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In this article, we look at a hat-guessing game, in which each player must guess the color of their own hat while only seeing the hats of the other players. We focus on the case of two hat colors and a countably infinite number of players.…

Probability · Mathematics 2025-10-28 Nathaniel Eldredge

We consider two-player turn-based games with zero-reachability and zero-safety objectives generated by extended vector addition systems with states. Although the problem of deciding the winner in such games is undecidable in general, we…

Computer Science and Game Theory · Computer Science 2010-02-15 Tomas Brazdil , Petr Jancar , Antonin Kucera

We prove computational intractability of variants of checkers: (1) deciding whether there is a move that forces the other player to win in one move is NP-complete; (2) checkers where players must always be able to jump on their turn is…

Computational Complexity · Computer Science 2018-06-15 Jeffrey Bosboom , Spencer Congero , Erik D. Demaine , Martin L. Demaine , Jayson Lynch

We define a version of the Ehrenfeucht-Fra\"iss\'e game in the setting of metric model theory and continuous first-order logic and show that the second player having a winning strategy in a game of length $n$ exactly corresponds to being…

Logic · Mathematics 2024-04-26 Åsa Hirvonen , Joni Puljujärvi

We prove the existence and computability of optimal strategies in weighted limit games, zero-sum infinite-duration games with a B\"uchi-style winning condition requiring to produce infinitely many play prefixes that satisfy a given regular…

Computer Science and Game Theory · Computer Science 2020-09-25 Aniello Murano , Sasha Rubin , Martin Zimmermann

In a strong game played on the edge set of a graph G there are two players, Red and Blue, alternating turns in claiming previously unclaimed edges of G (with Red playing first). The winner is the first one to claim all the edges of some…

Discrete Mathematics · Computer Science 2015-07-19 Asaf Ferber , Pascal Pfister

We establish a generic result concerning order independence of a dominance relation on finite games. It allows us to draw conclusions about order independence of various dominance relations in a direct and simple way.

Computer Science and Game Theory · Computer Science 2011-01-06 Krzysztof R. Apt

Blackwell games are infinite games of imperfect information. The two players simultaneously make their moves, and are then informed of each other's moves. Payoff is determined by a Borel measurable function $f$ on the set of possible…

Logic · Mathematics 2009-09-25 Marco R. Vervoort

In tug-of-war, two players compete by moving a counter along edges of a graph, each winning the right to move at a given turn according to the flip of a possibly biased coin. The game ends when the counter reaches the boundary, a fixed…

Probability · Mathematics 2026-02-10 Yujie Fu , Alan Hammond , Gábor Pete

Escalation in games is when agents keep playing forever. Based on formal proofs we claim that if agents assume that resource are infinite, escalation is rational.

Logic in Computer Science · Computer Science 2020-06-29 Pierre Lescanne

The directions of an infinite graph $G$ are a tangle-like description of its ends: they are choice functions that choose compatibly for all finite vertex sets $X\subseteq V(G)$ a component of $G-X$. Although every direction is induced by a…

Combinatorics · Mathematics 2021-01-19 Jan Kurkofka , Ruben Melcher

Positions of chess players in intransitive (rock-paper-scissors) relations are considered. Namely, position A of White is preferable (it should be chosen if choice is possible) to position B of Black, position B of Black is preferable to…

History and Overview · Mathematics 2022-12-22 Alexander Poddiakov

Delay games are two-player games of infinite duration in which one player may delay her moves to obtain a lookahead on her opponent's moves. We consider delay games with winning conditions expressed in weak monadic second order logic with…

Computer Science and Game Theory · Computer Science 2016-01-28 Martin Zimmermann

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 consider games played on an infinite probabilistic arena where the first player aims at satisfying generalized B\"uchi objectives almost surely, i.e., with probability one. We provide a fixpoint characterization of the winning sets and…

Logic in Computer Science · Computer Science 2013-06-13 Nathalie Bertrand , Philippe Schnoebelen

We consider a dynamical approach to sequential games. By restricting the convertibility relation over strategy profiles, we obtain a semi-potential (in the sense of Kukushkin), and we show that in finite games the corresponding restriction…

Computer Science and Game Theory · Computer Science 2016-09-15 Stéphane Le Roux , Arno Pauly

We prove the existence and computability of optimal strategies in weighted limit games, zero-sum infinite-duration games with a B\"uchi-style winning condition requiring to produce infinitely many play prefixes that satisfy a given regular…

Computer Science and Game Theory · Computer Science 2020-09-08 Aniello Murano , Sasha Rubin , Martin Zimmermann

A checkers-like model game with a simplified set of rules is studied through extensive simulations of agents with different expertise and strategies. The introduction of complementary strategies, in a quite general way, provides a tool to…

Artificial Intelligence · Computer Science 2016-08-26 J. Quetzalcóatl Toledo-Marín , Rogelio Díaz-Méndez , Marcelo del Castillo Mussot

Subgame perfect equilibria are specific Nash equilibria in perfect information games in extensive form. They are important because they relate to the rationality of the players. They always exist in infinite games with continuous…

Computer Science and Game Theory · Computer Science 2015-10-01 Stephane Le Roux

We demonstrate the usefulness of adding delay to infinite games with quantitative winning conditions. In a delay game, one of the players may delay her moves to obtain a lookahead on her opponent's moves. We show that determining the winner…

Computer Science and Game Theory · Computer Science 2017-04-21 Martin Zimmermann