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Related papers: General Cops and Robbers Games with randomness

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Computing worst-case robust strategies in pursuit-evasion games (PEGs) is time-consuming, especially when real-world factors like partial observability are considered. While important for general security purposes, real-time applicable…

Machine Learning · Computer Science 2026-05-15 Runyu Lu , Ruochuan Shi , Yuanheng Zhu , Dongbin Zhao

Effectively positioning pursuers in pursuit-evasion games without prior knowledge of evader locations remains a significant challenge. A novel approach that combines game-theoretic control theory with Graph Neural Networks is introduced in…

Multiagent Systems · Computer Science 2025-10-14 Gabriel Smithline , Scott Nivison

We describe here a new concept of one group chasing another, called "group chase and escape", by presenting a simple model. We will show that even a simple model can demonstrate rather rich and complex behavior. In particular, there are…

Adaptation and Self-Organizing Systems · Physics 2015-03-13 Atsushi Kamimura , Toru Ohira

We consider a game in which a cop searches for a moving robber on a connected graph using distance probes, which is a slight variation on one introduced by Seager. Carragher, Choi, Delcourt, Erickson and West showed that for any $n$-vertex…

Combinatorics · Mathematics 2017-11-23 John Haslegrave , Richard A. B. Johnson , Sebastian Koch

We consider several variants of the classical Cops and Robbers game. We treat the version where the robber can move R > 1 edges at a time, establishing a general upper bound of N / \alpha ^{(1-o(1))\sqrt{log_\alpha N}}, where \alpha = 1 +…

Combinatorics · Mathematics 2010-04-15 Alan Frieze , Michael Krivelevich , Po-Shen Loh

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

The game of Cops and Robbers is a well known pursuit-evasion game played on graphs. It has been proved \cite{bounded_degree} that cubic graphs can have arbitrarily large cop number $c(G)$, but the known constructions show only that the set…

Traditional game-theoretic research for security applications primarily focuses on the allocation of external protection resources to defend targets. This work puts forward the study of a new class of games centered around strategically…

Computer Science and Game Theory · Computer Science 2024-10-29 Niclas Boehmer , Minbiao Han , Haifeng Xu , Milind Tambe

In this paper, we consider a variant of the cops and robbers game on a graph, introduced by Kinnersley and Peterson, in which every time the robber uses an edge, it is removed from the graph, known as bridge-burning cops and robbers. In…

Combinatorics · Mathematics 2020-11-21 Rebekah Herrman , Peter van Hintum , Stephen G. Z. Smith

A new surveillance-evasion differential game is posed and solved in which an agile pursuer (the prying pedestrian) seeks to remain within a given surveillance range of a less agile evader that aims to escape. In contrast to previous…

Systems and Control · Electrical Eng. & Systems 2025-05-13 Philipp Braun , Timothy L. Molloy , Iman Shames

We consider the cop-throttling number of a graph $G$ for the game of Cops and Robbers, which is defined to be the minimum of $(k + \text{capt}_k(G))$, where $k$ is the number of cops and $\text{capt}_k(G)$ is the minimum number of rounds…

Combinatorics · Mathematics 2018-02-27 Jane Breen , Boris Brimkov , Joshua Carlson , Leslie Hogben , K. E. Perry , Carolyn Reinhart

We consider the cops and robber game variant consisting of one cop and one robber on time-varying graphs (TVG). The considered TVGs are edge periodic graphs, i.e., for each edge, a binary string $s_e$ determines in which time step the edge…

Computational Complexity · Computer Science 2021-07-13 Nils Morawietz , Petra Wolf

General game playing (GGP) is a framework for evaluating an agent's general intelligence across a wide range of tasks. In the GGP competition, an agent is given the rules of a game (described as a logic program) that it has never seen…

Artificial Intelligence · Computer Science 2019-06-25 Andrew Cropper , Richard Evans , Mark Law

We study a variant of the Cops and Robbers game on graphs in which the robbers damage the visited vertices, aiming to maximize the number of damaged vertices. For that game with one cop against $s$ robbers a conjecture was made by Carlson,…

Combinatorics · Mathematics 2025-09-16 Miloš Stojaković , Lasse Wulf

We analyze the pedestrian evacuation of a rectangular room with a single door considering a Lattice Gas scheme with the addition of behavioral aspects of the pedestrians. The movement of the individuals is based on random and rational…

Adaptation and Self-Organizing Systems · Physics 2015-06-17 S. Bouzat , M. N. Kuperman

We consider a variation of a cops and robbers game in which the cop---here referred to as "hunter"---is not constrained by the graph but must play in the dark against a "mole." We characterize the graphs---which we will call…

Combinatorics · Mathematics 2014-05-15 Natasha Komarov , Peter Winkler

We consider a surrounding variant of cops and robbers on graphs of bounded genus. We obtain bounds on the number of cops required to surround a robber on planar graphs, toroidal graphs, and outerplanar graphs. We also obtain improved bounds…

Combinatorics · Mathematics 2019-11-05 Peter Bradshaw , Seyyed Aliasghar Hosseini

We present two zero-sum games modeling situations where one player attacks (or hides in) a finite dimensional nonempty compact set, and the other tries to prevent the attack (or find him). The first game, called patrolling game, corresponds…

Optimization and Control · Mathematics 2019-07-03 Tristan Garrec

In spam and malware detection, attackers exploit randomization to obfuscate malicious data and increase their chances of evading detection at test time; e.g., malware code is typically obfuscated using random strings or byte sequences to…

Machine Learning · Computer Science 2016-09-07 Samuel Rota Bulò , Battista Biggio , Ignazio Pillai , Marcello Pelillo , Fabio Roli

The cop throttling number $th_c(G)$ of a graph $G$ for the game of Cops and Robbers is the minimum of $k + capt_k(G)$, where $k$ is the number of cops and $capt_k(G)$ is the minimum number of rounds needed for $k$ cops to capture the robber…