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Feedback loops between strategies and the environment are commonly observed in socio-ecological, evolution-ecological, and psychology-economic systems. However, the impact of mutations in these feedback processes is often overlooked. This study proposes a novel model that integrates the public goods game with environmental feedback, considering the presence of mutations. In our model, the enhancement factor of the public goods game combines positive and negative incentives from the environment. By employing replicator–mutator (RM) equations, we provide an objective understanding of the system's evolutionary state, focusing on identifying conditions that foster cooperation and prevent the tragedy of the commons. Specifically, mutations play a crucial role in the RM dynamics, leading to the emergence of an oscillatory tragedy of the commons. By verifying the Hopf bifurcation condition, we establish the existence of a stable limit cycle, providing valuable insights into sustained oscillation strategies. Moreover, the feedback mechanism inherent in the public goods game model offers a fresh perspective on effectively addressing the classic dilemma of the tragedy of the commons. [ABSTRACT FROM AUTHOR]

Complex networks are widespread in real-world environments across diverse domains. Real-world networks tend to form spontaneously through interactions between individual agents. Inspired by this, we design an evolutionary game model in which agents participate in a prisoner's dilemma game (PDG) with their neighboring agents. Agents can autonomously modify their connections with neighbors using reinforcement learning to avoid unfavorable environments. Interestingly, our findings reveal some remarkable results. Exploiting reinforcement learning-based adaptive networks improves cooperation when juxtaposed with existing PDGs performed on homogeneous networks. At the same time, the network's topology evolves from homogeneous to heterogeneous states. This change occurs as players gain experience from past games and become more astute in deciding whether to join PDGs with their current neighbors or disconnect from the least profitable neighbors. Instead, they seek out more favorable environments by establishing connections with second-order neighbors with higher rewards. By calculating the degree distribution and modularity of the adaptive network in a steady state, we confirm that the adaptive network follows a power law and has a clear community structure, indicating that the adaptive network is similar to networks in the real world. Our study reports a new phenomenon in evolutionary game theory on networks. It proposes a new perspective to generate scale-free networks, which is generating scale-free networks by the evolution of homogeneous networks rather than typical ways of network growth and preferential connection. Our results provide new aspects to understanding the network structure, the emergence of cooperation, and the behavior of actors in nature and society. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to study how a decision-making rule for vaccination can affect epidemic spreading by exploiting the Bush–Mosteller (BM) model, one of the methodologies in reinforcement learning in artificial intelligence (AI), which can realize the systematic process of learning in humans, on complex networks. We consider the BM model with two stages—vaccination and epidemiological processes—and address two independent rules about fixed loss consideration and average payoff of neighbors to update agent's vaccination behavior for various stimuli, such as loss of payoffs and environments during the vaccination process. Higher sensitivity not only favors higher vaccination coverage rates but also delays the transition point in relative vaccination costs when transitioning from full vaccination (inoculation level 1) to incomplete vaccination (inoculation level less than 1). Extensive numerical simulations demonstrate that the vaccination dilemma can be overcome to some extent, and the distribution of the intended vaccination probabilities in both independent rules is either normal or skewed when different parameters are considered. Since AI is contributing to many fields, we expect that our BM-empowered learning can ultimately resolve the vaccination dilemma. [ABSTRACT FROM AUTHOR]

Recognizing surrounding situations, such as enemy attacks, which can be realized by predator–prey relationships, is one of the common behaviors of the population in ecosystems. In this paper, we explore the relationship between such species' behavior and biodiversity in the spatial rock–paper–scissors game by employing the ecological concept "vigilance." In order to describe the vigilance process, we adopt a multiplex structure where two distinct layers describe virtual and physical interactions. By investigating the process of evolution in species, we also found that species with different vigilance go together. In addition, by utilizing the dynamic time warping method, we found that species with the same vigilance have consistent behavior, but species with different vigilance have diverse behavior. Our findings may lead to broader interpretations of mechanisms promoting biodiversity via vigilance in species ecosystems. [ABSTRACT FROM AUTHOR]

We investigate evolving dynamics of cyclically competing species on spatially extended systems with considering a specific region, which is called the "wildlife refuge," one of the institutional ways to preserve species biodiversity. Through Monte-Carlo simulations, we found that the refuge can play not groundbreaking but an important role in species survival. Species coexistence is maintained at a moderate mobility regime, which traditionally leads to the collapse of coexistence, and eventually, the extinction is postponed depending on the competition rate rather than the portion of the refuge. Incorporating the extinction probability and Fourier transform supported our results in both stochastic and analogous ways. Our findings may provide valuable evidence to assist fields of ecological/biological sciences in understanding the presence and construction of refuges for wildlife with associated effects on species biodiversity. [ABSTRACT FROM AUTHOR]