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This work contains the mathematical exploration of a few prototypical games in which central concepts from statistics and probability theory naturally emerge. The first two kinds of games are termed Fisher and Bayesian games, which are…

Statistics Theory · Mathematics 2024-02-27 Jozsef Konczer

The semi-random graph process is a single player game in which the player is initially presented an empty graph on $n$ vertices. In each round, a vertex $u$ is presented to the player independently and uniformly at random. The player then…

Combinatorics · Mathematics 2022-02-21 Pu Gao , Calum MacRury , Pawel Pralat

Given a symmetric $n\times n$ matrix $P$ with $0 \le P(u, v)\le 1$, we define a random graph $G_{n, P}$ on $[n]$ by independently including any edge $\{u, v\}$ with probability $P(u, v)$. For $k\ge 1$ let $\mathcal{A}_k$ be the property of…

Combinatorics · Mathematics 2020-12-23 Tony Johansson

Given a graph G with n vertices and k players, each of which is placing a facility on one of the vertices of G, we define the score of the i'th player to be the number of vertices for which, among all players, the facility placed by the…

Data Structures and Algorithms · Computer Science 2017-06-06 Roee David , Nimrod Talmon

In this paper a relationship is established between the domination game and minimal edge cuts. It is proved that the game domination number of a connected graph can be bounded above in terms of the size of minimal edge cuts. In particular,…

Combinatorics · Mathematics 2018-10-25 Sandi Klavžar , Douglas F. Rall

Mean-payoff games are important quantitative models for open reactive systems. They have been widely studied as games of full observation. In this paper we investigate the algorithmic properties of several sub-classes of mean-payoff games…

Computer Science and Game Theory · Computer Science 2017-10-10 Paul Hunter , Arno Pauly , Guillermo A. Pérez , Jean-François Raskin

Motivated by the controller placement problems in software-defined networks and the fair division principles of classical "cake cutting", we investigate the following two-player zero-sum game. In our model, a defender places a limited…

Computational Complexity · Computer Science 2026-05-19 Grzegorz Gutowski , Konstanty Junosza-Szaniawski , Antonio Lauerbach , Alexander Wolff

The semi-random graph process is a single player game in which the player is initially presented an empty graph on $n$ vertices. In each round, a vertex $u$ is presented to the player independently and uniformly at random. The player then…

Combinatorics · Mathematics 2023-07-11 Paweł Prałat , Harjas Singh

In two-player finite-state stochastic games of partial observation on graphs, in every state of the graph, the players simultaneously choose an action, and their joint actions determine a probability distribution over the successor states.…

Computer Science and Game Theory · Computer Science 2011-07-13 Krishnendu Chatterjee , Laurent Doyen

Given a c-colored graph G, a vertex of G is happy if it has the same color as all its neighbors. The notion of happy vertices was introduced by Zhang and Li to compute the homophily of a graph. Eto, et al. introduced the Maker-Maker version…

Discrete Mathematics · Computer Science 2026-01-13 Mathieu Hilaire , Perig Montfort , Nacim Oijid

We study the Maker-Breaker domination game played by Dominator and Staller on the vertex set of a given graph. Dominator wins when the vertices he has claimed form a dominating set of the graph. Staller wins if she makes it impossible for…

Combinatorics · Mathematics 2024-04-17 Jovana Forcan , Jiayue Qi

We introduce a new setting of algorithmic problems in random graphs, studying the minimum number of queries one needs to ask about the adjacency between pairs of vertices of ${\mathcal G}(n,p)$ in order to typically find a subgraph…

Combinatorics · Mathematics 2016-08-05 Asaf Ferber , Michael Krivelevich , Benny Sudakov , Pedro Vieira

This short note establishes positionality of mean-payoff games over infinite game graphs by constructing a well-founded monotone universal graph.

Logic in Computer Science · Computer Science 2023-05-02 Pierre Ohlmann

A main question in graphical models and causal inference is whether, given a probability distribution $P$ (which is usually an underlying distribution of data), there is a graph (or graphs) to which $P$ is faithful. The main goal of this…

Statistics Theory · Mathematics 2018-01-30 Kayvan Sadeghi

We study the following Maker/Breaker game. Maker and Breaker take turns in choosing vertices from a given n-uniform hypergraph F, with Maker going first. Maker's goal is to completely occupy a hyperedge and Breaker tries to avoid this. Beck…

Computer Science and Game Theory · Computer Science 2008-10-14 Heidi Gebauer

We study two games proposed by Erd\H{o}s, and one game by Bensmail and Mc Inerney, all sharing a common setup: two players alternately colour edges of a complete graph, or in the biased version, they colour $p$ and $q$ edges respectively on…

Combinatorics · Mathematics 2025-10-30 Stijn Cambie , Michiel Provoost

We introduce a natural generalization of the Erd\H{o}s-R\'enyi random graph model in which random instances of a fixed motif are added independently. The binomial random motif graph $G(H,n,p)$ is the random (multi)graph obtained by adding…

Combinatorics · Mathematics 2019-07-30 Michael Anastos , Peleg Michaeli , Samantha Petti

We discuss winning possibilities of players in various variants of cops and robber game played on large random graphs, a testbed for various kinds of network queries, search problems in particular. We explore the use of logic frameworks to…

Logic in Computer Science · Computer Science 2025-12-01 Sourav Chakraborty , Sujata Ghosh , Smiha Samanta

Temporal graphs are a popular modelling mechanism for dynamic complex systems that extend ordinary graphs with discrete time. Simply put, time progresses one unit per step and the availability of edges can change with time. We consider the…

Logic in Computer Science · Computer Science 2024-01-30 Pete Austin , Sougata Bose , Patrick Totzke

In the Localization game played on graphs, a set of cops uses distance probes to identify the location of an invisible robber. We present an extension of the game and its main parameter, the localization number, to directed graphs. We…

Combinatorics · Mathematics 2022-08-17 Anthony Bonato , Ryan Cushman , Trent G. Marbach , Brittany Pittman