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Zero-sum stochastic games generalize the notion of Markov Decision Processes (i.e. controlled Markov chains, or stochastic dynamic programming) to the 2-player competitive case : two players jointly control the evolution of a state…

Optimization and Control · Mathematics 2019-05-17 Jérôme Renault

Graph games are fundamental in strategic reasoning of multi-agent systems and their environments. We study a new family of graph games which combine stochastic environmental uncertainties and auction-based interactions among the agents,…

Computer Science and Game Theory · Computer Science 2024-12-30 Guy Avni , Martin Kurečka , Kaushik Mallik , Petr Novotný , Suman Sadhukhan

We formalize the problem of maximizing the mean-payoff value with high probability while satisfying a parity objective in a Markov decision process (MDP) with unknown probabilistic transition function and unknown reward function. Assuming…

Artificial Intelligence · Computer Science 2018-08-24 Jan Křetínský , Guillermo A. Pérez , Jean-François Raskin

We develop value iteration-based algorithms to solve in a unified manner different classes of combinatorial zero-sum games with mean-payoff type rewards. These algorithms rely on an oracle, evaluating the dynamic programming operator up to…

Computer Science and Game Theory · Computer Science 2024-11-12 Xavier Allamigeon , Stéphane Gaubert , Ricardo D. Katz , Mateusz Skomra

We consider a dynamic programming (DP) approach to approximately solving an infinite-horizon constrained Markov decision process (CMDP) problem with a fixed initial-state for the expected total discounted-reward criterion with a…

Optimization and Control · Mathematics 2023-08-08 Hyeong Soo Chang

Mean-payoff games (MPGs) are infinite duration two-player zero-sum games played on weighted graphs. Under the hypothesis of perfect information, they admit memoryless optimal strategies for both players and can be solved in…

Logic in Computer Science · Computer Science 2015-04-14 Paul Hunter , Guillermo A. Pérez , Jean-François Raskin

Value iteration is a commonly used and empirically competitive method in solving many Markov decision process problems. However, it is known that value iteration has only pseudo-polynomial complexity in general. We establish a somewhat…

Artificial Intelligence · Computer Science 2013-01-07 Omid Madani

We consider Markov Decision Processes (MDPs) with mean-payoff parity and energy parity objectives. In system design, the parity objective is used to encode \omega-regular specifications, and the mean-payoff and energy objectives can be used…

Computer Science and Game Theory · Computer Science 2011-04-18 Krishnendu Chatterjee , Laurent Doyen

The paper proposes a natural measure space of zero-sum perfect information games with upper semicontinuous payoffs. Each game is specified by the game tree, and by the assignment of the active player and of the capacity to each node of the…

Computer Science and Game Theory · Computer Science 2021-04-22 János Flesch , Arkadi Predtetchinski , Ville Suomala

We consider dynamic programming problems with a large time horizon, and give sufficient conditions for the existence of the uniform value. As a consequence, we obtain an existence result when the state space is precompact, payoffs are…

Optimization and Control · Mathematics 2009-04-20 Jérôme Renault

This paper is concerned with two-person dynamic zero-sum games. Let games for some family have common dynamics, running costs and capabilities of players, and let these games differ in densities only. We show that the Dynamic Programming…

Optimization and Control · Mathematics 2017-09-26 Dmitry Khlopin

Markov decision processes (MDP) are a well-established model for sequential decision-making in the presence of probabilities. In robust MDP (RMDP), every action is associated with an uncertainty set of probability distributions, modelling…

Artificial Intelligence · Computer Science 2024-12-16 Tobias Meggendorfer , Maximilian Weininger , Patrick Wienhöft

We consider two-player games played on weighted directed graphs with mean-payoff and total-payoff objectives, two classical quantitative objectives. While for single-dimensional games the complexity and memory bounds for both objectives…

Computer Science and Game Theory · Computer Science 2014-11-04 Krishnendu Chatterjee , Laurent Doyen , Mickael Randour , Jean-François Raskin

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

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

The paper is devoted to dynamic games. We consider a general enough framework, which is not limited to e.g. differential games and could accommodate both discrete and continuous time. Assuming common dynamics, we study two game families…

Optimization and Control · Mathematics 2018-04-25 Dmitry Khlopin

This paper considers mean field games in a multi-agent Markov decision process (MDP) framework. Each player has a continuum state and binary action. By active control, a player can bring its state to a resetting point. All players are…

Optimization and Control · Mathematics 2017-01-25 Minyi Huang , Yan Ma

In game theory, players have continuous expected payoff functions and can use fixed point theorems to locate equilibria. This optimization method requires that players adopt a particular type of probability measure space. Here, we introduce…

Optimization and Control · Mathematics 2007-05-23 Michael J. Gagen , Kae Nemoto

We prove that zero-sum Dynkin games in continuous time with partial and asymmetric information admit a value in randomised stopping times when the stopping payoffs of the players are general \cadlag measurable processes. As a by-product of…

Probability · Mathematics 2022-06-08 Tiziano De Angelis , Nikita Merkulov , Jan Palczewski

A valuation for a player in a game in extensive form is an assignment of numeric values to the players moves. The valuation reflects the desirability moves. We assume a myopic player, who chooses a move with the highest valuation.…

Machine Learning · Computer Science 2007-05-23 Philippe Jehiel , Dov Samet