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We use system-theoretic passivity methods to study evolutionary Nash equilibria learning in large populations of agents engaged in strategic, non-cooperative interactions. The agents follow learning rules (rules for short) that capture…

We introduce an evolutionary game on hypergraphs in which decisions between a risky alternative and a safe one are taken in social groups of different sizes. The model naturally reproduces choice shifts, namely the differences between the…

We study evolutionary games with a continuous trait space in which replicator dynamics are restricted to the manifold of multidimensional Gaussian distributions. We demonstrate that the replicator equations are natural gradient flow for…

The preferences of players in non-cooperative games represent their choice in the set of available options, which meet the completeness property if players are able to compare any pair of available options. In the existing literature, the…

Nash equilibria provide a principled framework for modeling interactions in multi-agent decision-making and control. However, many equilibrium-seeking methods implicitly assume that each agent has access to the other agents' objectives and…

Adversarial training is a standard technique for training adversarially robust models. In this paper, we study adversarial training as an alternating best-response strategy in a 2-player zero-sum game. We prove that even in a simple…

In this paper, we study closed-loop strong equilibrium strategies for the time-inconsistent control problem with higher-order moments formulated by [Wang et al. SIAM J. Control. Optim., 63 (2025), 1560--1589]. Since time-inconsistency makes…

We consider two models of computation for Tarski's order preserving function f related to fixed points in a complete lattice: the oracle function model and the polynomial function model. In both models, we find the first polynomial time…

This paper introduces an evolutionary dynamics based on imitate the better realization (IBR) rule. Under this rule, agents in a population game imitate the strategy of a randomly chosen opponent whenever the opponent`s realized payoff is…

In this paper, a Nash-type fictitious game framework is introduced to handle a time-inconsistent linear-quadratic optimal control. The Nash-type game in this framework is called fictitious as it is between the decision maker (called real…

A noncooperative differential (dynamic) game model of opinion dynamics is proposed. In this game, the agents' motives are shaped by their expectations of the nature of others' opinions as well as how susceptible they are to get influenced…

In this paper, we consider a linear quadratic stochastic two-person nonzero-sum differential game. Open-loop and closed-loop Nash equilibria are introduced. The existence of the former is characterized by the solvability of a system of…

Social dilemmas concern a natural conflict between cooperation and self interests among individuals in large populations. The emergence of cooperation and its maintenance is the key for the understanding of fundamental concepts about the…

This paper proposes a novel approach for locally stable convergence to Nash equilibrium in duopoly noncooperative games based on a distributed event-triggered control scheme. The proposed approach employs extremum seeking, with sinusoidal…

We investigate the fluctuations induced by irrationality in simple games with a large number of competing players. We show that Nash equilibria in such games are ``weakly'' stable: irrationality propagates and amplifies through players'…

Non-cooperative dynamic game theory provides a principled approach to modeling sequential decision-making among multiple noncommunicative agents. A key focus has been on finding Nash equilibria in two-agent zero-sum dynamic games under…

In bi-matrix games the Bishop-Cannings theorem of the classical evolutionary game theory does not permit pure evolutionarily stable strategies (ESSs) when a mixed ESS exists. We find the necessary form of two-qubit initial quantum states…

We study the evolutionary dynamics of games under environmental feedback using replicator equations for two interacting populations. One key feature is to consider jointly the co-evolution of the dynamic payoff matrices and the state of the…

In finite games mixed Nash equilibria always exist, but pure equilibria may fail to exist. To assess the relevance of this nonexistence, we consider games where the payoffs are drawn at random. In particular, we focus on games where a large…

Zero-sum games such as chess and poker are, abstractly, functions that evaluate pairs of agents, for example labeling them `winner' and `loser'. If the game is approximately transitive, then self-play generates sequences of agents of…