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Recent advances in mean-field game literature enable the reduction of large-scale multi-agent problems to tractable interactions between a representative agent and a population distribution. However, existing approaches typically assume a…

Trusting others and reciprocating the received trust with trustworthy actions are fundaments of economic and social interactions. The trust game (TG) is widely used for studying trust and trustworthiness and entails a sequential interaction…

We study a system in which N agents have to decide between two strategies \theta_i (i \in 1... N), for defection or cooperation, when interacting with other n agents (either spatial neighbors or randomly chosen ones). After each round, they…

Here, we develop numerical methods for finite-state mean-field games (MFGs) that satisfy a monotonicity condition. MFGs are determined by a system of differential equations with initial and terminal boundary conditions. These non-standard…

We develop a mean-field theory of the growth, exchange and distribution (GED) model introduced by Kang et al. (preceding paper) that accurately describes the phase transition in the limit that the number of agents $N$ approaches infinity.…

We study the existence of strong solutions for mean-field forward-backward stochastic differential equations (FBSDEs) with measurable coefficients and their implication on the Nash equilibrium of a multi-population mean-field game. More…

In this paper we investigate a generalisation of a Boltzmann mean field game (BMFG) for knowledge growth, originally introduced by the economists Lucas and Moll. In BMFG the evolution of the agent density with respect to their knowledge…

As Large Language Models (LLMs) increasingly operate as autonomous decision-makers in interactive and multi-agent systems and human societies, understanding their strategic behaviour has profound implications for safety, coordination, and…

We consider the mean-field game price formation model introduced by Gomes and Sa\'ude. In this MFG model, agents trade a commodity whose supply can be deterministic or stochastic. Agents maximize profit, taking into account current and…

The success of modern civilization is built upon widespread cooperation in human society, deciphering the mechanisms behind has being a major goal for centuries. A crucial fact is, however, largely missing in most prior studies that games…

Knowledge spillovers occur when a firm researches a new technology and that technology is adapted or adopted by another firm, resulting in a social value of the technology that is larger than the initially predicted private value. As a…

The spread of an epidemic disease and the population's collective behavioural response are deeply intertwined, influencing each other's evolution. Such a co-evolution typically has been overlooked in mathematical models, limiting their…

Motivated by the climate crisis that is currently ravaging the planet, we propose and analyze a novel framework for the evolution of anthropogenic climate impact in which the evolution of human environmental behavior and environmental…

The dynamics of minority games with agents trading on different time scales is studied via dynamical mean-field theory. We analyze the case where the agents' decision-making process is deterministic and its stochastic generalization with…

Rising inequalities around the globe bring into question our economic systems and the origin of such inequalities. Here we propose a toy agent-based model where each entity is simultaneously producing and consuming indivisible goods. We…

Here we present an agent-based model where agents interact with other agents by playing a hybrid of dictator and ultimatum games in a co-evolving social network. The basic assumption about the behaviour of the agents in both games is that…

Mean Field Control Games (MFCG), introduced in [Angiuli et al., 2022a], represent competitive games between a large number of large collaborative groups of agents in the infinite limit of number and size of groups. In this paper, we prove…

Collusion among autonomous agents poses a critical security threat in embodied multi-agent systems (MAS), where coordinated behaviors can deviate from global objectives and lead to real-world consequences. Existing defenses, primarily based…

Matrix games like Prisoner's Dilemma have guided research on social dilemmas for decades. However, they necessarily treat the choice to cooperate or defect as an atomic action. In real-world social dilemmas these choices are temporally…

This paper analyzes a class of infinite-time-horizon stochastic games with singular controls motivated from the partially reversible problem. It provides an explicit solution for the mean-field game (MFG) and presents sensitivity analysis…