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Solving parity games is a major building block for numerous applications in reactive program verification and synthesis. While they can be solved efficiently in practice, no known approach has a polynomial worst-case runtime complexity. We…

Computer Science and Game Theory · Computer Science 2023-07-28 Tobias Hecking , Swathy Muthukrishnan , Alexander Weinert

We initiate the study of the phantom version of Maker-Breaker positional games. In a phantom game, the moves of one of the players are hidden from the other player, who still has the complete information. We look at the biased $(a:b)$…

Combinatorics · Mathematics 2025-07-31 Dennis Clemens , Fabian Hamann , Mirjana Mikalački , Yannick Mogge , Miloš Stojaković

The classical Maker-Breaker positional game is played on a board which is a hypergraph $\mathcal{H}$, with two players, Maker and Breaker, alternately claiming vertices of $\mathcal{H}$ until all the vertices are claimed. When the game…

Discrete Mathematics · Computer Science 2026-01-15 Guillaume Bagan , Quentin Deschamps , Florian Galliot , Mirjana Mikalački , Nacim Oijid

We study two positional games played on hypergraphs, whose edges may be interpreted as winning sets. Two players take turns picking a previously unpicked vertex of the hypergraph. We say a player fills an edge if that player has picked all…

Discrete Mathematics · Computer Science 2026-04-14 Florian Galliot

Reachability games are two-player games played on a graph, where the objective of $\texttt{REACH}$ player is to reach the target set whereas the objective of $\texttt{SAFE}$ player is to stay away from the target set. Reachability games…

Artificial Intelligence · Computer Science 2026-05-12 Krishnendu Chatterjee , Ehsan Kafshdar Goharshady , Mehrdad Karrabi , Maximilian Seeliger , Đorđe Žikelić

We introduce and study a Maker-Breaker type game in which the issue is to create or avoid two disjoint dominating sets in graphs without isolated vertices. We prove that the maker has a winning strategy on all connected graphs if the game…

Combinatorics · Mathematics 2014-11-20 Csilla Bujtás , Zsolt Tuza

Colonel Blotto games with discrete strategy spaces effectively illustrate the intricate nature of multidimensional strategic reasoning. This paper studies the equilibrium set of such games where, in line with prior experimental work, the…

Computer Science and Game Theory · Computer Science 2024-03-28 Christian Ewerhart , Stanisław Kaźmierowski

This paper studies a language-based opacity enforcement in a two-player, zero-sum game on a graph. In this game, player 1 (P1) wins if it can achieve a secret temporal goal described by the language of a finite automaton, no matter what…

Systems and Control · Electrical Eng. & Systems 2023-04-05 Chongyang Shi , Abhishek N. Kulkarni , Hazhar Rahmani , Jie Fu

We present a new game, Dots & Polygons, played on a planar point set. Players take turns connecting two points, and when a player closes a (simple) polygon, the player scores its area. We show that deciding whether the game can be won from…

Computational Geometry · Computer Science 2020-05-27 Kevin Buchin , Mart Hagedoorn , Irina Kostitsyna , Max van Mulken , Jolan Rensen , Leo van Schooten

We introduce a general framework for positional games in which players score points by claiming a prescribed portion of each winning set, extending the notion of scoring Maker-Breaker games. In the scoring variant, Maker gains a point by…

Discrete Mathematics · Computer Science 2026-03-06 Eric Duchêne , Valentin Gledel , Miloš Stojaković

We introduce a two-player game, in which each player extends a given sequence by picking a free element in a domain D of the real line. The aim of the players is to control the parity of the number of transpositions necessary to put the…

Combinatorics · Mathematics 2009-04-06 Elise Janvresse , Steve Kalikow , Thierry De La Rue

Partial methods play an important role in formal methods and beyond. Recently such methods were developed for parity games, where polynomial-time partial solvers decide the winners of a subset of nodes. We investigate here how effective…

Logic in Computer Science · Computer Science 2016-09-15 Patrick Ah-Fat , Michael Huth

The $(m,b)$ Maker-Breaker percolation game on $(\mathbb{Z}^2)_p$, introduced by Day and Falgas-Ravry, is played in the following way. Before the game starts, each edge of $\mathbb{Z}^2$ is removed independently with probability $1-p$. After…

Probability · Mathematics 2024-02-28 Vojtěch Dvořák , Adva Mond , Victor Souza

The number of quantifiers needed to express first-order properties is captured by two-player combinatorial games called multi-structural (MS) games. We play these games on linear orders and strings, and introduce a technique we call…

Logic in Computer Science · Computer Science 2024-04-08 Marco Carmosino , Ronald Fagin , Neil Immerman , Phokion Kolaitis , Jonathan Lenchner , Rik Sengupta , Ryan Williams

We study \emph{partial-information} two-player turn-based games on graphs with omega-regular objectives, when the partial-information player has \emph{limited memory}. Such games are a natural formalization for reactive synthesis when the…

Formal Languages and Automata Theory · Computer Science 2020-02-19 Dhananjay Raju , Rüdiger Ehlers , Ufuk Topcu

A cellular game is a dynamical system in which cells, placed in some discrete structure, are regarded as playing a game with their immediate neighbors. Individual strategies may be either deterministic or stochastic. Strategy success is…

adap-org · Physics 2008-02-03 Lenore Levine

We consider some biased Maker-Breaker games. Starting with the complete $k$-uniform hypergraph on $n$ vertices, at each turn Maker claims one edge, and then Breaker claims $b$ edges. Maker's goal is to obtain a set of edges having some…

Combinatorics · Mathematics 2025-09-04 Patrick Bennett , Alan Frieze , Wesley Pegden

Iterated coopetitive games capture the situation when one must efficiently balance between cooperation and competition with the other agents over time in order to win the game (e.g., to become the player with highest total utility).…

Computer Science and Game Theory · Computer Science 2022-03-11 Shivakumar Mahesh , Nicholas Bishop , Le Cong Dinh , Long Tran-Thanh

In a monotonic sequence game, two players alternately choose elements of a sequence from some fixed ordered set. The game ends when the resulting sequence contains either an ascending subsequence of length a or a descending one of length d.…

Combinatorics · Mathematics 2007-05-23 M. Albert , R. Aldred , M. Atkinson , C. Handley , D. Holton , D. McCaughan , B. Sagan

J. Beck has shown that if two players alternately select previously unchosen points from the plane, Player 1 can always build a congruent copy of any given finite goal set G, in spite of Player 2's efforts to stop him. We give a finite goal…

Combinatorics · Mathematics 2011-01-25 Wesley Pegden