We propose a model for the evolutionary ecology of words as one attempt to extend evolutionary game theory and agent-based models by utilizing the rich linguistic expressions of Large Language Models (LLMs). Our model enables the emergence and evolution of diverse and infinite options for interactions among agents. Within the population, each agent possesses a short word (or phrase) generated by an LLM and moves within a spatial environment. When agents become adjacent, the outcome of their interaction is determined by the LLM based on the relationship between their words, with the loser's word being replaced by the winner's. Word mutations, also based on LLM outputs, may occur. We conducted preliminary experiments assuming that ``strong animal species" would survive. The results showed that from an initial population consisting of well-known species, many species emerged both gradually and in a punctuated equilibrium manner. Each trial demonstrated the unique evolution of diverse populations, with one type of large species becoming dominant, such as terrestrial animals, marine life, or extinct species, which were ecologically specialized and adapted ones across diverse extreme habitats. We also conducted a long-term experiment with a large population, demonstrating the emergence and coexistence of diverse species.

Institutions play a critical role in enabling communities to manage common-pool resources and avert tragedies of the commons. However, a fundamental issue arises: Individuals typically perceive participation as advantageous only after an institution is established, creating a paradox: How can institutions form if no one will join before a critical mass exists? We term this conundrum the institution bootstrapping problem and propose that misperception, specifically, agents' erroneous belief that an institution already exists, could resolve this paradox. By integrating well-documented psychological phenomena, including cognitive biases, probability distortion, and perceptual noise, into a game-theoretic framework, we demonstrate how these factors collectively mitigate the bootstrapping problem. Notably, unbiased perceptual noise (e.g., noise arising from agents' heterogeneous physical or social contexts) drastically reduces the critical mass of cooperators required for institutional emergence. This effect intensifies with greater diversity of perceptions. We explain this counter-intuitive result through asymmetric boundary conditions: proportional underestimation of low-probability sanctions produces distinct outcomes compared to equivalent overestimation. Furthermore, the type of perceptual distortion, proportional versus absolute, yields qualitatively different evolutionary pathways. These findings challenge conventional assumptions about rationality in institutional design, highlighting how "noisy" cognition can paradoxically enhance cooperation. Finally, we contextualize these insights within broader discussions of multi-agent system design and collective action. Our analysis underscores the importance of incorporating human-like cognitive constraints, not just idealized rationality, into models of institutional emergence and resilience.

Personalized cancer treatment is revolutionizing oncology by leveraging precision medicine and advanced computational techniques to tailor therapies to individual patients. Despite its transformative potential, challenges such as limited generalizability, interpretability, and reproducibility of predictive models hinder its integration into clinical practice. Current methodologies often rely on black-box machine learning models, which, while accurate, lack the transparency needed for clinician trust and real-world application. This paper proposes the development of an innovative framework that bridges Kolmogorov-Arnold Networks (KANs) and Evolutionary Game Theory (EGT) to address these limitations. Inspired by the Kolmogorov-Arnold representation theorem, KANs offer interpretable, edge-based neural architectures capable of modeling complex biological systems with unprecedented adaptability. Their integration into the EGT framework enables dynamic modeling of cancer progression and treatment responses. By combining KAN's computational precision with EGT's mechanistic insights, this hybrid approach promises to enhance predictive accuracy, scalability, and clinical usability.

This paper presents a physics-informed deep learning approach for predicting the replicator equation, allowing accurate forecasting of population dynamics. This methodological innovation allows us to derive governing differential or difference equations for systems that lack explicit mathematical models. We used the SINDy model first introduced by Fasel, Kaiser, Kutz, Brunton, and Brunt 2016a to get the replicator equation, which will significantly advance our understanding of evolutionary biology, economic systems, and social dynamics. NTRODUCTION Game theory helps to understand how strategic behaviours evolve and persist in biological, social, and economic systems where individuals interact. It also helps in how complex social behaviours and strategies can evolve and persist in diverse contexts.

Cooperative behavior is prevalent in both human society and nature. Understanding the emergence and maintenance of cooperation among self-interested individuals remains a significant challenge in evolutionary biology and social sciences. Reinforcement learning (RL) provides a suitable framework for studying evolutionary game theory as it can adapt to environmental changes and maximize expected benefits. In this study, we employ the State-Action-Reward-State-Action (SARSA) algorithm as the decision-making mechanism for individuals in evolutionary game theory. Initially, we apply SARSA to imitation learning, where agents select neighbors to imitate based on rewards. This approach allows us to observe behavioral changes in agents without independent decision-making abilities. Subsequently, SARSA is utilized for primary agents to independently choose cooperation or betrayal with their neighbors. We evaluate the impact of SARSA on cooperation rates by analyzing variations in rewards and the distribution of cooperators and defectors within the network.

