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Generalized Geography is a combinatorial game played on a directed graph. Players take turns moving a token from vertex to vertex, deleting a vertex after moving the token away from it. A player unable to move loses. It is well known that…

Computational Complexity · Computer Science 2021-08-24 Nathan Fox , Carson Geissler

Suppose a Bayesian agent seeks to traverse a graph. Each time she crosses an edge, she pays a price. The first time she reaches a node, there is a payoff. She has an opponent who can reduce the payoffs. This paper uses adversarial risk…

Optimization and Control · Mathematics 2026-02-12 David Banks , Elvan Ceyhan , Leah Johnson , Li Zhou

We start with the well-known game below: Two players hold a sheet of paper to their forehead on which a positive integer is written. The numbers are consecutive and each player can only see the number of the other one. In each time step,…

Combinatorics · Mathematics 2013-02-26 Felix Günther , Irina Mustata

A gambler moves on the vertices $1, \ldots, n$ of a graph using the probability distribution $p_{1}, \ldots, p_{n}$. A cop pursues the gambler on the graph, only being able to move between adjacent vertices. What is the expected number of…

Discrete Mathematics · Computer Science 2017-01-09 Jesse Geneson

We study routing games where every agent sequentially decides her next edge when she obtains the green light at each vertex. Because every edge only has capacity to let out one agent per round, an edge acts as a FIFO waiting queue that…

Computer Science and Game Theory · Computer Science 2018-10-29 Anisse Ismaili

Neighborhood Lights Out is a game played on graphs. Begin with a graph and a vertex labeling of the graph from the set $\{0,1,2,\dots, \ell-1\}$ for $\ell \in \mathbb{N}$. The game is played by toggling vertices: when a vertex is toggled,…

Combinatorics · Mathematics 2020-07-08 Lauren Keough , Darren Parker

We study the positional game where two players, Maker and Breaker, alternately select respectively $1$ and $b$ previously unclaimed edges of $K_n$. Maker wins if she succeeds in claiming all edges of some odd cycle in $K_n$ and Breaker wins…

Combinatorics · Mathematics 2019-06-11 Jan Corsten , Adva Mond , Alexey Pokrovskiy , Christoph Spiegel , Tibor Szabó

We consider zero-sum games in which players move between adjacent states, where in each pair of adjacent states one state dominates the other. The states in our game can represent positional advantages in physical conflict such as high…

Computer Science and Game Theory · Computer Science 2024-07-11 Farid Arthaud , Edan Orzech , Martin Rinard

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

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

Given a tree $T=(V,E)$ on $n$ vertices, we consider the $(1 : q)$ Maker-Breaker tree embedding game ${\mathcal T}_n$. The board of this game is the edge set of the complete graph on $n$ vertices. Maker wins ${\mathcal T}_n$ if and only if…

Combinatorics · Mathematics 2010-10-15 Asaf Ferber , Dan Hefetz , Michael Krivelevich

We consider a biased version of Maker-Breaker domination games, which were recently introduced by Gledel, Ir{\v{s}}i{\v{c}}, and Klav{\v{z}}ar. Two players, Dominator and Staller, alternatingly claim vertices of a graph $G$ where Dominator…

Combinatorics · Mathematics 2024-08-02 Ali Deniz Bagdas , Dennis Clemens , Fabian Hamann , Yannick Mogge

A law in a multiagent system is a set of constraints imposed on agents' behaviours to avoid undesirable outcomes. The paper considers two types of laws: useful laws that, if followed, completely eliminate the undesirable outcomes and…

Multiagent Systems · Computer Science 2026-01-13 Qi Shi , Pavel Naumov

Turn-based discounted-sum games are two-player zero-sum games played on finite directed graphs. The vertices of the graph are partitioned between player 1 and player 2. Plays are infinite walks on the graph where the next vertex is decided…

Computer Science and Game Theory · Computer Science 2024-05-21 Ali Asadi , Krishnendu Chatterjee , Raimundo Saona , Jakub Svoboda

In the Constructor-Blocker game, two players, Constructor and Blocker, alternatively claim unclaimed edges of the complete graph $K_n$. For given graphs $F$ and $H$, Constructor can only claim edges that leave her graph $F$-free, while…

Combinatorics · Mathematics 2024-01-02 József Balogh , Ce Chen , Sean English

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 study the problem of deciding the winner of reachability switching games for zero-, one-, and two-player variants. Switching games provide a deterministic analogue of stochastic games. We show that the zero-player case is NL-hard, the…

Formal Languages and Automata Theory · Computer Science 2023-06-22 John Fearnley , Martin Gairing , Matthias Mnich , Rahul Savani

Cops and Robbers is a game played on a graph where a set of cops attempt to capture a single robber. The game proceeds in rounds, where each round first consists of the cops' turn, followed by the robber's turn. In the cops' turn, every cop…

Discrete Mathematics · Computer Science 2025-07-03 Prosenjit Bose , Pat Morin , Karthik Murali

We consider a model of two competing microswimming agents engaged in a pursue-evasion task within a low-Reynolds-number environment. Agents can only perform simple maneuvers and sense hydrodynamic disturbances, which provide ambiguous…

Fluid Dynamics · Physics 2022-03-04 Francesco Borra , Luca Biferale , Massimo Cencini , Antonio Celani

We introduce and study coverage games - a novel framework for multi-agent planning in settings in which a system operates several agents but does not have full control on them, or interacts with an environment that consists of several…

Computer Science and Game Theory · Computer Science 2026-03-24 Orna Kupferman , Noam Shenwald