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Nash equilibrium is a solution concept in non-strictly competitive, non-cooperative game theory that finds applications in various scientific and engineering disciplines. A non-strictly competitive, non-cooperative game model is presented…
We revisit in this paper the relation between evolution of species and the mathematical tool of evolutionary games, which has been used to model and predict it. We indicate known shortcoming of this model that restricts the capacity of…
In many real-world large-scale decision problems, self-interested agents have individual dynamics and optimize their own long-term payoffs. Important examples include the competitive access to shared resources (e.g., roads, energy, or…
Generative Adversarial Networks (GANs) have recently attracted considerable attention in the AI community due to its ability to generate high-quality data of significant statistical resemblance to real data. Fundamentally, GAN is a game…
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…
This work proposes a policy learning algorithm for seeking generalised feedback Nash equilibria (GFNE) in $N_P$-player noncooperative dynamic games. We consider linear-quadratic games with stochastic dynamics and design a best-response…
We consider a repeatedly played generalized Nash equilibrium game. This induces a multi-agent online learning problem with joint constraints. An important challenge in this setting is that the feasible set for each agent depends on the…
We develop a game-theoretic framework for predicting and steering the behavior of populations of large language models (LLMs) through Nash equilibrium (NE) analysis. To avoid the intractability of equilibrium computation in open-ended text…
Equilibria of realistic multiplayer games constitute a key solution concept both in practical applications, such as online advertising auctions and electricity markets, and in analytical frameworks used to study strategic voting in…
Shared-constraint games are noncooperative $N$-player games where players are coupled through a common coupling constraint. It is known that such games admit two kinds of equilibria -- generalized Nash equilibria (GNE) and variational…
This paper introduces a consensus-based generalized multi-population aggregative game coordination approach with application to electric vehicles charging under transmission line constraints. The algorithm enables agents to seek an…
Decoding how rational agents should behave in shared systems remains a critical challenge within theoretical computer science, artificial intelligence and economics studies. Central to this challenge is the task of computing the solution…
This paper explores aggregative games in a network of general linear systems subject to external disturbances. To deal with external disturbances, distributed strategy-updating rules based on internal model are proposed for the case with…
We consider the problem of computing Nash equilibria in potential games where each player's strategy set is subject to private uncoupled constraints. This scenario is frequently encountered in real-world applications like road network…
Generative adversarial networks (GANs) represent a zero-sum game between two machine players, a generator and a discriminator, designed to learn the distribution of data. While GANs have achieved state-of-the-art performance in several…
Nash equilibrium serves as a fundamental mathematical tool in economics and game theory. However, it classically assumes knowledge of player utilities, whereas economics generally regards preferences as more fundamental. To leverage…
The generalized Nash equilibrium problem (GNEP) is a kind of game to find strategies for a group of players such that each player's objective function is optimized. Solutions for GNEPs are called generalized Nash equilibria (GNEs). In this…
We prove input-to-state stability (ISS) of perturbed Newton-type methods for generalized equations arising from Nash equilibrium (NE) and generalized NE (GNE) problems. This ISS property allows the use of inexact computations in…
Most work in game theory assumes that players are perfect reasoners and have common knowledge of all significant aspects of the game. In earlier work, we proposed a framework for representing and analyzing games with possibly unaware…
We introduce a new solution concept for bounded rational agents in finite normal-form general-sum games called Generalized Quantal Response Equilibrium (GQRE) which generalizes Quantal Response Equilibrium~\citep{mckelvey1995quantal}. In…