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In two-player zero-sum stochastic games, where two competing players make decisions under uncertainty, a pair of optimal strategies is traditionally described by Nash equilibrium and computed under the assumption that the players have…

Optimization and Control · Mathematics 2019-07-30 Yagiz Savas , Mohamadreza Ahmadi , Takashi Tanaka , Ufuk Topcu

We study a class of two-player zero-sum stochastic games known as \textit{blind stochastic games}, where players neither observe the state nor receive any information about it during the game. A central concept for analyzing long-duration…

Optimization and Control · Mathematics 2025-11-24 Krishnendu Chatterjee , David Lurie , Raimundo Saona , Bruno Ziliotto

We present a systematic investigation of the quantum games, constructed using a novel repeated game protocol, when played repeatedly ad infinitum. We focus on establishing that such repeated games -- by virtue of inherent quantum-mechanical…

Quantum Physics · Physics 2024-02-27 Archan Mukhopadhyay , Saikat Sur , Tanay Saha , Shubhadeep Sadhukhan , Sagar Chakraborty

We study continuity properties of stochastic game problems with respect to various topologies on information structures, defined as probability measures characterizing a game. We will establish continuity properties of the value function…

Optimization and Control · Mathematics 2022-11-02 Ian Hogeboom-Burr , Serdar Yüksel

Probabilistic game structures combine both nondeterminism and stochasticity, where players repeatedly take actions simultaneously to move to the next state of the concurrent game. Probabilistic alternating simulation is an important tool to…

Logic in Computer Science · Computer Science 2019-07-10 Chenyi Zhang , Jun Pang

We consider two-player stochastic games played on a finite graph for infinitely many rounds. Stochastic games generalize both Markov decision processes (MDP) by adding an adversary player, and two-player deterministic games by adding…

Computer Science and Game Theory · Computer Science 2022-02-28 Laurent Doyen

We study two-player reachability games on finite graphs. At each state the interaction between the players is concurrent and there is a stochastic Nature. Players also play stochastically. The literature tells us that 1) Player B, who wants…

Computer Science and Game Theory · Computer Science 2021-10-29 Benjamin Bordais , Patricia Bouyer , Stéphane Le Roux

We consider two-player games played in real time on game structures with clocks where the objectives of players are described using parity conditions. The games are \emph{concurrent} in that at each turn, both players independently propose…

Logic in Computer Science · Computer Science 2019-03-14 Krishnendu Chatterjee , Thomas A. Henzinger , Vinayak S. Prabhu

We consider concurrent mean-payoff games, a very well-studied class of two-player (player 1 vs player 2) zero-sum games on finite-state graphs where every transition is assigned a reward between 0 and 1, and the payoff function is the…

Computer Science and Game Theory · Computer Science 2014-10-02 Krishnendu Chatterjee , Rasmus Ibsen-Jensen

We study strategic interaction in data-driven games where players face uncertainty about payoff distributions inferred from finite samples. To model calibrated attitudes toward such uncertainty, we formulate distributionally robust games…

Computer Science and Game Theory · Computer Science 2026-05-28 Bharat Gangwani , Arunesh Sinha

We consider two-player partial-observation stochastic games on finite-state graphs where player 1 has partial observation and player 2 has perfect observation. The winning condition we study are \omega-regular conditions specified as parity…

Logic in Computer Science · Computer Science 2014-01-15 Krishnendu Chatterjee , Laurent Doyen , Sumit Nain , Moshe Y. Vardi

Two-player stochastic games are games with two 2 players and a randomised entity called "nature". A natural question to ask in this framework is the existence of strategies that ensure that an event happens with probability 1 (almost-sure…

Computer Science and Game Theory · Computer Science 2018-06-27 Youssouf Oualhadj , Léo Tible , Daniele Varacca

Stochastic two-player games model systems with an environment that is both adversarial and stochastic. The adversarial part of the environment is modeled by a player (Player 2) who tries to prevent the system (Player 1) from achieving its…

Computer Science and Game Theory · Computer Science 2025-06-11 Laurent Doyen , Pranshu Gaba , Shibashis Guha

We consider two-player games played in real time on game structures with clocks and parity objectives. The games are concurrent in that at each turn, both players independently propose a time delay and an action, and the action with the…

Logic in Computer Science · Computer Science 2008-07-09 Krishnendu Chatterjee , Thomas A. Henzinger , Vinayak Prabhu

Two-player games on graphs are widely studied in formal methods as they model the interaction between a system and its environment. The game is played by moving a token throughout a graph to produce an infinite path. There are several…

Logic in Computer Science · Computer Science 2019-06-10 Guy Avni , Thomas A. Henzinger , Ventsislav Chonev

In this paper we introduce polytopal stochastic games, an extension of two-player, zero-sum, turn-based stochastic games, in which we may have uncertainty over the transition probabilities. In these games the uncertainty over the…

Logic in Computer Science · Computer Science 2025-02-26 Pablo F. Castro , Pedro D'Argenio

We investigate multi-round team competitions between two teams, where each team selects one of its players simultaneously in each round and each player can play at most once. The competition defines an extensive-form game with perfect…

Computer Science and Game Theory · Computer Science 2016-02-25 Kai Jin , Pingzhong Tang , Shiteng Chen

Stochastic timed games (STGs), introduced by Bouyer and Forejt, naturally generalize both continuous-time Markov chains and timed automata by providing a partition of the locations between those controlled by two players (Player Box and…

Logic in Computer Science · Computer Science 2016-07-20 S Akshay , Patricia Bouyer , Shankara Narayanan Krishna , Lakshmi Manasa , Ashutosh Trivedi

We study 2-player turn-based perfect-information stochastic games with countably infinite state space. The players aim at maximizing/minimizing the probability of a given event (i.e., measurable set of infinite plays), such as reachability,…

Computer Science and Game Theory · Computer Science 2017-04-18 Stefan Kiefer , Richard Mayr , Mahsa Shirmohammadi , Dominik Wojtczak

We study the complexity of solving two-player infinite duration games played on a fixed finite graph, where the control of a node is not predetermined but rather assigned randomly. In classic random-turn games, control of each node is…

Computer Science and Game Theory · Computer Science 2026-01-13 Sarvin Bahmani , Rasmus Ibsen-Jensen , Soumyajit Paul , Sven Schewe , Friedrich Slivovsky , Qiyi Tang , Dominik Wojtczak , Shufang Zhu