Related papers: Discovering Expert-Level Nash Equilibrium Algorith…
AI in Math deals with mathematics in a constructive manner so that reasoning becomes automated, less laborious, and less error-prone. For algorithms, the question becomes how to automate analyses for specific problems. For the first time,…
Nash equilibrium is one of the most influential solution concepts in game theory. With the development of computer science and artificial intelligence, there is an increasing demand on Nash equilibrium computation, especially for Internet…
Generative artificial intelligence (Generative AI), and in particular Large Language Models (LLMs) have gained significant popularity among researchers and industrial communities, paving the way for integrating LLMs in different domains,…
The Nash equilibrium is an important benchmark for behaviour in systems of strategic autonomous agents. Polymatrix games are a succinct and expressive representation of multiplayer games that model pairwise interactions between players. The…
Contemporary applications of machine learning in two-team e-sports and the superior expressivity of multi-agent generative adversarial networks raise important and overlooked theoretical questions regarding optimization in two-team games.…
We design a distributed algorithm to seek generalized Nash equilibria of a robust game with uncertain coupled constraints. Due to the uncertainty of parameters in set constraints, we aim to find a generalized Nash equilibrium in the worst…
This work proposes a novel set of techniques for approximating a Nash equilibrium in a finite, normal-form game. It achieves this by constructing a new reformulation as solving a parameterized system of multivariate polynomials with tunable…
A fundamental open problem in monotone game theory is the computation of a specific generalized Nash equilibrium (GNE) among all the available ones, e.g. the optimal equilibrium with respect to a system-level objective. The existing GNE…
Consider a strongly monotone game where the players' utility functions include a reward function and a linear term for each dimension, with coefficients that are controlled by the manager. Gradient play converges to a unique Nash…
Computing equilibria of games is a central task in computer science. A large number of results are known for \emph{Nash equilibrium} (NE). However, these can be adopted only when coalitions are not an issue. When instead agents can form…
The computational characterization of game-theoretic solution concepts is a central topic in artificial intelligence, with the aim of developing computationally efficient tools for finding optimal ways to behave in strategic interactions.…
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…
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…
We investigate the problem of equilibrium computation for "large" $n$-player games. Large games have a Lipschitz-type property that no single player's utility is greatly affected by any other individual player's actions. In this paper, we…
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…
We study the randomized query complexity of approximate Nash equilibria (ANE) in large games. We prove that, for some constant $\epsilon>0$, any randomized oracle algorithm that computes an $\epsilon$-ANE in a binary-action, $n$-player game…
In this paper, we aim to design a distributed approximate algorithm for seeking Nash equilibria of an aggregative game. Due to the local set constraints of each player, projectionbased algorithms have been widely employed for solving such…
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…
Prediction is a well-studied machine learning task, and prediction algorithms are core ingredients in online products and services. Despite their centrality in the competition between online companies who offer prediction-based products,…
The multi-cluster games are addressed in this paper, where all players team up with the players in the cluster that they belong to, and compete against the players in other clusters to minimize the cost function of their own cluster. The…