index Per Article: 2.0] [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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Nag Chowdhury S, Banerjee J, Perc M, Ghosh D. Eco-evolutionary cyclic dominance among predators, prey, and parasites. J Theor Biol 2023; 564:111446. [PMID: 36868345 DOI: 10.1016/j.jtbi.2023.111446] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2022] [Revised: 02/24/2023] [Accepted: 02/25/2023] [Indexed: 03/05/2023]
Abstract
Predator-prey interactions are one of ecology's central research themes, but with many interdisciplinary implications across the social and natural sciences. Here we consider an often-overlooked species in these interactions, namely parasites. We first show that a simple predator-prey-parasite model, inspired by the classical Lotka-Volterra equations, fails to produce a stable coexistence of all three species, thus failing to provide a biologically realistic outcome. To improve this, we introduce free space as a relevant eco-evolutionary component in a new mathematical model that uses a game-theoretical payoff matrix to describe a more realistic setup. We then show that the consideration of free space stabilizes the dynamics by means of cyclic dominance that emerges between the three species. We determine the parameter regions of coexistence as well as the types of bifurcations leading to it by means of analytical derivations as well as by means of numerical simulations. We conclude that the consideration of free space as a finite resource reveals the limits of biodiversity in predator-prey-parasite interactions, and it may also help us in the determination of factors that promote a healthy biota.
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Affiliation(s)
- Sayantan Nag Chowdhury
- Department of Environmental Science and Policy, University of California, Davis, CA 95616, USA
| | - 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; 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; 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, 203 B.T. Road, Kolkata 700108, India.
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Nag Chowdhury S, Rakshit S, Hens C, Ghosh D. Interlayer antisynchronization in degree-biased duplex networks. Phys Rev E 2023; 107:034313. [PMID: 37073037 DOI: 10.1103/physreve.107.034313] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2022] [Accepted: 03/09/2023] [Indexed: 04/20/2023]
Abstract
With synchronization being one of nature's most ubiquitous collective behaviors, the field of network synchronization has experienced tremendous growth, leading to significant theoretical developments. However, most previous studies consider uniform connection weights and undirected networks with positive coupling. In the present article, we incorporate the asymmetry in a two-layer multiplex network by assigning the ratio of the adjacent nodes' degrees as the weights to the intralayer edges. Despite the presence of degree-biased weighting mechanism and attractive-repulsive coupling strengths, we are able to find the necessary conditions for intralayer synchronization and interlayer antisynchronization and test whether these two macroscopic states can withstand demultiplexing in a network. During the occurrence of these two states, we analytically calculate the oscillator's amplitude. In addition to deriving the local stability conditions for interlayer antisynchronization via the master stability function approach, we also construct a suitable Lyapunov function to determine a sufficient condition for global stability. We provide numerical evidence to show the necessity of negative interlayer coupling strength for the occurrence of antisynchronization, and such repulsive interlayer coupling coefficients cannot destroy intralayer synchronization.
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Affiliation(s)
- Sayantan Nag Chowdhury
- Department of Environmental Science and Policy, University of California, Davis, California 95616, USA
- Technology Innovation Hub (TIH), IDEAS (Institute of Data Engineering Analytics and Science Foundation), Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Sarbendu Rakshit
- Department of Mechanical Engineering, University of California, Riverside, California 92521, USA
| | - Chittaranjan Hens
- Center for Computational Natural Sciences and Bioinformatics, International Institute of Information Technology, Gachibowli, Hyderabad 500032, India
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
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Chatterjee S, Nag Chowdhury S, Ghosh D, Hens C. Controlling species densities in structurally perturbed intransitive cycles with higher-order interactions. CHAOS (WOODBURY, N.Y.) 2022; 32:103122. [PMID: 36319275 DOI: 10.1063/5.0102599] [Citation(s) in RCA: 13] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/10/2022] [Accepted: 09/14/2022] [Indexed: 06/16/2023]
Abstract
The persistence of biodiversity of species is a challenging proposition in ecological communities in the face of Darwinian selection. The present article investigates beyond the pairwise competitive interactions and provides a novel perspective for understanding the influence of higher-order interactions on the evolution of social phenotypes. Our simple model yields a prosperous outlook to demonstrate the impact of perturbations on intransitive competitive higher-order interactions. Using a mathematical technique, we show how alone the perturbed interaction network can quickly determine the coexistence equilibrium of competing species instead of solving a large system of ordinary differential equations. It is possible to split the system into multiple feasible cluster states depending on the number of perturbations. Our analysis also reveals that the ratio between the unperturbed and perturbed species is inversely proportional to the amount of employed perturbation. Our results suggest that nonlinear dynamical systems and interaction topologies can be interplayed to comprehend species' coexistence under adverse conditions. Particularly, our findings signify that less competition between two species increases their abundance and outperforms others.
