THE IMPACT OF COMPLEX INTERACTIONS ON THE EVOLUTION OF COOPERATION IN THE PUBLIC GOODS GAME

Authors

  • Maja Duh University of Maribor, Faculty of Medicine, Institute of Physiology, Maribor, Slovenia; University of Maribor, Faculty of Natural Sciences and Mathematics, Department of Physics, Maribor, Slovenia; Alma Mater Europaea University, Maribor, Slovenia, https://orcid.org/0000-0003-2910-8720
  • Marko Gosak University of Maribor, Faculty of Medicine, Institute of Physiology, Maribor, Slovenia; University of Maribor, Faculty of Natural Sciences and Mathematics, Department of Physics, Maribor, Slovenia; Alma Mater Europaea University, Maribor, Slovenia https://orcid.org/0000-0001-9735-0485
  • Matjaž Perc University of Maribor, Faculty of Natural Sciences and Mathematics, Department of Physics, Maribor, Slovenia; Community Healthcare Center Dr. Adolf Drolc Maribor, Maribor, Slovenia; Complexity Science Hub Vienna, Vienna, Austria; Kyung Hee University, Department of Physics, Seoul, Republic of Korea https://orcid.org/0000-0002-3087-541X

DOI:

https://doi.org/10.18690/analipazu.15.1-2.1-17.2025

Keywords:

evolutionary game theory, public goods game, complex networks, multilayer networks, Monte Carlo simulations

Abstract

The emergence and persistence of cooperation among selfish individuals remain one of the most significant challenges that continues to intrigue scientists across various research fields. Evolutionary game theory has become a key tool in these studies, providing a robust theoretical framework to describe the evolutionary dynamics of strategies in social dilemmas. Simultaneously, advances in network science have significantly enhanced our understanding of numerous complex systems in the real world, including the development of cooperation in group decision-making and collective actions. A critical factor in this context is how individuals are embedded within society. Research over the past decades has showed that social network structure critically impacts cooperation. Moreover, as individuals are often mobile in most real-world scenarios, mobility and population mixing also play a crucial role in the evolution of cooperation. The primary aim of our study was to examine how different interaction networks and player mixing influence the evolution of cooperation in the public goods game.

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Author Biographies

  • Maja Duh, University of Maribor, Faculty of Medicine, Institute of Physiology, Maribor, Slovenia; University of Maribor, Faculty of Natural Sciences and Mathematics, Department of Physics, Maribor, Slovenia; Alma Mater Europaea University, Maribor, Slovenia,

    Maja Duh, University of Maribor, Faculty of Medicine, Institute of Physiology, Maribor, Slovenia; University of Maribor, Faculty of Natural Sciences and Mathematics, Department of Physics, Maribor, Slovenia; Alma Mater Europaea University, Maribor, Slovenia, maja.duh3@um.si 

  • Marko Gosak, University of Maribor, Faculty of Medicine, Institute of Physiology, Maribor, Slovenia; University of Maribor, Faculty of Natural Sciences and Mathematics, Department of Physics, Maribor, Slovenia; Alma Mater Europaea University, Maribor, Slovenia

    Marko Gosak, University of Maribor, Faculty of Medicine, Institute of Physiology, Maribor, Slovenia; University of Maribor, Faculty of Natural Sciences and Mathematics, Department of Physics, Maribor, Slovenia; Alma Mater Europaea University, Maribor, Slovenia, marko.gosak@um.si 

  • Matjaž Perc, University of Maribor, Faculty of Natural Sciences and Mathematics, Department of Physics, Maribor, Slovenia; Community Healthcare Center Dr. Adolf Drolc Maribor, Maribor, Slovenia; Complexity Science Hub Vienna, Vienna, Austria; Kyung Hee University, Department of Physics, Seoul, Republic of Korea

    Matjaž Perc, University of Maribor, Faculty of Natural Sciences and Mathematics, Department of Physics, Maribor, Slovenia; Community Healthcare Center Dr. Adolf Drolc Maribor, Maribor, Slovenia; Complexity Science Hub Vienna, Vienna, Austria; Kyung Hee University, Department of Physics, Seoul, Republic of Korea, matjaz.perc@um.si 

References

Alvarez-Rodriguez, U. in drugi (2020). Evolutionary Dynamics of Higher-Order Interactions in Social Networks. Nature Human Behaviour 5(5): 586–95.

