English
Related papers

Related papers: Selfish Cops and Active Robber: Multi-Player Pursu…

200 papers

We expand on earlier research on the topic by discussing an infinitely repeated game model with a subgame perfect equilibrium strategy profile (SPE) as a solution concept that diminishes incentives to violate speed limits in a carrot and…

General Economics · Economics 2024-02-16 Mika Sutela , Nino Lindström

We provide a sublinear bound on the cop throttling number of a connected graph. Related to the graph searching game Cops and Robbers, the cop throttling number, written $\mathrm{th}_c(G)$, is given by…

Combinatorics · Mathematics 2019-01-28 Anthony Bonato , Sean English

The cop number of a graph $G$ is the smallest $k$ such that $k$ cops win the game of cops and robber on $G$. We investigate the maximum cop number of geometric intersection graphs, which are graphs whose vertices are represented by…

We prove that every finite two-person shortest path game, where the local cost of every move is positive for each player, has a Nash equilibrium (NE) in pure stationary strategies, which can be computed in polynomial time. We also extend…

Discrete Mathematics · Computer Science 2025-05-22 Endre Boros , Khaled Elbassioni , Vladimir Gurvich , Mikhail Vyalyi

This paper presents a game theoretic formulation of a graph traversal problem, with applications to robots moving through hazardous environments in the presence of an adversary, as in military and security scenarios. The blue team of robots…

Computer Science and Game Theory · Computer Science 2024-10-01 James Berneburg , Xuan Wang , Xuesu Xiao , Daigo Shishika

A relational characterization of cop-win graphs was provided by Nowakowski and Winkler in their seminal paper on the game of Cops and Robbers. As a by-product of that characterization, each cop-win graph is assigned a unique ordinal, which…

Combinatorics · Mathematics 2019-05-16 Anthony Bonato , Przemysław Gordinowicz , Gena Hahn

We study a problem of trust in a distributed system in which a common resource is shared by multiple parties. In such naturally information-limited settings, parties abide by a behavioral protocol that leads to fair sharing of the resource.…

Computer Science and Game Theory · Computer Science 2013-07-08 Christopher Griffin , George Kesidis

We present two efficient algorithms that compute the optimal strategy for cop in the game of Cop v.s. Gambler where the gambler's strategy is not optimal but known to the cop. The first algorithm is analogous to Bellman-Ford algorithm for…

Combinatorics · Mathematics 2017-01-11 Shen-Fu Tsai

In the game of Cops and Robbers, the capture time of a graph is the minimum number of moves needed by the cops to capture the robber, assuming optimal play. We prove that the capture time of the $n$-dimensional hypercube is $\Theta (n\ln…

Combinatorics · Mathematics 2013-08-16 Anthony Bonato , William B. Kinnersley , P. Gordinowicz , P. Pralat

Shmuel Gal and Jerome Casas have recently introduced a game theoretic model that combines search and pursuit by a predator for a prey animal. The prey (hider) can hide in a finite number of locations. The predator (searcher) can inspect any…

Computer Science and Game Theory · Computer Science 2019-12-10 Steve Alpern , Viciano Lee

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

This paper aims to reduce the communication and computation costs of the Nash equilibrium seeking strategy for the $N$-coalition noncooperative games proposed in [1]. The objective is achieved in two manners: 1. An interference graph is…

Optimization and Control · Mathematics 2019-06-05 Maojiao Ye , Guoqiang Hu , Frank L. Lewis , Lihua Xie

We study a recently introduced class of strategic games that is motivated by and generalizes Schelling's well-known residential segregation model. These games are played on undirected graphs, with the set of agents partitioned into multiple…

Computer Science and Game Theory · Computer Science 2019-11-25 Aishwarya Agarwal , Edith Elkind , Jiarui Gan , Alexandros A. Voudouris

In the $(s,d)$-spy game over a graph, introduced by Cohen et al. in 2016, one spy and $k$ guards occupy vertices of a graph and, at each turn, each guard may move along one edge and the spy may move along at most $s$ edges. The guards win…

Discrete Mathematics · Computer Science 2023-10-12 Eurinardo Costa , Nicolas Martins , Rudini Sampaio

We study noncooperative games, in which each player's objective is composed of a sequence of ordered- and potentially conflicting-preferences. Problems of this type naturally model a wide variety of scenarios: for example, drivers at a busy…

Computer Science and Game Theory · Computer Science 2025-07-08 Dong Ho Lee , Lasse Peters , David Fridovich-Keil

Synthesis of finite-state controllers from high-level specifications in multi-agent systems can be reduced to solving multi-player concurrent games over finite graphs. The complexity of solving such games with qualitative objectives for…

Computer Science and Game Theory · Computer Science 2018-09-28 Shaull Almagor , Rajeev Alur , Suguman Bansal

Pursuit-evasion games, such as the game of Revolutionaries and Spies, are a simplified model for network security. In the game we consider in this paper, a team of $r$ revolutionaries tries to hold an unguarded meeting consisting of $m$…

Combinatorics · Mathematics 2014-06-12 Dieter Mitsche , Pawel Pralat

We consider a new probabilistic graph searching game played on graphs, inspired by the familiar game of Cops and Robbers. In Zombies and Survivors, a set of zombies attempts to eat a lone survivor loose on a given graph. The zombies…

Discrete Mathematics · Computer Science 2015-03-31 Anthony Bonato , Dieter Mitsche , Xavier Pérez-Giménez , Paweł Prałat

We present a numerical approach to finding optimal trajectories for players in a multi-body, asset-guarding game with nonlinear dynamics and non-convex constraints. Using the Iterative Best Response (IBR) scheme, we solve for each player's…

Systems and Control · Electrical Eng. & Systems 2020-11-04 Emmanuel Sin , Murat Arcak , Douglas Philbrick , Peter Seiler

We survey results at the intersection of topological graph theory and the game of Cops and Robbers, focusing on results, conjectures, and open problems for the cop number of a graph embedded on a surface. After a discussion on results for…

Combinatorics · Mathematics 2018-04-24 Anthony Bonato , Bojan Mohar