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Motivated by a biological scenario illustrated in the YouTube video \url{ https://www.youtube.com/watch?v=Z_mXDvZQ6dU} where a neutrophil chases a bacteria cell moving in random directions, we present a variant of the cop and robber game on…

Combinatorics · Mathematics 2020-04-02 Pamela Harris , Erik Insko , Alicia Prieto-Langarica , Rade Stoisavljevic , Shaun Sullivan

We study two impartial games introduced by Anderson and Harary and further developed by Barnes. Both games are played by two players who alternately select previously unselected elements of a finite group. The first player who builds a…

Combinatorics · Mathematics 2024-02-12 Dana C. Ernst , Nandor Sieben

Fictitious play is a popular learning algorithm in which players that utilize the history of actions played by the players and the knowledge of their own payoff matrix can converge to the Nash equilibrium under certain conditions on the…

Computer Science and Game Theory · Computer Science 2021-10-13 Bhaskar Vundurthy , Aris Kanellopoulos , Vijay Gupta , Kyriakos Vamvoudakis

The notions of entanglement and nonlocality are among the most striking ingredients found in quantum information theory. One tool to better understand these notions is the model of nonlocal games; a mathematical framework that abstractly…

Quantum Physics · Physics 2017-04-26 Vincent Russo

We show a parallel repetition theorem for the entangled value $\omega^*(G)$ of any two-player one-round game $G$ where the questions $(x,y) \in \mathcal{X}\times\mathcal{Y}$ to Alice and Bob are drawn from a product distribution on…

Quantum Physics · Physics 2014-06-16 Rahul Jain , Attila Pereszlényi , Penghui Yao

This paper proposes and studies a general form of dynamic $N$-player non-cooperative games called $\alpha$-potential games, where the change of a player's value function upon her unilateral deviation from her strategy is equal to the change…

Optimization and Control · Mathematics 2025-04-02 Xin Guo , Xinyu Li , Yufei Zhang

We train a single, goal-conditioned policy that can solve many robotic manipulation tasks, including tasks with previously unseen goals and objects. We rely on asymmetric self-play for goal discovery, where two agents, Alice and Bob, play a…

Two-player zero-sum "graph games" are a central model, which proceeds as follows. A token is placed on a vertex of a graph, and the two players move it to produce an infinite "play", which determines the winner or payoff of the game.…

Computer Science and Game Theory · Computer Science 2022-11-28 Guy Avni , Ismael Jecker , Djordje Zikelic

We consider the weighted version of the Tron game on graphs where two players, Alice and Bob, each build their own path by claiming one vertex at a time, starting with Alice. The vertices carry non-negative weights that sum up to 1 and…

Combinatorics · Mathematics 2014-12-15 Daniel Hoske , Jonathan Rollin , Torsten Ueckerdt , Stefan Walzer

We study an impartial game introduced by Anderson and Harary. The game is played by two players who alternately choose previously-unselected elements of a finite group. The first player who builds a generating set from the jointly-selected…

Group Theory · Mathematics 2024-02-12 Bret J. Benesh , Dana C. Ernst , Nandor Sieben

We introduce the class of pay or play games, which captures scenarios in which each decision maker is faced with a choice between two actions: one with a fixed payoff and an- other with a payoff dependent on others' selected actions. This…

Computer Science and Game Theory · Computer Science 2013-09-27 Sigal Oren , Michael Schapira , Moshe Tennenholtz

The paper is concerned with distributed learning and optimization in large-scale settings. The well-known Fictitious Play (FP) algorithm has been shown to achieve Nash equilibrium learning in certain classes of multi-agent games. However,…

Optimization and Control · Mathematics 2015-06-16 B. Swenson , S. Kar , J. Xavier

Tit-for-Tat strategy is a strategy in repeated two-player symmetric games which imitates the previous action of the opponent. We show that the Tit-for-Tat strategy is a zero-determinant strategy, which unilaterally equalizes the expected…

Physics and Society · Physics 2022-04-22 Masahiko Ueda

Reinforcement learning (RL) methods have been actively applied in the field of robotics, allowing the system itself to find a solution for a task otherwise requiring a complex decision-making algorithm. In this paper, we present a novel…

Human-Computer Interaction · Computer Science 2021-08-04 Ekaterina Karmanova , Valerii Serpiva , Stepan Perminov , Aleksey Fedoseev , Dzmitry Tsetserukou

We introduce a variant of Wythoff's Game that we call $m$-Modular Wythoff's Game. In the original Wythoff's Game, players can take a positive number of tokens from one pile, or they can take a positive number of tokens from both piles if…

Combinatorics · Mathematics 2024-02-22 Tanya Khovanova , Shuheng Niu

Two-player quantitative zero-sum games provide a natural framework to synthesize controllers with performance guarantees for reactive systems within an uncontrollable environment. Classical settings include mean-payoff games, where the…

Logic in Computer Science · Computer Science 2016-07-11 Patricia Bouyer , Nicolas Markey , Mickael Randour , Kim G. Larsen , Simon Laursen

On a filtered probability space $(\Omega ,\mathcal{F}, (\mathcal{F}_t)_{t\in[0,\infty]}, \mathbb{P})$, we consider the two-player non-zero-sum stopping game $u^i := \mathbb{E}[U^i(\rho,\tau)],\ i=1,2$, where the first player choose a…

Optimization and Control · Mathematics 2015-08-18 Zhou Zhou

We study a dynamic game with a large population of players who choose actions from a finite set in continuous time. Each player has a state in a finite state space that evolves stochastically with their actions. A player's reward depends…

Systems and Control · Electrical Eng. & Systems 2025-11-04 Leonardo Pedroso , Andrea Agazzi , W. P. M. H. Heemels , Mauro Salazar

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

The classical Maker-Breaker positional game is played on a board which is a hypergraph $\mathcal{H}$, with two players, Maker and Breaker, alternately claiming vertices of $\mathcal{H}$ until all the vertices are claimed. When the game…

Discrete Mathematics · Computer Science 2026-01-15 Guillaume Bagan , Quentin Deschamps , Florian Galliot , Mirjana Mikalački , Nacim Oijid