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We introduce achievement positional games, a convention for positional games which encompasses the Maker-Maker and Maker-Breaker conventions. We consider two hypergraphs, one red and one blue, on the same vertex set. Two players, Left and…

Discrete Mathematics · Computer Science 2026-03-20 Florian Galliot , Jonas Sénizergues

We introduce a way to parameterize automata and games on finite graphs with natural numbers. The parameters are accessed essentially by allowing counting down from the parameter value to 0 and branching depending on whether 0 has been…

Computer Science and Game Theory · Computer Science 2018-09-11 Arno Pauly

In the inference attacks studied in Quantitative Information Flow (QIF), the attacker typically tries to interfere with the system in the attempt to increase its leakage of secret information. The defender, on the other hand, typically…

Cryptography and Security · Computer Science 2018-05-22 Mário S. Alvim , Konstantinos Chatzikokolakis , Yusuke Kawamoto , Catuscia Palamidessi

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

Two-player games on graphs are widely studied in formal methods as they model the interaction between a system and its environment. The game is played by moving a token throughout a graph to produce an infinite path. There are several…

Logic in Computer Science · Computer Science 2019-06-10 Guy Avni , Thomas A. Henzinger , Ventsislav Chonev

In the Maker-Breaker domination game, Dominator and Staller play on a graph $G$ by taking turns in which each player selects a not yet played vertex of $G$. Dominator's goal is to select all the vertices in a dominating set, while Staller…

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

An alternating graph is a directed graph whose vertex set is partitioned into two classes, existential and universal. This forms the basic arena for a plethora of infinite duration two-player games where Player~$\square$ and~$\ocircle$…

Data Structures and Algorithms · Computer Science 2025-08-14 Carlo Comin , Romeo Rizzi

We study the Maker-Breaker $H$-game played on the edge set of the random graph $G_{n,p}$. In this game two players, Maker and Breaker, alternately claim unclaimed edges of $G_{n,p}$, until all the edges are claimed. Maker wins if he claims…

Combinatorics · Mathematics 2014-01-20 Rajko Nenadov , Angelika Steger , Miloš Stojaković

In this paper we introduce and study the domination game on hypergraphs. This is played on a hypergraph $\mathcal{H}$ by two players, namely Dominator and Staller, who alternately select vertices such that each selected vertex enlarges the…

Combinatorics · Mathematics 2017-10-03 Csilla Bujtás , Balázs Patkós , Zsolt Tuza , Máté vizer

Static and dynamic equilibria in noisy binary choice games on graphs are considered. Equations defining static quantal response equilibria (QRE) for binary choice games on graphs with arbitrary topology and noise distribution are written.…

Computer Science and Game Theory · Computer Science 2019-12-23 Andrey Leonidov , Alexey Savvateev , Andrew G. Semenov

In the compulsive gambler process there is a finite set of agents who meet pairwise at random times ($i$ and $j$ meet at times of a rate-$\nu_{ij}$ Poisson process) and, upon meeting, play an instantaneous fair game in which one wins the…

Probability · Mathematics 2014-06-06 David Aldous , Daniel Lanoue , Justin Salez

Given an increasing graph property $\cal F$, the strong Avoider-Avoider $\cal F$ game is played on the edge set of a complete graph. Two players, Red and Blue, take turns in claiming previously unclaimed edges with Red going first, and the…

Computer Science and Game Theory · Computer Science 2025-05-30 Miloš Stojaković , Jelena Stratijev

We study the following combinatorial game played by two players, Alice and Bob, which generalizes the Pizza game considered by Brown, Winkler and others. Given a connected graph G with nonnegative weights assigned to its vertices, the…

Discrete Mathematics · Computer Science 2013-08-07 Josef Cibulka , Jan Kynčl , Viola Mészáros , Rudolf Stolař , Pavel Valtr

We consider a Maker-Breaker type game on the plane, in which each player takes $t$ points on their $t^\textrm{th}$ turn. Maker wins if he obtains $n$ points on a line (in any direction) without any of Breaker's points between them. We show…

Combinatorics · Mathematics 2015-01-08 Joshua Erde , Mark Walters

Zero forcing is a combinatorial game played on a graph where the goal is to start with all vertices unfilled and to change them to filled at minimal cost. In the original variation of the game there were two options. Namely, to fill any one…

Zero forcing is a combinatorial game played on a graph with the ultimate goal of changing the colour of all the vertices at minimal cost. Originally this game was conceived as a one player game, but later a two-player version was devised…

Consider a rooted Galton-Watson tree $T$, to each of whose edges we assign, independently, a weight that equals $+1$ with probability $p_{1}$, $0$ with probability $p_{0}$ and $-1$ with probability $p_{-1}=1-p_{1}-p_{0}$. We play a game on…

Probability · Mathematics 2025-01-16 Sayar Karmakar , Moumanti Podder , Souvik Roy , Soumyarup Sadhukhan

We consider perfect-information reachability stochastic games for 2 players on infinite graphs. We identify a subclass of such games, and prove two interesting properties of it: first, Player Max always has optimal strategies in games from…

Computer Science and Game Theory · Computer Science 2011-06-10 Václav Brožek

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

We introduce the rendezvous game with adversaries. In this game, two players, {\sl Facilitator} and {\sl Disruptor}, play against each other on a graph. Facilitator has two agents, and Disruptor has a team of $k$ agents located in some…

Discrete Mathematics · Computer Science 2021-03-12 Fedor V. Fomin , Petr A. Golovach , Dimitrios M. Thilikos