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Related papers: General limit value in zero-sum stochastic games

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In a mean-payoff parity game, one of the two players aims both to achieve a qualitative parity objective and to minimize a quantitative long-term average of payoffs (aka. mean payoff). The game is zero-sum and hence the aim of the other…

Computer Science and Game Theory · Computer Science 2020-01-15 Laure Daviaud , Marcin Jurdzinski , Ranko Lazic

We prove in a dynamic programming framework that uniform convergence of the finite horizon values implies that asymptotically the average accumulated payoff is constant on optimal trajectories. We analyze and discuss several possible…

Optimization and Control · Mathematics 2010-12-24 Sylvain Sorin , Xavier Venel , Guillaume Vigeral

This work is mainly concerned with the so-called limit theory for mean-field games. Adopting the weak formulation paradigm put forward by Carmona and Lacker, we consider a fully non-Markovian setting allowing for drift control and…

Probability · Mathematics 2023-12-25 Dylan Possamaï , Ludovic Tangpi

We study two-player zero-sum stochastic games, and propose a form of independent learning dynamics called Doubly Smoothed Best-Response dynamics, which integrates a discrete and doubly smoothed variant of the best-response dynamics into…

Computer Science and Game Theory · Computer Science 2023-03-07 Zaiwei Chen , Kaiqing Zhang , Eric Mazumdar , Asuman Ozdaglar , Adam Wierman

Many high-stakes decision-making problems, such as those found within cybersecurity and economics, can be modeled as competitive resource allocation games. In these games, multiple players must allocate limited resources to overcome their…

Computer Science and Game Theory · Computer Science 2024-01-10 N'yoma Diamond , Fabricio Murai

The classical, complete-information two-player games assume that the problem data (in particular the payoff matrix) is known exactly by both players. In a now famous result, Nash has shown that any such game has an equilibrium in mixed…

Computer Science and Game Theory · Computer Science 2015-12-11 Nicolas Loizou

We introduce a new non-zero-sum game of optimal stopping with asymmetric exercise opportunities. Given a stochastic process modelling the value of an asset, one player observes and can act on the process continuously, while the other player…

Probability · Mathematics 2024-05-16 José Luis Pérez , Neofytos Rodosthenous , Kazutoshi Yamazaki

Schmidt's game is a powerful tool for studying properties of certain sets which arise in Diophantine approximation theory, number theory, and dynamics. Recently, many new results have been proven using this game. In this paper we address…

Logic · Mathematics 2019-02-20 Lior Fishman , Tue Ly , David S. Simmons

Linear system games are a generalization of Mermin's magic square game introduced by Cleve and Mittal. They show that perfect strategies for linear system games in the tensor-product model of entanglement correspond to finite-dimensional…

Quantum Physics · Physics 2017-02-01 Richard Cleve , Li Liu , William Slofstra

Semidefinite programming can be considered over any real closed field, including fields of Puiseux series equipped with their nonarchimedean valuation. Nonarchimedean semidefinite programs encode parametric families of classical…

Optimization and Control · Mathematics 2018-02-22 Xavier Allamigeon , Stéphane Gaubert , Ricardo D. Katz , Mateusz Skomra

We propose a novel algorithm for the solution of mean-payoff games that merges together two seemingly unrelated concepts introduced in the context of parity games, small progress measures and quasi dominions. We show that the integration of…

Logic in Computer Science · Computer Science 2019-07-16 Massimo Benerecetti , Daniele Dell'Erba , Fabio Mogavero

In this paper, we investigate a partially observable zero sum games where the state process is a discrete time Markov chain. We consider a general utility function in the optimization criterion. We show the existence of value for both…

Optimization and Control · Mathematics 2022-11-16 Arnab Bhabak , Subhamay saha

n infinite two-player zero-sum game with a Borel winning set, in which the opponent's actions are monitored eventually but not necessarily immediately after they are played, is determined. The proof relies on a representation of the game as…

Logic · Mathematics 2011-07-06 Eran Shmaya

The convexification numerical method with the rigorously established global convergence property is constructed for a problem for the Mean Field Games System of the second order. This is the problem of the retrospective analysis of a game…

Numerical Analysis · Mathematics 2023-06-30 Michael V. Klibanov , Jingzhi Li , Zhipeng Yang

Function approximation (FA) has been a critical component in solving large zero-sum games. Yet, little attention has been given towards FA in solving \textit{general-sum} extensive-form games, despite them being widely regarded as being…

Computer Science and Game Theory · Computer Science 2023-04-04 Chun Kai Ling , J. Zico Kolter , Fei Fang

Two-player zero-sum games are a well-established model for synthesising controllers that optimise some performance criterion. In such games one player represents the controller, while the other describes the (adversarial) environment, and…

Computer Science and Game Theory · Computer Science 2010-06-04 Marta Kwiatkowska , Gethin Norman , Ashutosh Trivedi

We consider a dynamic programming problem with arbitrary state space and bounded rewards. Is it possible to define in an unique way a limit value for the problem, where the "patience" of the decision-maker tends to infinity ? We consider,…

Optimization and Control · Mathematics 2013-01-04 Jérôme Renault

We study graphs and two-player games in which rewards are assigned to states, and the goal of the players is to satisfy or dissatisfy certain property of the generated outcome, given as a mean payoff property. Since the notion of…

Logic in Computer Science · Computer Science 2016-04-22 Tomáš Brázdil , Vojtěch Forejt , Antonín Kučera , Petr Novotný

In this paper, we introduce discrete-time linear mean-field games subject to an infinite-horizon discounted-cost optimality criterion. The state space of a generic agent is a compact Borel space. At every time, each agent is randomly…

Systems and Control · Electrical Eng. & Systems 2023-01-18 Naci Saldi

We consider a mean field game describing the limit of a stochastic differential game of $N$-players whose state dynamics are subject to idiosyncratic and common noise and that can be absorbed when they hit a prescribed region of the state…

Probability · Mathematics 2022-05-25 Matteo Burzoni , Luciano Campi