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In this short note we study a class of multi-player, turn-based games with deterministic state transitions and reachability / safety objectives (this class contains as special cases "classic" two-player reachability and safety games as well…

Computer Science and Game Theory · Computer Science 2018-10-05 Athanasios Kehagias

We study optimal equilibria in multi-player games. An equilibrium is optimal for a player, if her payoff is maximal. A tempting approach to solving this problem is to seek optimal Nash equilibria, the standard form of equilibria where no…

Computer Science and Game Theory · Computer Science 2013-07-09 Anshul Gupta , Sven Schewe

In this paper, we consider discrete-time dynamic games of the mean-field type with a finite number $N$ of agents subject to an infinite-horizon discounted-cost optimality criterion. The state space of each agent is a locally compact Polish…

Systems and Control · Computer Science 2017-01-17 Naci Saldi , Tamer Başar , Maxim Raginsky

In this paper, we study finite-agent linear-quadratic games on graphs. Specifically, we propose a comprehensive framework that extends the existing literature by incorporating heterogeneous and interpretable player interactions. Compared to…

Optimization and Control · Mathematics 2025-11-19 Ruimeng Hu , Jihao Long , Haosheng Zhou

We study dynamic finite-player and mean-field stochastic games within the framework of Markov perfect equilibria (MPE). Our focus is on discrete time and space structures without monotonicity. Unlike their continuous-time analogues,…

Optimization and Control · Mathematics 2025-09-29 Felix Höfer , H. Mete Soner , Atilla Yılmaz

Art heritage cities are popular tourist destinations but for many of them overcrowding is becoming an issue. In this paper, we address the problem of modeling and analytically studying the flow of tourists along the narrow alleys of the…

Optimization and Control · Mathematics 2019-08-09 Fabio Bagagiolo , Silvia Faggian , Rosario Maggistro , Raffaele Pesenti

We consider learning approximate Nash equilibria for discrete-time mean-field games with nonlinear stochastic state dynamics subject to both average and discounted costs. To this end, we introduce a mean-field equilibrium (MFE) operator,…

Systems and Control · Electrical Eng. & Systems 2022-11-11 Berkay Anahtarcı , Can Deha Karıksız , Naci Saldi

We introduce a new mean field kinetic model for systems of rational agents interacting in a game theoretical framework. This model is inspired from non-cooperative anonymous games with a continuum of players and Mean-Field Games. The large…

Mathematical Physics · Physics 2012-12-27 Pierre Degond , Jian-Guo Liu , Christian Ringhofer

We show that in any $n$-player $m$-action normal-form game, we can obtain an approximate equilibrium by sampling any mixed-action equilibrium a small number of times. We study three types of equilibria: Nash, correlated and coarse…

Computer Science and Game Theory · Computer Science 2014-10-21 Yakov Babichenko , Siddharth Barman , Ron Peretz

This paper studies a discrete-time major-minor mean field game of stopping where the major player can choose either an optimal control or stopping time. We look for the relaxed equilibrium as a randomized stopping policy, which is…

Optimization and Control · Mathematics 2025-10-13 Xiang Yu , Jiacheng Zhang , Keyu Zhang , Zhou Zhou

We consider a general-sum N-player linear-quadratic game with stochastic dynamics over a finite horizon and prove the global convergence of the natural policy gradient method to the Nash equilibrium. In order to prove the convergence of the…

Optimization and Control · Mathematics 2022-08-16 Ben Hambly , Renyuan Xu , Huining Yang

We study turn-based quantitative multiplayer non zero-sum games played on finite graphs with reachability objectives. In such games, each player aims at reaching his own goal set of states as soon as possible. A previous work on this model…

Computer Science and Game Theory · Computer Science 2019-03-14 Thomas Brihaye , Véronique Bruyère , Julie De Pril , Hugo Gimbert

We discuss a natural game of competition and solve the corresponding mean field game with \emph{common noise} when agents' rewards are \emph{rank dependent}. We use this solution to provide an approximate Nash equilibrium for the finite…

Probability · Mathematics 2016-10-18 Erhan Bayraktar , Yuchong Zhang

We investigate an infinite-horizon time-inconsistent mean-field game (MFG) in a discrete time setting. We first present a classic equilibrium for the MFG and its associated existence result. This classic equilibrium aligns with the…

Optimization and Control · Mathematics 2024-09-13 Erhan Bayraktar , Zhenhua Wang

We study a mean field optimal control problem with general non-Markovian dynamics, including both common noise and jumps. We show that its minimizers are Nash equilibria of an associated mean field game of controls. These types of games are…

Optimization and Control · Mathematics 2025-05-12 Felix Höfer , H. Mete Soner

This paper proposes and studies a class of discrete-time finite-time-horizon Stackelberg mean-field games, with one leader and an infinite number of identical and indistinguishable followers. In this game, the objective of the leader is to…

Optimization and Control · Mathematics 2022-10-11 Xin Guo , Anran Hu , Jiacheng Zhang

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…

Computer Science and Game Theory · Computer Science 2026-03-19 Mahdis Rabbani , Navid Mojahed , Shima Nazari

We prove that in a normal form n-player game with m actions for each player, there exists an approximate Nash equilibrium where each player randomizes uniformly among a set of O(log(m) + log(n)) pure strategies. This result induces an…

Computer Science and Game Theory · Computer Science 2013-07-19 Yakov Babichenko , Ron Peretz

We consider static finite-player network games and their continuum analogs, graphon games. Existence and uniqueness results are provided, as well as convergence of the finite-player network game optimal strategy profiles to their analogs…

Optimization and Control · Mathematics 2019-11-26 Rene Carmona , Daniel Cooney , Christy Graves , Mathieu Lauriere

This paper is concerned with non-zero sum differential games of mean-field stochastic differential equations with partial information and convex control domain. First, applying the classical convex variations, we obtain stochastic maximum…

Optimization and Control · Mathematics 2016-01-11 Hua Xiao , Shuaiqi Zhang