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Related papers: A Search Game on a Hypergraph with Booby Traps

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Consider a two-person zero-sum search game between a hider and a searcher. The hider hides among $n$ discrete locations, and the searcher successively visits individual locations until finding the hider. Known to both players, a search at…

Machine Learning · Statistics 2021-03-18 Jake Clarkson , Kyle Y. Lin , Kevin D. Glazebrook

The graph grabbing game is played on a non-negatively weighted connected graph by Alice and Bob who alternately claim a non-cut vertex from the remaining graph, where Alice plays first, to maximize the weights on their respective claimed…

Combinatorics · Mathematics 2020-07-24 Sopon Boriboon , Teeradej Kittipassorn

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

A divisible treasure is located at a node $H$ of a network. From a given start node a group of $n$ Searchers each seek to reach $H$ first, dividing the treasure equally with the other first arrivers. This type of search game is called…

Computer Science and Game Theory · Computer Science 2026-05-20 Steve Alpern , Mark Broom

The localization game is a two player combinatorial game played on a graph $G=(V,E)$. The cops choose a set of vertices $S_1 \subseteq V$ with $|S_1|=k$. The robber then chooses a vertex $v \in V$ whose location is hidden from the cops, but…

Combinatorics · Mathematics 2022-09-07 Lyuben Lichev , Dieter Mitsche , Pawel Pralat

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

In a Maker-Breaker game on a graph $G$, Breaker and Maker alternately claim edges of $G$. Maker wins if, after all edges have been claimed, the graph induced by his edges has some desired property. We consider four Maker-Breaker games…

Combinatorics · Mathematics 2013-09-24 Andrew Beveridge , Andrzej Dudek , Alan Frieze , Tobias Muller , Milos Stojakovic

We consider a generalization of the densest subhypergraph problem where nonnegative rewards are given for including partial hyperedges in a dense subhypergraph. Prior work addressed this problem only in cases where reward functions are…

Data Structures and Algorithms · Computer Science 2025-06-17 Vedangi Bengali , Nikolaj Tatti , Iiro Kumpulainen , Florian Adriaens , Nate Veldt

In the Maker-Breaker resolving game, two players named Resolver and Spoiler alternately select unplayed vertices of a given graph $G$. The aim of Resolver is to select all the vertices of some resolving set of $G$, while Spoiler aims to…

Combinatorics · Mathematics 2025-12-02 Savitha K S , Sandi Klavžar , Tijo James

The game of Cops and Robber is a pursuit-evasion game which is usually played on a connected graph. In the game, a set of cops and a robber move around the vertices of a graph along edges, where the cops aim to capture the robber, while the…

Combinatorics · Mathematics 2021-07-27 Pinkaew Siriwong , Ratinan Boonklurb , Henry Liu , Sirirat Singhun

The Cops and Robber game on geodesic spaces is a pursuit-evasion game with discrete steps which captures the behavior of the game played on graphs, as well as that of continuous pursuit-evasion games. One of the outstanding open problems…

Combinatorics · Mathematics 2024-02-09 Vesna Iršič , Bojan Mohar , Alexandra Wesolek

With the increasing sophistication of attacks on cyber-physical systems, deception has emerged as an effective tool to improve system security and safety by obfuscating the attacker's perception. In this paper, we present a solution to the…

Computer Science and Game Theory · Computer Science 2020-07-16 Abhishek N. Kulkarni , Huan Luo , Nandi O. Leslie , Charles A. Kamhoua , Jie Fu

We introduce a discrete-time search game, in which two players compete to find an object first. The object moves according to a time-varying Markov chain on finitely many states. The players know the Markov chain and the initial probability…

Computer Science and Game Theory · Computer Science 2020-08-28 Benoit Duvocelle , János Flesch , Mathias Staudigl , Dries Vermeulen

In the Hunters and Rabbit game, $k$ hunters attempt to shoot an invisible rabbit on a given graph $G$. In each round, the hunters select $k$ vertices to shoot at, while the rabbit moves along an edge of $G$. The hunters win if, at any…

Combinatorics · Mathematics 2025-12-05 Walid Ben-Ameur , Harmender Gahlawat , Alessandro Maddaloni

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 game in which a cop searches for a moving robber on a graph using distance probes, studied by Carragher, Choi, Delcourt, Erickson and West, which is a slight variation on one introduced by Seager. Carragher, Choi, Delcourt,…

Combinatorics · Mathematics 2020-08-12 John Haslegrave , Richard A. B. Johnson , Sebastian Koch

This paper studies a 3D multiplayer reach-avoid differential game with a goal region and a play region. Multiple pursuers defend the goal region by consecutively capturing multiple evaders in the play region. The players have heterogeneous…

Optimization and Control · Mathematics 2020-02-17 Rui Yan , Xiaoming Duan , Zongying Shi , Yisheng Zhong , Francesco Bullo

The following optimal stopping problem is considered. The vertices of a graph $G$ are revealed one by one, in a random order, to a selector. He aims to stop this process at a time $t$ that maximizes the expected number of connected…

Combinatorics · Mathematics 2021-10-05 Fabrício Siqueira Benevides , Małgorzata Sulkowska

We consider a game played between a hider, who hides a static object in one of several possible positions in a bounded planar region, and a searcher, who wishes to reach the object by querying sensors placed in the plane. The searcher is a…

Computer Science and Game Theory · Computer Science 2015-03-19 Alessandro Borri , Shaunak D. Bopardikar , Joao P. Hespanha , Maria D. Di Benedetto

We investigate the interrelation between graph searching games and games with imperfect information. As key consequence we obtain that parity games with bounded imperfect information can be solved in PTIME on graphs of bounded DAG-width…

Computer Science and Game Theory · Computer Science 2015-03-19 Bernd Puchala , Roman Rabinovich