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Graph games provide the foundation for modeling and synthesis of reactive processes. Such games are played over graphs where the vertices are controlled by two adversarial players. We consider graph games where the objective of the first…

Computer Science and Game Theory · Computer Science 2017-06-21 Krishnendu Chatterjee , Monika Henzinger , Alexander Svozil

We study multiplayer turn-based games played on a finite directed graph such that each player aims at satisfying an omega-regular Boolean objective. Instead of the well-known notions of Nash equilibrium (NE) and subgame perfect equilibrium…

Computer Science and Game Theory · Computer Science 2018-09-12 Thomas Brihaye , Véronique Bruyère , Aline Goeminne , Jean-François Raskin

We transform a Muller game with n vertices into a safety game with (n!)^3 vertices whose solution allows to determine the winning regions of the Muller game and to compute a finite-state winning strategy for one player. This yields a novel…

Logic in Computer Science · Computer Science 2012-10-10 Daniel Neider , Roman Rabinovich , Martin Zimmermann

We study biased {\em orientation games}, in which the board is the complete graph $K_n$, and Maker and Breaker take turns in directing previously undirected edges of $K_n$. At the end of the game, the obtained graph is a tournament. Maker…

Combinatorics · Mathematics 2011-07-12 Ido Ben-Eliezer , Michael Krivelevich , Benny Sudakov

In this paper, we propose a new efficient algorithm to compute the value function for zero-sum stopping games featuring two players with opposing interests. This can be seen as a game version of the ''forward algorithm'' for (one-player)…

Probability · Mathematics 2026-02-03 Nhat-Thang Le

We consider imperfect information stochastic games where we require the players to use pure (i.e. non randomised) strategies. We consider reachability, safety, B\"uchi and co-B\"uchi objectives, and investigate the existence of…

Formal Languages and Automata Theory · Computer Science 2018-03-28 Arnaud Carayol , Christof Löding , Olivier Serre

Game theory is usually considered applied mathematics, but a few game-theoretic results, such as Borel determinacy, were developed by mathematicians for mathematics in a broad sense. These results usually state determinacy, i.e. the…

Logic · Mathematics 2014-05-09 Stéphane Le Roux

Nonzero-sum stochastic differential games with impulse controls offer a realistic and far-reaching modelling framework for applications within finance, energy markets, and other areas, but the difficulty in solving such problems has…

Numerical Analysis · Mathematics 2020-06-29 Diego Zabaljauregui

Mean-payoff games play a central role in quantitative synthesis and verification. In a single-dimensional game a weight is assigned to every transition and the objective of the protagonist is to assure a non-negative limit-average weight.…

Logic in Computer Science · Computer Science 2014-10-22 Yaron Velner

We consider infinite-state turn-based stochastic games of two players, Box and Diamond, who aim at maximizing and minimizing the expected total reward accumulated along a run, respectively. Since the total accumulated reward is unbounded,…

Computer Science and Game Theory · Computer Science 2012-08-09 Tomáš Brázdil , Antonín Kučera , Petr Novotný

We present BL-WoLF, a framework for learnability in repeated zero-sum games where the cost of learning is measured by the losses the learning agent accrues (rather than the number of rounds). The game is adversarially chosen from some…

Computer Science and Game Theory · Computer Science 2009-09-29 Vincent Conitzer , Tuomas Sandholm

We suggest a new algorithm for two-person zero-sum undiscounted stochastic games focusing on stationary strategies. Given a positive real $\epsilon$, let us call a stochastic game $\epsilon$-ergodic, if its values from any two initial…

Computer Science and Game Theory · Computer Science 2015-08-17 Endre Boros , Khaled Elbassioni , Vladimir Gurvich , Kazuhisa Makino

We consider a variant of sequential testing by betting where, at each time step, the statistician is presented with multiple data sources (arms) and obtains data by choosing one of the arms. We consider the composite global null hypothesis…

Methodology · Statistics 2026-03-19 Ricardo J. Sandoval , Ian Waudby-Smith , Michael I. Jordan

A positional game is a game where two players sequentially label vertices of a hypergraph, consisting of a board and a collection of winning sets, with colors assigned to each player until all vertices of the board are claimed. The first…

Combinatorics · Mathematics 2021-09-02 Pranav Avadhanam , Siddhartha G. Jena

We investigate the transfinite game values arising in infinite chess, providing both upper and lower bounds on the supremum of these values---the omega one of chess---with two senses depending on whether one considers only finite positions…

Logic · Mathematics 2014-02-25 C. D. A. Evans , Joel David Hamkins

In this paper, we consider two-player zero-sum matrix and stochastic games and develop learning dynamics that are payoff-based, convergent, rational, and symmetric between the two players. Specifically, the learning dynamics for matrix…

Machine Learning · Computer Science 2024-09-06 Zaiwei Chen , Kaiqing Zhang , Eric Mazumdar , Asuman Ozdaglar , Adam Wierman

Admissibility has been studied for games of infinite duration with Boolean objectives. We extend here this study to games of infinite duration with quantitative objectives. First, we show that, un- der the assumption that optimal worst-case…

Logic in Computer Science · Computer Science 2016-11-29 Romain Brenguier , Guillermo A. Pérez , Jean-François Raskin , Ocan Sankur

Mean payoff stochastic games can be studied by means of a nonlinear spectral problem involving the Shapley operator: the ergodic equation. A solution consists in a scalar, called the ergodic constant, and a vector, called bias. The…

Optimization and Control · Mathematics 2016-05-17 Antoine Hochart

The Maker-Maker convention of positional games is played on a hypergraph whose edges are interpreted as winning sets. Two players take turns picking a previously unpicked vertex, aiming at being first to pick all the vertices of some edge.…

Discrete Mathematics · Computer Science 2025-04-22 Florian Galliot , Jonas Sénizergues

The article introduces a notion of a stochastic game with failure states and proposes two logical systems with modality "coalition has a strategy to transition to a non-failure state with a given probability while achieving a given goal."…

Artificial Intelligence · Computer Science 2019-10-11 Pavel Naumov , Kevin Ros