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Affiliation(s)
- Sourin Chatterjee
- Department of Mathematics and Statistics, Indian Institute of Science Education and Research, Kolkata, West Bengal 741246, India
| | - Sayantan Nag Chowdhury
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Chittaranjan Hens
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, 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: 8] [Impact Index Per Article: 4.0] [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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7
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Liu J, Peng Y, Zhu P, Yu Y. The Polarization of the Coupling Strength of Interdependent Networks Stimulates Cooperation. ENTROPY (BASEL, SWITZERLAND) 2022; 24:694. [PMID: 35626577 PMCID: PMC9141804 DOI: 10.3390/e24050694] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/15/2022] [Revised: 04/27/2022] [Accepted: 05/09/2022] [Indexed: 11/16/2022]
Abstract
We introduce a mixed network coupling mechanism and study its effects on how cooperation evolves in interdependent networks. This mechanism allows some players (conservative-driven) to establish a fixed-strength coupling, while other players (radical-driven) adjust their coupling strength through the evolution of strategy. By means of numerical simulation, a hump-like relationship between the level of cooperation and conservative participant density is revealed. Interestingly, interspecies interactions stimulate polarization of the coupling strength of radical-driven players, promoting cooperation between two types of players. We thus demonstrate that a simple mixed network coupling mechanism substantially expands the scope of cooperation among structured populations.
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Affiliation(s)
- Jinzhuo Liu
- School of Software, Yunnan University, Kunming 650504, China
- School of Artificial Intelligence, Optics and Electronics (iOPEN), Northwestern Polytechnical University, Xi'an 710072, China
| | - Yunchen Peng
- School of Software, Yunnan University, Kunming 650504, China
| | - Peican Zhu
- School of Artificial Intelligence, Optics and Electronics (iOPEN), Northwestern Polytechnical University, Xi'an 710072, China
| | - Yong Yu
- School of Software, Yunnan University, Kunming 650504, China
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8
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Amaral MA, de Oliveira MM. Criticality and Griffiths phases in random games with quenched disorder. Phys Rev E 2022; 104:064102. [PMID: 35030882 DOI: 10.1103/physreve.104.064102] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2021] [Accepted: 11/22/2021] [Indexed: 11/07/2022]
Abstract
The perceived risk and reward for a given situation can vary depending on resource availability, accumulated wealth, and other extrinsic factors such as individual backgrounds. Based on this general aspect of everyday life, here we use evolutionary game theory to model a scenario with randomly perturbed payoffs in a prisoner's dilemma game. The perception diversity is modeled by adding a zero-average random noise in the payoff entries and a Monte Carlo simulation is used to obtain the population dynamics. This payoff heterogeneity can promote and maintain cooperation in a competitive scenario where only defectors would survive otherwise. In this work, we give a step further, understanding the role of heterogeneity by investigating the effects of quenched disorder in the critical properties of random games. We observe that payoff fluctuations induce a very slow dynamic, making the cooperation decay behave as power laws with varying exponents, instead of the usual exponential decay after the critical point, showing the emergence of a Griffiths phase. We also find a symmetric Griffiths phase near the defector's extinction point when fluctuations are present, indicating that Griffiths phases may be frequent in evolutionary game dynamics and play a role in the coexistence of different strategies.
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Affiliation(s)
- Marco A Amaral
- Instituto de Artes, Humanidades e Ciências, Universidade Federal do Sul da Bahia, Teixeira de Freitas-BA, 45996-108 Brazil
| | - Marcelo M de Oliveira
- Departamento de Física e Matemática, Universidade Federal de São João del Rei, Ouro Branco-MG, 36420-000 Brazil
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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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10
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Chowdhury SN, Rakshit S, Buldú JM, Ghosh D, Hens C. Antiphase synchronization in multiplex networks with attractive and repulsive interactions. Phys Rev E 2021; 103:032310. [PMID: 33862752 DOI: 10.1103/physreve.103.032310] [Citation(s) in RCA: 18] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2020] [Accepted: 02/16/2021] [Indexed: 06/12/2023]
Abstract
A series of recent publications, within the framework of network science, have focused on the coexistence of mixed attractive and repulsive (excitatory and inhibitory) interactions among the units within the same system, motivated by the analogies with spin glasses as well as to neural networks, or ecological systems. However, most of these investigations have been restricted to single layer networks, requiring further analysis of the complex dynamics and particular equilibrium states that emerge in multilayer configurations. This article investigates the synchronization properties of dynamical systems connected through multiplex architectures in the presence of attractive intralayer and repulsive interlayer connections. This setting enables the emergence of antisynchronization, i.e., intralayer synchronization coexisting with antiphase dynamics between coupled systems of different layers. We demonstrate the existence of a transition from interlayer antisynchronization to antiphase synchrony in any connected bipartite multiplex architecture when the repulsive coupling is introduced through any spanning tree of a single layer. We identify, analytically, the required graph topologies for interlayer antisynchronization and its interplay with intralayer and antiphase synchronization. Next, we analytically derive the invariance of intralayer synchronization manifold and calculate the attractor size of each oscillator exhibiting interlayer antisynchronization together with intralayer synchronization. The necessary conditions for the existence of interlayer antisynchronization along with intralayer synchronization are given and numerically validated by considering Stuart-Landau oscillators. Finally, we also analytically derive the local stability condition of the interlayer antisynchronization state using the master stability function approach.
