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We investigate mean field game systems under invariance conditions for the state space, otherwise called {\it viability conditions} for the controlled dynamics. First we analyze separately the Hamilton-Jacobi and the Fokker-Planck…

Analysis of PDEs · Mathematics 2019-03-18 Alessio Porretta , Michele Ricciardi

We consider a two-player zero-sum stochastic differential game in which one of the players has a private information on the game. Both players observe each other, so that the non-informed player can try to guess his missing information. Our…

Probability · Mathematics 2011-06-15 Christine Grün

In this paper, we investigate the robustness of stationary mean-field equilibria in the presence of model uncertainties, specifically focusing on infinite-horizon discounted cost functions. To achieve this, we initially establish…

Systems and Control · Electrical Eng. & Systems 2026-04-10 Uğur Aydın , Naci Saldi

We study the problem of characterizing the set of games that are consistent with observed equilibrium play. Our contribution is to develop and analyze a new methodology based on convex optimization to address this problem for many classes…

Computer Science and Game Theory · Computer Science 2017-03-23 Juba Ziani , Venkat Chandrasekaran , Katrina Ligett

The problem of computing the smallest fixed point of an order-preserving map arises in the study of zero-sum positive stochastic games. It also arises in static analysis of programs by abstract interpretation. In this context, the discount…

Optimization and Control · Mathematics 2014-02-04 Assalé Adjé , Stéphane Gaubert , Eric Goubault

This paper investigates the discrete-time asynchronous games in which noncooperative agents seek to minimize their individual cost functions. Building on the assumption of partial asynchronism, i.e., each agent updates at least once within…

Optimization and Control · Mathematics 2025-08-13 Zifan Wang , Xinlei Yi , Michael M. Zavlanos , Karl H. Johansson

We introduce quantitative reductions, a novel technique for structuring the space of quantitative games and solving them that does not rely on a reduction to qualitative games. We show that such reductions exhibit the same desirable…

Computer Science and Game Theory · Computer Science 2020-03-25 Alexander Weinert

Financial markets are often driven by latent factors which traders cannot observe. Here, we address an algorithmic trading problem with collections of heterogeneous agents who aim to perform optimal execution or statistical arbitrage, where…

Mathematical Finance · Quantitative Finance 2019-04-02 Philippe Casgrain , Sebastian Jaimungal

For a class of finite horizon first order mean field games and associated N-player games, we give a simple proof of convergence of symmetric N-player Nash equilibria in distributed open-loop strategies to solutions of the mean field game in…

Optimization and Control · Mathematics 2019-03-11 Markus Fischer , Francisco J. Silva

We consider finite horizon stochastic mean field games in which the state space is a network. They are described by a system coupling a backward in time Hamilton-Jacobi-Bellman equation and a forward in time Fokker-Planck equation. The…

Analysis of PDEs · Mathematics 2019-03-08 Yves Achdou , Manh-Khang Dao , Olivier Ley , Nicoletta Tchou

We consider two classes of constrained finite state-action stochastic games. First, we consider a two player nonzero sum single controller constrained stochastic game with both average and discounted cost criterion. We consider the same…

Optimization and Control · Mathematics 2012-06-11 Vikas Vikram Singh , N. Hemachandra

In this paper, we consider mean-field games where the interaction of each player with the mean-field takes into account not only the states of the players but also their collective behavior, To do so, we develop a random variable framework…

Analysis of PDEs · Mathematics 2015-06-23 Diogo A. Gomes , Vardan K. Voskanyan

The numbers game is a one-player game played on a finite simple graph with certain "amplitudes" assigned to its edges and with an initial assignment of real numbers to its nodes. The moves of the game successively transform the numbers at…

Combinatorics · Mathematics 2008-10-31 Robert G. Donnelly

It is well known that the (unique) value of a stochastic control problem or a two person zero sum game under Isaacs condition can be characterized through a PDE driven by the Hamiltonian. Our goal of this paper is to extend this classical…

Optimization and Control · Mathematics 2024-08-20 Bixing Qiao , Jianfeng Zhang

The numbers game is a one-player game played on a finite simple graph with certain "amplitudes" assigned to its edges and with an initial assignment of real numbers to its nodes. The moves of the game successively transform the numbers at…

Combinatorics · Mathematics 2008-10-31 Robert G. Donnelly , Kimmo Eriksson

We investigate a linear quadratic stochastic zero-sum game where two players lobby a political representative to invest in a wind turbine farm. Players are time-inconsistent because they discount performance with a non-constant rate. Our…

General Economics · Economics 2023-09-04 Ali Lazrak , Hanxiao Wang , Jiongmin Yong

We present a deterministic algorithm, solving discounted games with $n$ nodes in $n^{O(1)}\cdot (2 + \sqrt{2})^n$-time. For bipartite discounted games our algorithm runs in $n^{O(1)}\cdot 2^n$-time. Prior to our work no deterministic…

Data Structures and Algorithms · Computer Science 2020-10-27 Alexander Kozachinskiy

In a mean field game of controls, players seek to minimize a cost that depends on the joint distribution of players' states and controls. We consider an ergodic problem for second-order mean field games of controls with state constraints,…

Analysis of PDEs · Mathematics 2026-04-10 Jameson Graber , Kyle Rosengartner

We introduce a way to parameterize automata and games on finite graphs with natural numbers. The parameters are accessed essentially by allowing counting down from the parameter value to 0 and branching depending on whether 0 has been…

Computer Science and Game Theory · Computer Science 2018-09-11 Arno Pauly

The paper deals with a zero-sum differential game in which the dynamical system is described by a fractional differential equation with the Caputo derivative of an order $\alpha \in (0, 1).$ The goal of the first (second) player is to…

Optimization and Control · Mathematics 2019-08-06 Mikhail Gomoyunov