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We study parity games in which one of the two players controls only a small number $k$ of nodes and the other player controls the $n-k$ other nodes of the game. Our main result is a fixed-parameter algorithm that solves bipartite parity…

Computational Complexity · Computer Science 2015-12-12 Matthias Mnich , Heiko Röglin , Clemens Rösner

Two-player zero-sum "graph games" are a central model, which proceeds as follows. A token is placed on a vertex of a graph, and the two players move it to produce an infinite "play", which determines the winner or payoff of the game.…

Computer Science and Game Theory · Computer Science 2022-11-28 Guy Avni , Ismael Jecker , Djordje Zikelic

We study infinite two-player win/lose games $(A,B,W)$ where $A,B$ are finite and $W \subseteq (A \times B)^\omega$. At each round Player 1 and Player 2 concurrently choose one action in $A$ and $B$, respectively. Player 1 wins iff the…

Computer Science and Game Theory · Computer Science 2021-07-22 Patricia Bouyer , Stéphane Le Roux , Nathan Thomasset

We study a random game in which two players in turn play a fixed number of moves. For each move, there are two possible choices. To each possible outcome of the game we assign a winner in an i.i.d. fashion with a fixed parameter p. In the…

Probability · Mathematics 2024-09-05 Natalia Cardona-Tobón , Anja Sturm , Jan M. Swart

Turn-based discounted-sum games are two-player zero-sum games played on finite directed graphs. The vertices of the graph are partitioned between player 1 and player 2. Plays are infinite walks on the graph where the next vertex is decided…

Computer Science and Game Theory · Computer Science 2024-05-21 Ali Asadi , Krishnendu Chatterjee , Raimundo Saona , Jakub Svoboda

Graph games with {\omega}-regular winning conditions provide a mathematical framework to analyze a wide range of problems in the analysis of reactive systems and programs (such as the synthesis of reactive systems, program repair, and the…

Data Structures and Algorithms · Computer Science 2017-06-16 Krishnendu Chatterjee , Wolfgang Dvořák , Monika Henzinger , Veronika Loitzenbauer

We study two types of two player, perfect information games with no chance moves, played on the edge set of the binomial random graph ${\mathcal G}(n,p)$. In each round of the $(1 : q)$ Waiter-Client Hamiltonicity game, the first player,…

Combinatorics · Mathematics 2017-02-17 Dan Hefetz , Michael Krivelevich , Wei En Tan

Let $(X, \mathcal{F})$ be a hypergraph. The Maker-Breaker game on $(X, \mathcal{F})$ is a combinatorial game between two players, Maker and Breaker. Beginning with Maker, the players take turns claiming vertices from $X$ that have not yet…

Discrete Mathematics · Computer Science 2025-02-28 Finn Orson Koepke

Two standard algorithms for approximately solving two-player zero-sum concurrent reachability games are value iteration and strategy iteration. We prove upper and lower bounds of 2^(m^(Theta(N))) on the worst case number of iterations…

Computer Science and Game Theory · Computer Science 2012-03-02 Kristoffer Arnsfelt Hansen , Rasmus Ibsen-Jensen , Peter Bro Miltersen

We study a combinatorial coloring game between two players, Spoiler and Algorithm, who alternate turns. First, Spoiler places a new token at a vertex in $G$, and Algorithm responds by assigning a color to the new token. Algorithm must…

Combinatorics · Mathematics 2017-12-27 Kevin G. Milans , Michael C. Wigal

In the Maker-Breaker domination game played on a graph $G$, Dominator's goal is to select a dominating set and Staller's goal is to claim a closed neighborhood of some vertex. We study the cases when Staller can win the game. If Dominator…

Combinatorics · Mathematics 2024-02-14 Csilla Bujtás , Pakanun Dokyeesun , Sandi Klavžar

The isolation game is played on a graph $G$ by two players who take turns playing a vertex such that if $X$ is the set of already played vertices, then a vertex can be selected only if it dominates a vertex from a nontrivial component of $G…

Combinatorics · Mathematics 2026-04-02 Csilla Bujtás , Tanja Dravec , Michael A. Henning , Sandi Klavžar

The domination game is an optimization game played by two players, Dominator and Staller, who alternately select vertices in a graph $G$. A vertex is said to be dominated if it has been selected or is adjacent to a selected vertex. Each…

Combinatorics · Mathematics 2023-02-03 Leo Versteegen

Parity games are simple infinite games played on finite graphs with a winning condition that is expressive enough to capture nested least and greatest fixpoints. Through their tight relationship to the modal mu-calculus, they are used in…

Logic in Computer Science · Computer Science 2019-09-18 Tom van Dijk

Two-player graph games have found numerous applications, most notably in the synthesis of reactive systems from temporal specifications, but also in verification. The relevance of infinite-state systems in these areas has lead to…

Logic in Computer Science · Computer Science 2023-11-08 Philippe Heim , Rayna Dimitrova

We consider zero-sum games on infinite graphs, with objectives specified as sets of infinite words over some alphabet of colors. A well-studied class of objectives is the one of $\omega$-regular objectives, due to its relation to many…

Computer Science and Game Theory · Computer Science 2023-06-22 Patricia Bouyer , Mickael Randour , Pierre Vandenhove

In this paper, we study the average case complexity of the Unique Games problem. We propose a natural semi-random model, in which a unique game instance is generated in several steps. First an adversary selects a completely satisfiable…

Data Structures and Algorithms · Computer Science 2011-04-20 Alexandra Kolla , Konstantin Makarychev , Yury Makarychev

The Maker-Breaker domination game (MBD game) is a two-player game played on a graph $G$ by Dominator and Staller. They alternately select unplayed vertices of $G$. The goal of Dominator is to form a dominating set with the set of vertices…

Combinatorics · Mathematics 2025-12-10 Athira Divakaran , Tanja Dravec , Tijo James , Sandi Klavžar , Latha S Nair

In games with a large number of players where players may have overlapping objectives, the analysis of stable outcomes typically depends on player types. A special case is when a large part of the player population consists of imitation…

Computer Science and Game Theory · Computer Science 2010-06-18 Soumya Paul , R. Ramanujam

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