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Affiliation(s)
- Sayantan Nag Chowdhury
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata-700108, India
| | - Sarbendu Rakshit
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata-700108, India
| | - Javier M Buldú
- Laboratory of Biological Networks, Center for Biomedical Technology-UPM, Madrid 28223, Spain
- Complex Systems Group and GISC, Universidad Rey Juan Carlos, Móstoles 28933, Spain
- Unmanned Systems Research Institute, Northwestern Polytechnical University, Xi'an 710072, China
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata-700108, India
| | - Chittaranjan Hens
- 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: 6] [Impact Index Per Article: 2.0] [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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Abstract
The combination of complex networks and game theory is one of the most suitable ways to describe the evolutionary laws of various complex systems. In order to explore the evolution of group cooperation in multiple social dilemmas, a model of a group game with a double-layer network is proposed here. Firstly, to simulate a multiplayer game under multiple identities, we combine a double-layer network and public goods game. Secondly, in order to make an individual’s strategy selection process more in line with a practical context, a new strategy learning method that incorporates individual attributes is designed here, referred to as a “public goods game with selection preferences” (PGG-SP), which makes strategic choices that are more humane and diversified. Finally, a co-evolution mechanism for strategies and topologies is introduced based on the double-layer network, which effectively explains the dynamic game process in real life. To verify the role of multiple double-layer networks with a PGG-SP, four types of double-layer networks are applied in this paper. In addition, the corresponding game results are compared between single-layer, double-layer, static, and dynamic networks. Accordingly, the results show that double-layer networks can facilitate cooperation in group games.
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Dixit S, Nag Chowdhury S, Prasad A, Ghosh D, Shrimali MD. Emergent rhythms in coupled nonlinear oscillators due to dynamic interactions. CHAOS (WOODBURY, N.Y.) 2021; 31:011105. [PMID: 33754786 DOI: 10.1063/5.0039879] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/07/2020] [Accepted: 12/29/2020] [Indexed: 06/12/2023]
Abstract
The role of a new form of dynamic interaction is explored in a network of generic identical oscillators. The proposed design of dynamic coupling facilitates the onset of a plethora of asymptotic states including synchronous states, amplitude death states, oscillation death states, a mixed state (complete synchronized cluster and small amplitude desynchronized domain), and bistable states (coexistence of two attractors). The dynamical transitions from the oscillatory to the death state are characterized using an average temporal interaction approximation, which agrees with the numerical results in temporal interaction. A first-order phase transition behavior may change into a second-order transition in spatial dynamic interaction solely depending on the choice of initial conditions in the bistable regime. However, this possible abrupt first-order like transition is completely non-existent in the case of temporal dynamic interaction. Besides the study on periodic Stuart-Landau systems, we present results for the paradigmatic chaotic model of Rössler oscillators and the MacArthur ecological model.
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Affiliation(s)
- Shiva Dixit
- Department of Physics, Central University of Rajasthan, NH-8,Bandar Sindri, Ajmer 305 817, India
| | - Sayantan Nag Chowdhury
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Awadhesh Prasad
- Department of Physics and Astrophysics, University of Delhi, Delhi 110007, India
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Manish Dev Shrimali
- Department of Physics, Central University of Rajasthan, NH-8,Bandar Sindri, Ajmer 305 817, 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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Amaral MA, Javarone MA. Strategy equilibrium in dilemma games with off-diagonal payoff perturbations. Phys Rev E 2020; 101:062309. [PMID: 32688499 DOI: 10.1103/physreve.101.062309] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2020] [Accepted: 06/03/2020] [Indexed: 06/11/2023]
Abstract
We analyze the strategy equilibrium of dilemma games considering a payoff matrix affected by small and random perturbations on the off-diagonal. Notably, a recent work [Proc. R. Soc. A 476, 20200116 (2020)1364-502110.1098/rspa.2020.0116] reported that while cooperation is sustained by perturbations acting on the main diagonal, a less clear scenario emerges when perturbations act on the off-diagonal. Thus, the second case represents the core of this investigation, aimed at completing the description of the effects that payoff perturbations have on the dynamics of evolutionary games. Our results, achieved by analyzing the proposed model under a variety of configurations as different update rules, suggest that off-diagonal perturbations actually constitute a nontrivial form of noise. In particular, the most interesting effects are detected near the phase transition, as perturbations tend to move the strategy distribution towards nonordered states of equilibrium, supporting cooperation when defection is pervading the population, and supporting defection in the opposite case. To conclude, we identified a form of noise that, under controlled conditions, could be used to enhance cooperation and greatly delay its extinction.
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Affiliation(s)
- Marco A Amaral
- Instituto de Humanidades, Artes e Ciências, Universidade Federal do Sul da Bahia-BA, 45996-108, Brazil
| | - Marco A Javarone
- Department of Mathematics, University College London, London WC1E 6BT, United Kingdom
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