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The two-player, complete information game of Cops and Robber is played on undirected finite graphs. A number of cops and one robber are positioned on vertices and take turns in sliding along edges. The cops win if, after a move, a cop and…

Combinatorics · Mathematics 2021-12-23 Gwenaël Joret , Marcin Kamiński , Dirk Oliver Theis

In order to drive effectively, a driver must be aware of how they can expect other vehicles' behaviour to be affected by their decisions, and also how they are expected to behave by other drivers. One common family of methods for addressing…

Computer Science and Game Theory · Computer Science 2020-07-15 Jack Geary , Henry Gouk

Stochastic patrol routing is known to be advantageous in adversarial settings; however, the optimal choice of stochastic routing strategy is dependent on a model of the adversary. We adopt a worst-case omniscient adversary model from the…

Systems and Control · Electrical Eng. & Systems 2025-04-10 Yohan John , Gilberto Diaz-Garcia , Xiaoming Duan , Jason R. Marden , Francesco Bullo

This paper proposes a new lens for studying threshold games played on networks when the thresholds are heterogeneous. These are games where agents have two possible actions, and prefer action 1 if and only if enough of their neighbours…

Theoretical Economics · Economics 2025-08-07 Alastair Langtry , Sarah Taylor , Yifan Zhang

When securing complex infrastructures or large environments, constant surveillance of every area is not affordable. To cope with this issue, a common countermeasure is the usage of cheap but wide-ranged sensors, able to detect suspicious…

Artificial Intelligence · Computer Science 2015-06-10 Nicola Basilico , Giuseppe De Nittis , Nicola Gatti

In many applications, we want to influence the decisions of independent agents by designing incentives for their actions. We revisit a fundamental problem in this area, called GAME IMPLEMENTATION: Given a game in standard form and a set of…

Computer Science and Game Theory · Computer Science 2022-12-02 Jiehua Chen , Sebastian Vincent Haydn , Negar Layegh Khavidaki , Sofia Simola , Manuel Sorge

Cops and Robber is a family of two-player games played on graphs in which one player controls a number of cops and the other player controls a robber. In alternating turns, each player moves (all) their figures. The cops try to capture the…

Combinatorics · Mathematics 2024-01-11 Minh Tuan Ha , Paul Jungeblut , Torsten Ueckerdt , Paweł Żyliński

Objective: The study investigates the effect on cooperation in multiplayer games, when the population from which all individuals are drawn is structured - i.e. when a given individual is only competing with a small subset of the entire…

Computer Science and Game Theory · Computer Science 2016-02-08 Kaare B. Mikkelsen , Lars A. Bach

Basically, in (one-player) war Real Time Strategy (wRTS) games a human player controls, in real time, an army consisting of a number of soldiers and her aim is to destroy the opponent's assets where the opponent is a virtual (i.e.,…

Neural and Evolutionary Computing · Computer Science 2012-01-17 José A. García Gutiérrez , Carlos Cotta , Antonio J. Fernández-Leiva

Data injection attacks have recently emerged as a significant threat on the smart power grid. By launching data injection attacks, an adversary can manipulate the real-time locational marginal prices to obtain economic benefits. Despite the…

Cryptography and Security · Computer Science 2016-04-04 Anibal Sanjab , Walid Saad

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

In repeated games, players choose actions concurrently at each step. We consider a parameterized setting of repeated games in which the players form a population of an arbitrary size. Their utility functions encode a reachability objective.…

Computer Science and Game Theory · Computer Science 2025-10-06 Nathalie Bertrand , Patricia Bouyer , Luc Lapointe , Corto Mascle

Reachability games are two-player games played on a graph, where the objective of $\texttt{REACH}$ player is to reach the target set whereas the objective of $\texttt{SAFE}$ player is to stay away from the target set. Reachability games…

Artificial Intelligence · Computer Science 2026-05-12 Krishnendu Chatterjee , Ehsan Kafshdar Goharshady , Mehrdad Karrabi , Maximilian Seeliger , Đorđe Žikelić

The localization game is a pursuit-evasion game analogous to Cops and Robbers, where the robber is invisible and the cops send distance probes in an attempt to identify the location of the robber. We present a novel graph parameter called…

Combinatorics · Mathematics 2021-05-21 Natalie C. Behague , Anthony Bonato , Melissa A. Huggan , Trent G. Marbach , Brittany Pittman

Graph games of infinite length are a natural model for open reactive processes: one player represents the controller, trying to ensure a given specification, and the other represents a hostile environment. The evolution of the system…

Computer Science and Game Theory · Computer Science 2010-06-09 Julien Cristau , Claire David , Florian Horn

In this work, we analyze a sequential game played in a graph called the Multilevel Critical Node problem (MCN). A defender and an attacker are the players of this game. The defender starts by preventively interdicting vertices (vaccination)…

Computational Complexity · Computer Science 2020-10-05 Adel Nabli , Margarida Carvalho , Pierre Hosteins

The game subset take-away begins with a simplicial complex \Delta. Two players take turns removing any element of \Delta as well as all other elements which contain it, and the last player able to move wins. Graph Chomp is a special case of…

Combinatorics · Mathematics 2015-03-17 Tirasan Khandhawit , Lynnelle Ye

Temporal graphs extend ordinary graphs with discrete time that affects the availability of edges. We consider solving games played on temporal graphs where one player aims to explore the graph, i.e., visit all vertices. The complexity…

Computer Science and Game Theory · Computer Science 2025-06-16 Pete Austin , Nicolas Mazzocchi , Sougata Bose , Patrick Totzke

The Warden's Game is a 2-player game, played with a row of coins. One player (the prisoner) wants to get all coins to show tails; the other player (the warden) wants to delay that as long as possible. At each turn, one player transfers the…

Combinatorics · Mathematics 2018-07-26 Joseph DiMuro

The well-known Braess paradox in congestion games states that adding an additional road to a transportation network may increase the total travel time, and consequently decrease the overall efficiency. Motivated by this, this paper presents…

Computer Science and Game Theory · Computer Science 2018-02-13 Yuke Li , A. Stephen Morse