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At some places (see the references) Martin Erickson describes a certain game: "Two players alternately write O's (first player) and X's (second player) in the unoccupied cells of an n x n grid. The first player (if any) to occupy four cells…

Discrete Mathematics · Computer Science 2012-05-22 Thomas Jenrich

The domatic number of a graph is the maximum number of pairwise disjoint dominating sets admitted by the graph. We introduce a game based around this graph invariant. The domatic number game is played on a graph $G$ by two players, Alice…

Combinatorics · Mathematics 2025-08-15 Bert L. Hartnell , Douglas F. Rall

Poset games have been the object of mathematical study for over a century, but little has been written on the computational complexity of determining important properties of these games. In this introduction we develop the fundamentals of…

Computational Complexity · Computer Science 2015-06-26 Stephen A. Fenner , John Rogers

A query game is a pair of a set $Q$ of queries and a set $\mathcal{F}$ of functions, or codewords $f:Q\rightarrow \mathbb{Z}.$ We think of this as a two-player game. One player, Codemaker, picks a hidden codeword $f\in \mathcal{F}$. The…

Combinatorics · Mathematics 2023-07-11 Anders Martinsson

Common knowledge is crucial for safe group coordination. In its absence, humans must rely on shared knowledge, which is inherently limited in depth and therefore prone to coordination failures, because any finite-order knowledge attribution…

Multiagent Systems · Computer Science 2025-11-12 Thomas Bolander , Robin Engelhardt , Thomas S. Nicolet

Stackelberg planning is a recently introduced single-turn two-player adversarial planning model, where two players are acting in a joint classical planning task, the objective of the first player being hampering the second player from…

Artificial Intelligence · Computer Science 2024-03-27 Gregor Behnke , Marcel Steinmetz

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

We consider infinite duration alternating move games. These games were previously studied by Roth, Balcan, Kalai and Mansour. They presented an FPTAS for computing an approximated equilibrium, and conjectured that there is a polynomial…

Computer Science and Game Theory · Computer Science 2013-04-25 Yaron Velner

Consider a two-person zero-sum search game between a hider and a searcher. The hider hides among $n$ discrete locations, and the searcher successively visits individual locations until finding the hider. Known to both players, a search at…

Optimization and Control · Mathematics 2023-05-18 Jake Clarkson , Kyle Y Lin

The Levine hat game requires $n$ players, each wearing an infinite random stack of black and white hats, to guess the location of a black hat on their own head seeing only the hats worn by all the other players. They are allowed a strategy…

Mastermind game is a two players zero sum game of imperfect information. The first player, called codemaker, chooses a secret code and the second player, called codebreaker, tries to break the secret code by making as few guesses as…

Data Structures and Algorithms · Computer Science 2016-11-21 Mourad El Ouali , Christian Glazik , Volkmar Sauerland , Anand Srivastav

Collectible card games are challenging, widely played games that have received increasing attention from the AI research community in recent years. Despite important breakthroughs, the field still poses many unresolved challenges. This work…

Artificial Intelligence · Computer Science 2024-12-11 Ronaldo e Silva Vieira , Anderson Rocha Tavares , Luiz Chaimowicz

We prove an optimal strategy for the children's game Guess Who? assuming the official rules are in use and that both players ask `classical' questions with a bipartite response. Applying a technique described in [Rabern, B \& Rabern, L…

Combinatorics · Mathematics 2026-02-17 David Cushing , Stuart Gipp , Ezra Levick , Em Rickinson , David I. Stewart

Adversarial multiplayer games are an important object of study in multiagent learning. In particular, polymatrix zero-sum games are a multiplayer setting where Nash equilibria are known to be efficiently computable. Towards understanding…

Computer Science and Game Theory · Computer Science 2026-04-13 Alexandros Hollender , Gilbert Maystre , Sai Ganesh Nagarajan

In a classical chess round-robin tournament, each of $n$ players wins, draws, or loses a game against each of the other $n-1$ players. A win rewards a player with 1 points, a draw with 1/2 point, and a loss with 0 points. We are interested…

Probability · Mathematics 2023-11-28 Yaakov Malinovsky

This paper investigates the potential benefits of cooperation in scenarios where finitely many agents compete for shared resources, leading to congestion and thereby reduced rewards. By appropriate coordination the members of the…

Computer Science and Game Theory · Computer Science 2024-10-10 Riya Sultana , Veeraruna Kavitha

Edouard Zeckendorf proved that every positive integer $n$ can be uniquely written \cite{Ze} as the sum of non-adjacent Fibonacci numbers, known as the Zeckendorf decomposition. Based on Zeckendorf's decomposition, we have the Zeckendorf…

We consider approximating the minmax value of a multi-player game in strategic form. Tightening recent bounds by Borgs et al., we observe that approximating the value with a precision of epsilon log n digits (for any constant epsilon>0 is…

Computer Science and Game Theory · Computer Science 2008-12-18 Kristoffer Arnsfelt Hansen , Thomas Dueholm Hansen , Peter Bro Miltersen , Troels Bjerre Sørensen

In many settings, there is an organizer who would like to divide a set of agents into $k$ coalitions, and cares about the friendships within each coalition. Specifically, the organizer might want to maximize utilitarian social welfare,…

Computer Science and Game Theory · Computer Science 2024-08-15 Hodaya Barr , Yohai Trabelsi , Sarit Kraus , Liam Roditty , Noam Hazon

We study the problem of computing Stackelberg equilibria Stackelberg games whose underlying structure is in congestion games, focusing on the case where each player can choose a single resource (a.k.a. singleton congestion games) and one of…

Computer Science and Game Theory · Computer Science 2018-08-31 Matteo Castiglioni , Alberto Marchesi , Nicola Gatti , Stefano Coniglio