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We consider a group of agents on a graph who repeatedly play the prisoner's dilemma game against their neighbors. The players adapt their actions to the past behavior of their opponents by applying the win-stay lose-shift strategy. On a…

Probability · Mathematics 2007-05-23 Elchanan Mossel , Sebastien Roch

\textit{Pursuit-evasion games} have been intensively studied for several decades due to their numerous applications in artificial intelligence, robot motion planning, database theory, distributed computing, and algorithmic theory.…

Discrete Mathematics · Computer Science 2023-07-11 Harmender Gahlawat , Meirav Zehavi

The game of Cat Herding is one in which cat and herder players alternate turns, with the evasive cat moving along non-trivial paths between vertices, and the herder deleting single edges from the graph. Eventually the cat cannot move, and…

Combinatorics · Mathematics 2025-05-13 Rylo Ashmore , Danny Dyer , Rebecca Milley

Semi-supervised learning is a popular class of techniques to learn from labeled and unlabeled data. The paper proposes an application of a recently proposed approach of graph transduction that exploits game theoretic notions to the problem…

Computer Vision and Pattern Recognition · Computer Science 2018-06-26 Tewodros Mulugeta Dagnew , Dalia Coppi , Marcello Pelillo , Rita Cucchiara

In this paper, we propose a general graph optimization based framework for localization, which can accommodate different types of measurements with varying measurement time intervals. Special emphasis will be on range-based localization.…

Robotics · Computer Science 2020-01-27 Xu Fang , Chen Wang , Thien-Minh Nguyen , Lihua Xie

Here we merge the two fields of Cops and Robbers and Graph Pebbling to introduce the new topic of Cops and Robbers Pebbling. Both paradigms can be described by moving tokens (the cops) along the edges of a graph to capture a special token…

Combinatorics · Mathematics 2026-02-10 Nancy Clarke , Joshua Forkin , Glenn Hurlbert

We study zombies and survivor, a variant of the game of cops and robber on graphs. In this variant, the single survivor plays the role of the robber and attempts to escape from the zombies that play the role of the cops. The zombies are…

Combinatorics · Mathematics 2022-04-27 Prosenjit Bose , Jean-Lou De Carufel , Thomas Shermer

Treasure hunt and rendezvous are fundamental tasks performed by mobile agents in graphs. In treasure hunt, an agent has to find an inert target (called treasure) situated at an unknown node of the graph. In rendezvous, two agents, initially…

Distributed, Parallel, and Cluster Computing · Computer Science 2023-10-03 Debasish Pattanayak , Andrzej Pelc

We introduce a variant of the Localization game in which the cops only have visibility one, along with the corresponding optimization parameter, the one-visibility localization number $\zeta_1$. By developing lower bounds using…

Combinatorics · Mathematics 2024-09-24 Anthony Bonato , Trent G. Marbach , Michael Molnar , JD Nir

The game of cops and robber is a turn based vertex pursuit game played on a connected graph between a team of cops and a single robber. The cops and the robber move alternately along the edges of the graph. We say the team of cops win the…

Combinatorics · Mathematics 2022-11-30 Uttam K. Gupta , Suchismita Mishra , Dinabandhu Pradhan

(abstract shortened to meet arxiv's length requirements) We investigate two variants of the classical Cops and robber game in graphs, recently introduced by Lee, Mart\'inez-Pedroza, and Rodr\'iguez-Quinche. The two versions are played in…

Combinatorics · Mathematics 2026-02-24 Louis Esperet , Harmender Gahlawat , Ugo Giocanti

Using mobile robots for autonomous patrolling of environments to prevent intrusions is a topic of increasing practical relevance. One of the most challenging scientific issues is the problem of finding effective patrolling strategies that,…

Computer Science and Game Theory · Computer Science 2009-12-18 Nicola Basilico , Nicola Gatti , Francesco Amigoni

We investigate various pursuit-evasion parameters on latin square graphs, including the cop number, metric dimension, and localization number. The cop number of latin square graphs is studied, and for $k$-MOLS$(n),$ bounds for the cop…

Combinatorics · Mathematics 2021-10-01 Shreya Ahirwar , Anthony Bonato , Leanna Gittins , Alice Huang , Trent G. Marbach , Tomer Zaidman

Interdicting a criminal with limited police resources is a challenging task as the criminal changes location over time. The size of the large transportation network further adds to the difficulty of this scenario. To tackle this issue, we…

Artificial Intelligence · Computer Science 2026-04-08 Sukanya Samanta , Kei Kimura , Makoto Yokoo , Palash Dey

We consider a variant of Cops and Robbers wherein each edge traversed by the robber is deleted from the graph. The focus is on determining the minimum number of cops needed to capture a robber on a graph $G$, called the {\em bridge-burning…

Combinatorics · Mathematics 2018-12-27 William B. Kinnersley , Eric Peterson

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

Various models to quantify the reliability of a network have been studied where certain components of the graph may fail at random and the probability that the remaining graph is connected is the proxy for reliability. In this work we…

Combinatorics · Mathematics 2020-11-24 Maimoonah Ahmed , Ben Cameron

In the game of Cops and Robbers, one of the most useful results is that an isometric path in a graph can be guarded by one cop. In this paper, we introduce the concept of wide shadow in a subgraph, and use it to characterize all 1-guardable…

Combinatorics · Mathematics 2024-06-04 Sebastián González Hermosillo de la Maza , Bojan Mohar

We introduce a new class of network allocation games called graphical distance preservation games. Here, we are given a graph, called a topology, and a set of agents that need to be allocated to its vertices. Moreover, every agent has an…

Computer Science and Game Theory · Computer Science 2026-02-19 Argyrios Deligkas , Eduard Eiben , Tiger-Lily Goldsmith , Dušan Knop , Šimon Schierreich

We study a pursuit-evasion problem which can be viewed as an extension of the keep-away game. In the game, pursuer(s) will attempt to intersect or catch the evader, while the evader can visit a fixed set of locations, which we denote as the…

Robotics · Computer Science 2022-06-17 Weifu Wang , Ping Li