Boguñá, M., Papadopoulos, F. in Krioukov, F. (2010). Sustaining the Internet with Hyperbolic Mapping. Nature Communications 1(6): 1–8.

Castellano, C., Fortunato, S. in Loreto, V. (2009). Statistical Physics of Social Dynamics. Reviews of Modern Physics 81(2): 591–646.

Cinyabuguma, M., Page, T. in Putterman, L. (2005). Cooperation under the Threat of Expulsion in a Public Goods Experiment. Journal of Public Economics 89(8 SPEC. ISS.): 1421–35.

Duh, M. (2024). Vpliv mešanja in kompleksnih interakcij na razvoj sodelovanja v igri javnih dobrin (Doktorska disertacija). Univerza v Mariboru.

Duh, M., Gosak, M. in Perc, M. (2021). Public Goods Games on Random Hyperbolic Graphs with Mixing. Chaos, Solitons and Fractals 144: 110720.

Duh, M., Gosak, M. in Perc, M. (2023). Unexpected paths to cooperation on tied hyperbolic networks. Europhysics Letters 142: 6.

Güth, W., Schmittberger, R. in Schwarze, B. (1982). An Experimental Analysis of Ultimatum Bargaining. Journal of Economic Behavior & Organization 3(4): 367–88.

Kleineberg, K. K. (2017). Metric Clusters in Evolutionary Games on Scale-Free Networks. Nature Communications 8(1).

Pacheco, J. M., Traulsen, A. in Nowak, M. A. (2006). Coevolution of Strategy and Structure in Complex Networks with Dynamical Linking. Physical Review Letters 97(25): 258103.

Pennisi, E. (2009). On the Origin of Cooperation. Science 325(5945): 1196–99.

Perc, M. in drugi (2013). Evolutionary Dynamics of Group Interactions on Structured Populations: A Review. Journal of the Royal Society Interface 10(80).

Rand, D. G. (2012). The Promise of Mechanical Turk: How Online Labor Markets Can Help Theorists Run Behavioral Experiments. Journal of Theoretical Biology 299: 172–79.

Rong, Z., Li, X. in Wang, X. (2007). Roles of Mixing Patterns in Cooperation on a Scale-Free Networked Game. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 76(2): 027101.

Santos, F. C., Rodrigues, J. F. in Pacheco, J. M. (2005). Epidemic Spreading and Cooperation Dynamics on Homogeneous Small-World Networks. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 72(5): 056128.

Smith, J. M. in Price, G. R. (1973). The Logic of Animal Conflict. Nature 246: 15–18.

Smith, J. M. (1982). Evolution and the Theory of Games. Cambridge University Press.

Szabó, G. in Fáth, G. (2007). Evolutionary Games on Graphs. Physics Reports 446(4–6): 97–216.

Traulsen, A. in Glynatsi, N. E. (2023). The Future of Theoretical Evolutionary Game Theory. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876).

Vukov, J. in Szabó, G. (2005). Evolutionary Prisoner’s Dilemma Game on Hierarchical Lattices. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 71(3): 036133.

Wang, Z., Szolnoki, A. in Perc, M. (2012). Evolution of Public Cooperation on Interdependent Networks: The Impact of Biased Utility Functions. Epl 97(4): 1–6.

Zuev, K., Boguñá, M., Bianconi, G. in Krioukov, D. (2015). Emergence of Soft Communities from Geometric Preferential Attachment. Scientific Reports 5: 1–9.

Published

04.12.2025

Issue

Section

Prispevki

How to Cite

Duh, M., Gosak, M., & Perc, M. (2025). THE IMPACT OF COMPLEX INTERACTIONS ON THE EVOLUTION OF COOPERATION IN THE PUBLIC GOODS GAME. Anali PAZU, 15(1-2), 1-17. https://doi.org/10.18690/analipazu.15.1-2.1-17.2025