1. Eco-evolutionary dynamics of multigames with mutationsSourav Roy, Sayantan Nag Chowdhury, Prakash Chandra Mali, Matjaž Perc, Dibakar Ghosh, 2022, original scientific article 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 selfinterested 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.
Keywords: public goods, cooperation, mutation, social physics, evolutionary dynamics
Published in DKUM: 15.07.2024; Views: 137; Downloads: 9
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2. Time delays shape the eco‑evolutionary dynamics of cooperationSourav Roy, Sayantan Nag Chowdhury, Srilena Kundu, Gourab Kumar Sar, Jeet Banerjee, Biswambhar Rakshit, Prakash Chandra Mali, Matjaž Perc, Dibakar Ghosh, 2023, original scientific article 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 selfsh individuals often assume instantaneous interactions, we take into consideration delays to investigate how these might afect 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 efective 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.
Keywords: cooperation, time delay, evolutionary dynamics, social dilemma, social physics
Published in DKUM: 04.04.2024; Views: 191; Downloads: 19
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3. The dynamics of a duopoly Stackelberg game with marginal costs among heterogeneous playersAtefeh Ahmadi, Sourav Roy, Mahtab Mehrabbeik, Dibakar Ghosh, Sajad Jafari, Matjaž Perc, 2023, original scientific article Abstract: One of the famous economic models in game theory is the duopoly Stackelberg model, in which a leader and a follower firm manufacture a single product in the market. Their goal is to obtain the maximum profit while competing with each other. The desired dynamics for a firm in a market is the convergence to its Nash equilibrium, but the dynamics of real-world markets are not always steady and can result in unpredictable market changes that exhibit chaotic behaviors. On the other hand, to approach reality more, the two firms in the market can be considered heterogeneous. The leader firm is bounded rationale, and the follower firm is adaptable. Modifying the cost function that affects the firms' profit by adding the marginal cost term is another step toward reality. We propose a Stackelberg model with heterogeneous players and marginal costs, which exhibits chaotic behavior. This model's equilibrium points, including the Nash equilibrium, are calculated by the backward induction method, and their stability analyses are obtained. The influence of changing each model parameter on the consequent dynamics is investigated through one-dimensional and two-dimensional bifurcation diagrams, Lyapunov exponents spectra, and Kaplan-Yorke dimension. Eventually, using a combination of state feedback and parameter adjustment methods, the chaotic solutions of the model are successfully tamed, and the model converges to its Nash equilibrium.
Keywords: nonlinear dynamics, game theory, stability analysis, public goods
Published in DKUM: 02.08.2023; Views: 459; Downloads: 49
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