Evolutionary Game Theory (EGT) and Artificial Intelligence (AI) are two fields that, at first glance, might seem distinct, but they have notable connections and intersections. The former focuses on the evolution of behaviors (or strategies) in a population, where individuals interact with others and update their strategies based on imitation (or social learning). The more successful a strategy is, the more prevalent it becomes over time. The latter, meanwhile, is centered on machine learning algorithms and (deep) neural networks. It is often from a single-agent perspective but increasingly involves multi-agent environments, in which intelligent agents adjust their strategies based on feedback and experience, somewhat akin to the evolutionary process yet distinct in their self-learning capacities. In light of the key components necessary to address real-world problems, including (i) learning and adaptation, (ii) cooperation and competition, (iii) robustness and stability, and altogether (iv) population dynamics of individual agents whose strategies evolve, the cross-fertilization of ideas between both fields will contribute to the advancement of mathematics of multi-agent learning systems, in particular, to the nascent domain of ``collective cooperative intelligence'' bridging evolutionary dynamics and multi-agent reinforcement learning.

This brief discusses evolutionary game theory as a powerful and unified mathematical tool to study evolution of collective behaviours. It summarises some of my recent research directions using evolutionary game theory methods, which include i) the analysis of statistical properties of the number of (stable) equilibria in a random evolutionary game, and ii) the modelling of safety behaviours' evolution and the risk posed by advanced Artificial Intelligence technologies in a technology development race. Finally, it includes an outlook and some suggestions for future researchers.

There isn't a day that goes by without hearing about some fascinating development in artificial intelligence research, whether that might be an AI that can process and produce language in a human-like way, or an AI that can unlock the mysteries folded up within a protein, or automatically make scientific discoveries. But in the headlong rush in the to find the next breakthrough, there are legitimate concerns that the competitive nature of the "AI race" might mean that things like safety and ethics are being inadvertently overlooked, resulting in phenomena like algorithmic bias, or an escalating AI arms race between rival military powers to build lethal autonomous weapons. All of these recent developments point to a need for better regulations when it comes to engineering and implementing AI. Of course, too much regulation might stifle innovation, but too little might also bring what could have been a preventable disaster. As an international research team from Teesside University, Universidade Nova de Lisboa, and Université Libre de Bruxelles now suggest, AI can also be used to navigate this delicate balance by determining which types of AI research projects might need more regulation than others. "Whether real or not, the belief in such a race for domain supremacy through AI, can make it real simply from its consequences," wrote the team in a paper that was published in the Journal of Artificial Intelligence Research.

Society is shaped by humans' unique capacity to take on another person's perspective - which might be the reason why modern societies have such extraordinary levels of cooperation. Writing for the Conversation, Arunas L. Radzvilavicius, a Postdoctoral Researcher of Evolutionary Biology at the University of Pennsylvania explains that social norms can shed light on why people display altruistic behaviour. Humans are far more likely to be kind to individuals they see as'good', than they are to people of'bad' reputation. But, he says, if everyone agrees that being altruistic toward other cooperators earns you a good reputation, cooperation will persist. A person who appears'good' to someone might seem like a bad individual from another person's perspective.

The interaction of multiple autonomous agents gives rise to highly dynamic and nondeterministic environments, contributing to the complexity in applications such as automated financial markets, smart grids, or robotics. Due to the sheer number of situations that may arise, it is not possible to foresee and program the optimal behaviour for all agents beforehand. Consequently, it becomes essential for the success of the system that the agents can learn their optimal behaviour and adapt to new situations or circumstances. The past two decades have seen the emergence of reinforcement learning, both in single and multi-agent settings, as a strong, robust and adaptive learning paradigm. Progress has been substantial, and a wide range of algorithms are now available. An important challenge in the domain of multi-agent learning is to gain qualitative insights into the resulting system dynamics. In the past decade, tools and methods from evolutionary game theory have been successfully employed to study multi-agent learning dynamics formally in strategic interactions. This article surveys the dynamical models that have been derived for various multi-agent reinforcement learning algorithms, making it possible to study and compare them qualitatively. Furthermore, new learning algorithms that have been introduced using these evolutionary game theoretic tools are reviewed. The evolutionary models can be used to study complex strategic interactions. Examples of such analysis are given for the domains of automated trading in stock markets and collision avoidance in multi-robot systems. The paper provides a roadmap on the progress that has been achieved in analysing the evolutionary dynamics of multi-agent learning by highlighting the main results and accomplishments.