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Nash equilibrium is the most commonly-used notion of equilibrium in game theory. However, it suffers from numerous problems. Some are well known in the game theory community; for example, the Nash equilibrium of repeated prisoner's dilemma…
Stochastic differential games have been used extensively to model agents' competitions in Finance, for instance, in P2P lending platforms from the Fintech industry, the banking system for systemic risk, and insurance markets. The recently…
In this paper, the problem of finding a generalized Nash equilibrium (GNE) of a networked game is studied. Players are only able to choose their decisions from a feasible action set. The feasible set is considered to be a private linear…
Nash equilibrium is a fundamental solution concept in extensive-form games, while its efficient computation is still far from straightforward. This paper considers finite $n$-player extensive-form games with perfect recall under the…
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…
Game theory has emerged as a powerful framework for modeling a large range of multi-agent scenarios. Many algorithmic solutions require discrete, finite games with payoffs that have a closed-form specification. In contrast, many real-world…
We address the generalized Nash equilibrium seeking problem for a population of agents playing aggregative games with affine coupling constraints. We focus on semi-decentralized communication architectures, where there is a central…
We consider structural and algorithmic questions related to the Nash dynamics of weighted congestion games. In weighted congestion games with linear latency functions, the existence of (pure Nash) equilibria is guaranteed by potential…
Continuous games are multiplayer games in which strategy sets are compact and utility functions are continuous. These games typically have a highly complicated structure of Nash equilibria, and numerical methods for the equilibrium…
In this paper, we propose an asynchronous distributed algorithm for the computation of generalized Nash equilibria in noncooperative games, where the players interact via an undirected communication graph. Specifically, we extend the paper…
An extensive literature in economics and social science addresses contests, in which players compete to outperform each other on some measurable criterion, often referred to as a player's score, or output. Players incur costs that are an…
In this article, we consider generalized Nash games where the associated constraint map is not necessarily self. The classical Nash equilibrium may not exist for such games and therefore we introduce the notion of best approximate solution…
While Nash equilibrium has emerged as the central game-theoretic solution concept, many important games contain several Nash equilibria and we must determine how to select between them in order to create real strategic agents. Several Nash…
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,…
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,…
We present two distributed algorithms for the computation of a generalized Nash equilibrium in monotone games. The first algorithm follows from a forward-backward-forward operator splitting, while the second, which requires the…
This work studies Nash equilibrium seeking for a class of stochastic aggregative games, where each player has an expectation-valued objective function depending on its local strategy and the aggregate of all players' strategies. We propose…
We consider seeking generalized Nash equilibria (GNE) for noncooperative games with coupled nonlinear constraints over networks. We first revisit a well-known gradientplay dynamics from a passivity-based perspective, and address that the…
We consider multi-agent decision making where each agent optimizes its convex cost function subject to individual and coupling constraints. The constraint sets are compact convex subsets of a Euclidean space. To learn Nash equilibria, we…
We propose a reinforcement learning algorithm for stationary mean-field games, where the goal is to learn a pair of mean-field state and stationary policy that constitutes the Nash equilibrium. When viewing the mean-field state and the…