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We provide a criterion for determining the winner in two-player win-lose alternating-move games on trees, in terms of the Hausdorff dimension of the target set. We focus our study on special cases, including the Gale-Stewart game on the…

Dynamical Systems · Mathematics 2026-05-14 Itamar Bellaïche , Auriel Rosenzweig

We introduce quantitative reductions, a novel technique for structuring the space of quantitative games and solving them that does not rely on a reduction to qualitative games. We show that such reductions exhibit the same desirable…

Computer Science and Game Theory · Computer Science 2020-03-25 Alexander Weinert

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

Parity games play a central role in model checking and satisfiability checking. Solving parity games is computationally expensive, among others due to the size of the games, which, for model checking problems, can easily contain $10^9$…

Logic in Computer Science · Computer Science 2016-03-22 S. Cranen , J. J. A. Keiren , T. A. C. Willemse

Traditional coding theory guarantees valid decoding only if a minority of symbols are adversarially manipulated. In contrast, the game of coding framework ensures reliable decoding, even in the presence of an adversarial majority. This…

Information Theory · Computer Science 2026-04-13 Hanzaleh Akbari Nodehi , Parsa Moradi , Soheil Mohajer , Mohammad Ali Maddah-Ali

We address the problem of solving parity games with imperfect information on finite graphs of bounded structural complexity. It is a major open problem whether parity games with perfect information can be solved in PTIME. Restricting the…

Computer Science and Game Theory · Computer Science 2017-03-03 Bernd Puchala , Roman Rabinovich

This paper presents a new lower bound for the discrete strategy improvement algorithm for solving parity games due to Voege and Jurdziski. First, we informally show which structures are difficult to solve for the algorithm. Second, we…

Computer Science and Game Theory · Computer Science 2009-01-20 Oliver Friedmann

The Cops and Robber game is played on undirected finite graphs. $k$ cops and one robber are positioned on vertices and take turn in moving along edges. The cops win if, after a move, a cop and the robber are on the same vertex. A graph is…

Combinatorics · Mathematics 2011-11-10 Dirk Oliver Theis

In this paper I study the natural selection between two games to determine, which game will dominate in the community as a result of natural selection. The formalization of this question in the form of a parametrized game and the…

Populations and Evolution · Quantitative Biology 2024-09-25 Georgiy Karev

We introduce a single-winner perspective on voting on matchings, in which voters have preferences over possible matchings in a graph, and the goal is to select a single collectively desirable matching. Unlike in classical matching problems,…

Computer Science and Game Theory · Computer Science 2026-01-28 Niclas Boehmer , Jessica Dierking

We study the problem of solving matrix games of the form $\min_{\mathbf{p}\in\Delta}\max_{\mathbf{w}\in\mathcal{W}}\mathbf{p}^{\top}A\mathbf{w}$, where $A$ is a matrix and $\Delta$ is the probability simplex. This problem encapsulates…

Computer Science and Game Theory · Computer Science 2026-02-10 Guy Kornowski , Ohad Shamir

Generalized Geography is a combinatorial game played on a directed graph. Players take turns moving a token from vertex to vertex, deleting a vertex after moving the token away from it. A player unable to move loses. It is well known that…

Computational Complexity · Computer Science 2021-08-24 Nathan Fox , Carson Geissler

We consider planning problems for graphs, Markov decision processes (MDPs), and games on graphs. While graphs represent the most basic planning model, MDPs represent interaction with nature and games on graphs represent interaction with an…

Data Structures and Algorithms · Computer Science 2018-04-20 Krishnendu Chatterjee , Wolfgang Dvořák , Monika Henzinger , Alexander Svozil

Arc-Kayles is a game where two players alternate removing two adjacent vertices until no move is left, the winner being the player who played the last move. Introduced in 1978, its computational complexity is still open. More recently,…

Combinatorics · Mathematics 2025-11-24 Kyle Burke , Antoine Dailly , Nacim Oijid

Balanced knockout tournaments are ubiquitous in sports competitions and are also used in decision-making and elections. The traditional computational question, that asks to compute a draw (optimal draw) that maximizes the winning…

Computer Science and Game Theory · Computer Science 2016-04-19 Krishnendu Chatterjee , Rasmus Ibsen-Jensen , Josef Tkadlec

We define a general framework of partition games for formulating two-player pebble games over finite structures. We show that one particular such game, which we call the invertible-map game, yields a family of polynomial-time approximations…

Logic in Computer Science · Computer Science 2015-03-20 Anuj Dawar , Bjarki Holm

We investigate games played between Maker and Breaker on an infinite complete graph whose vertices are coloured with colours from a given set, each colour appearing infinitely often. The players alternately claim edges, Makers aim being to…

Combinatorics · Mathematics 2023-04-26 Nathan Bowler , Marit Emde , Florian Gut

In two-player games on graphs, the players move a token through a graph to produce an infinite path, which determines the winner or payoff of the game. Such games are central in formal verification since they model the interaction between a…

Computer Science and Game Theory · Computer Science 2020-01-28 Guy Avni , Thomas A. Henzinger , Rasmus Ibsen-Jensen

Eternal vertex cover problem is a variant of the classical vertex cover problem modeled as a two player attacker-defender game. Computing eternal vertex cover number of graphs is known to be NP-hard in general and the complexity status of…

Discrete Mathematics · Computer Science 2022-01-19 Jasine Babu , K. Murali Krishnan , Veena Prabhakaran , Nandini J. Warrier

In the past three decades, deductive games have become interesting from the algorithmic point of view. Deductive games are two players zero sum games of imperfect information. The first player, called "codemaker", chooses a secret code and…

Data Structures and Algorithms · Computer Science 2013-03-27 Mourad El Ouali , Volkmar Sauerland