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This work studies the following question: can plays in a Muller game be stopped after a finite number of moves and a winner be declared. A criterion to do this is sound if Player 0 wins an infinite-duration Muller game if and only if she…

Computer Science and Game Theory · Computer Science 2010-06-09 John Fearnley , Martin Zimmermann

We study binary coordination games with random utility played in networks. A typical equilibrium is fuzzy -- it has positive fractions of agents playing each action. The set of average behaviors that may arise in an equilibrium typically…

Theoretical Economics · Economics 2021-09-01 Marcin Pęski

We consider deterministic mean field games in which the agents control their acceleration and are constrained to remain in a domain of R n. We study relaxed equilibria in the Lagrangian setting; they are described by a probability measure…

Analysis of PDEs · Mathematics 2021-11-04 Yves Achdou , Paola Mannucci , Claudio Marchi , Nicoletta Tchou

The multiplication game is a two-person game in which each player chooses a positive integer without knowledge of the other player's number. The two numbers are then multiplied together and the first digit of the product determines the…

Computer Science and Game Theory · Computer Science 2016-07-11 Kent E. Morrison

Player ONE chooses a meager set and player TWO, a nowhere dense set per inning. They play $\omega$ many innings. ONE's consecutive choices must form a (weakly) increasing sequence. TWO wins if the union of the chosen nowhere dense sets…

Logic · Mathematics 2009-09-25 Marion Scheepers

We derive multiparty games that, if the winning chance exceeds a certain limit, prove the incompatibility of the parties' causal relations with any partial order. This, in turn, means that the parties exert a back-action on the causal…

General Relativity and Quantum Cosmology · Physics 2025-05-15 Eleftherios-Ermis Tselentis , Ämin Baumeler

We propose a formulation of a general-sum bimatrix game as a bipartite directed graph with the objective of establishing a correspondence between the set of the relevant structures of the graph (in particular elementary cycles) and the set…

Computer Science and Game Theory · Computer Science 2007-05-23 Raghav Aras , Alain Dutech , François Charpillet

Coloring games are combinatorial games where the players alternate painting uncolored vertices of a graph one of $k > 0$ colors. Each different ruleset specifies that game's coloring constraints. This paper investigates six impartial…

Combinatorics · Mathematics 2012-02-28 Gabriel Beaulieu , Kyle Burke , Eric Duchêne

The Lipschitz constant of a finite normal-form game is the maximal change in some player's payoff when a single opponent changes his strategy. We prove that games with small Lipschitz constant admit pure {\epsilon}-equilibria, and pinpoint…

Combinatorics · Mathematics 2013-09-24 Yaron Azrieli , Eran Shmaya

We study an impartial avoidance game introduced by Anderson and Harary. The game is played by two players who alternately select previously unselected elements of a finite group. The first player who cannot select an element without making…

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

Any nonempty, compact, semi-algebraic set in [0, 1] n is the projection of the set of mixed equilibria of a finite game with 2 actions per player on its first n coordinates. A similar result follows for sets of equilibrium payoffs. The…

Optimization and Control · Mathematics 2016-01-11 Guillaume Vigeral , Yannick Viossat

Combinatorial Game Theory has also been called `additive game theory', whenever the analysis involves sums of independent game components. Such {\em disjunctive sums} invoke comparison between games, which allows abstract values to be…

Combinatorics · Mathematics 2021-01-29 Urban Larsson , Richard J. Nowakowski , Carlos P. Santos

We study a game first introduced by Martin (actually we use a slight variation of this game) which plays a role for measure analogous to the Banach-Mazur game for category. We first present proofs for the basic connections between this game…

Logic · Mathematics 2019-10-25 Logan Crone , Lior Fishman , Stephen Jackson , Houston Schuerger , David Simmons

The domination game is an optimization game played by two players, Dominator and Staller, who alternately select vertices in a graph $G$. A vertex is said to be dominated if it has been selected or is adjacent to a selected vertex. Each…

Combinatorics · Mathematics 2023-02-03 Leo Versteegen

The Maker-Breaker domination game (MBD game) is a two-player game played on a graph $G$ by Dominator and Staller. They alternately select unplayed vertices of $G$. The goal of Dominator is to form a dominating set with the set of vertices…

Combinatorics · Mathematics 2025-12-10 Athira Divakaran , Tanja Dravec , Tijo James , Sandi Klavžar , Latha S Nair

We analyze the domination game, where two players, Dominator and Staller, construct together a dominating set M in a given graph, by alternately selecting vertices into M. Each move must increase the size of the dominated set. The players…

Data Structures and Algorithms · Computer Science 2016-03-04 Neta Marcus , David Peleg

Coherent sets of desirable gamble sets is used as a model for representing an agents opinions and choice preferences under uncertainty. In this paper we provide some results about the axioms required for coherence and the natural extension…

Artificial Intelligence · Computer Science 2024-05-17 Catrin Campbell-Moore

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

Parsimonious games are a subset of constant sum homogeneous weighted majority games unequivocally described by their free type representation vector. We show that the minimal winning quota of parsimonious games satisfies a second order,…

Dynamical Systems · Mathematics 2014-02-21 Flavio Pressacco , Giacomo Plazzotta , Laura Ziani

A subset of the vertex set of a graph is geodetically convex if it contains every vertex on any shortest path between two elements of the subset. The convex hull of a set of vertices is the smallest convex set containing the set. We study…

Combinatorics · Mathematics 2025-05-14 Bret J. Benesh , Dana C. Ernst , Marie Meyer , Sarah K. Salmon , Nandor Sieben