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Related papers: Zero-sum Random Games on Directed Graphs

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We study a two-player game played on undirected graphs called {\sc Trail Trap}, which is a variant of a game known as {\sc Partizan Edge Geography}. One player starts by choosing any edge and moving a token from one endpoint to the other;…

The numbers game is a one-player game played on a finite simple graph with certain "amplitudes" assigned to its edges and with an initial assignment of real numbers to its nodes. The moves of the game successively transform the numbers at…

Combinatorics · Mathematics 2008-10-31 Robert G. Donnelly

We study two-player zero-sum stopping games in continuous time and infinite horizon. We prove that the value in randomized stopping times exists as soon as the payoff processes are right-continuous. In particular, as opposed to existing…

Optimization and Control · Mathematics 2007-05-23 Rida Laraki , Eilon Solan

The semi-random graph process is a single-player game that begins with 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 adaptively selects a vertex…

Combinatorics · Mathematics 2024-03-05 Natalie C. Behague , Trent G. Marbach , Pawel Pralat , Andrzej Rucinski

We study a noisy version of a min-max type zero-sum game on the $d$-ary tree. Each edge of the tree is assigned an i.i.d.\ cookie, distributed uniformly on $\{+1,-1\}$. The game is played as follows: starting at the root, two players…

Probability · Mathematics 2026-05-13 Omer Angel , Gourab Ray , Yinon Spinka

This paper introduced a pursuit and evasion game to be played on a connected graph. One player moves invisibly around the graph, and the other player must guess his position. At each time step the second player guesses a vertex, winning if…

Combinatorics · Mathematics 2017-01-24 John Haslegrave

This paper presents a learning dynamic with almost sure convergence guarantee for any stochastic game with turn-based controllers (on state transitions) as long as stage-payoffs induce a zero-sum or identical-interest game. Stage-payoffs…

Computer Science and Game Theory · Computer Science 2023-10-11 Muhammed O. Sayin

This paper is concerned with two-person dynamic zero-sum games. Let games for some family have common dynamics, running costs and capabilities of players, and let these games differ in densities only. We show that the Dynamic Programming…

Optimization and Control · Mathematics 2017-09-26 Dmitry Khlopin

The undirected edge geography is a two-player combinatorial game on an undirected rooted graph. The players alternatively perform a move consisting of choosing an edge incident to the root vertex, removing the chosen edge, and marking the…

Combinatorics · Mathematics 2025-04-17 Tharit Sereekiatdilok , Panupong Vichitkunakorn

We study a model of two-player, zero-sum, stopping games with asymmetric information. We assume that the payoff depends on two continuous-time Markov chains (X, Y), where X is only observed by player 1 and Y only by player 2, implying that…

Optimization and Control · Mathematics 2017-12-06 Fabien Gensbittel , Christine Grün

We study a version of the lights out game played on directed graphs. For a digraph $D$, we begin with a labeling of $V(D)$ with elements of $\mathbb{Z}_k$ for $k \ge 2$. When a vertex $v$ is toggled, the labels of $v$ and any vertex that…

Combinatorics · Mathematics 2026-02-04 T. Elise Dettling , Darren B. Parker

In this paper we study continuous-time two-player zero-sum optimal switching games on a finite horizon. Using the theory of doubly reflected BSDEs with interconnected barriers, we show that this game has a value and an equilibrium in the…

Optimization and Control · Mathematics 2018-06-04 Said Hamadène , Randall Martyr , John Moriarty

We consider a finite-horizon, zero-sum game in which both players control a stochastic differential equation by invoking impulses. We derive a control randomization formulation of the game and use the existence of a value for the randomized…

Optimization and Control · Mathematics 2025-05-13 Magnus Perninge

This work is concerned with the study of the Game of Graph Nim -- a class of two-player combinatorial games -- on graphs with $4$ edges. To each edge of such a graph is assigned a positive-integer-valued edge-weight, and during each round…

Combinatorics · Mathematics 2025-09-08 Sayar Karmakar , Moumanti Podder , Souvik Roy , Soumyarup Sadhukhan

We consider the general model of zero-sum repeated games (or stochastic games with signals), and assume that one of the players is fully informed and controls the transitions of the state variable. We prove the existence of the uniform…

Optimization and Control · Mathematics 2009-04-20 Jérôme Renault

In tug-of-war, two players compete by moving a counter along edges of a graph, each winning the right to move at a given turn according to the flip of a possibly biased coin. The game ends when the counter reaches the boundary, a fixed…

Probability · Mathematics 2026-02-10 Yujie Fu , Alan Hammond , Gábor Pete

The paper proposes a natural measure space of zero-sum perfect information games with upper semicontinuous payoffs. Each game is specified by the game tree, and by the assignment of the active player and of the capacity to each node of the…

Computer Science and Game Theory · Computer Science 2021-04-22 János Flesch , Arkadi Predtetchinski , Ville Suomala

We study the complexity of solving two-player infinite duration games played on a fixed finite graph, where the control of a node is not predetermined but rather assigned randomly. In classic random-turn games, control of each node is…

Computer Science and Game Theory · Computer Science 2026-01-13 Sarvin Bahmani , Rasmus Ibsen-Jensen , Soumyajit Paul , Sven Schewe , Friedrich Slivovsky , Qiyi Tang , Dominik Wojtczak , Shufang Zhu

In a strong game played on the edge set of a graph G there are two players, Red and Blue, alternating turns in claiming previously unclaimed edges of G (with Red playing first). The winner is the first one to claim all the edges of some…

Discrete Mathematics · Computer Science 2015-07-19 Asaf Ferber , Pascal Pfister

In statistical mechanical investigations on complex networks, it is useful to employ random graphs ensembles as null models, to compare with experimental realizations. Motivated by transcription networks, we present here a simple way to…

Statistical Mechanics · Physics 2009-11-11 F. Bassetti , M. Cosentino Lagomarsino , B. Bassetti , P. Jona