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Domination game [SIAM J.\ Discrete Math.\ 24 (2010) 979--991] and total domination game [Graphs Combin.\ 31 (2015) 1453--1462] are by now well established games played on graphs by two players, named Dominator and Staller. In this paper,…

We consider the strong Ramsey-type game $\mathcal{R}^{(k)}(\mathcal{H}, \aleph_0)$, played on the edge set of the infinite complete $k$-uniform hypergraph $K^k_{\mathbb{N}}$. Two players, called FP (the first player) and SP (the second…

Combinatorics · Mathematics 2016-05-26 Dan Hefetz , Christopher Kusch , Lothar Narins , Alexey Pokrovskiy , Clément Requilé , Amir Sarid

In this paper the set of value functions of all-possible zero-sum differential games with terminal payoff is characterized. The necessary and sufficient condition for a given function to be a value of some differential game with terminal…

Optimization and Control · Mathematics 2008-11-12 Yurii Averboukh

Delay games are two-player games of infinite duration in which one player may delay her moves to obtain a lookahead on her opponent's moves. We consider delay games with winning conditions expressed in weak monadic second order logic with…

Computer Science and Game Theory · Computer Science 2015-09-25 Martin Zimmermann

Two-player win/lose games of infinite duration are involved in several disciplines including computer science and logic. If such a game has deterministic winning strategies, one may ask how simple such strategies can get. The answer may…

Computer Science and Game Theory · Computer Science 2020-02-04 Stéphane Le Roux

This paper is concerned with games of infinite duration played over potentially infinite graphs. Recently, Ohlmann (LICS 2022) presented a characterisation of objectives admitting optimal positional strategies, by means of universal graphs:…

Formal Languages and Automata Theory · Computer Science 2025-03-26 Antonio Casares , Pierre Ohlmann

This paper contributes to the study of positional determinacy of infinite duration games played on potentially infinite graphs with neutral transitions. Recently, [Ohlmann, TheoretiCS 2023] established that positionality of…

Computer Science and Game Theory · Computer Science 2026-05-12 Antonio Casares , Pierre Ohlmann , Michał Skrzypczak , Igor Walukiewicz

Relying on recent generalizations of the Fra\"iss\'e theory to a broader category-theoretic context, we study the class of abstract finite games played between two players and show the existence of an infinitetly countable game which is…

General Mathematics · Mathematics 2025-11-18 Matheus Duzi , Paul Szeptycki , Walter Tholen

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

Escalation is the fact that in a game (for instance an auction), the agents play forever. It is not necessary to consider complex examples to establish its rationality. In particular, the $0,1$-game is an extremely simple infinite game in…

Computer Science and Game Theory · Computer Science 2013-06-11 Pierre Lescanne

Transfinite set theory including the axiom of choice supplies the following basic theorems: (1) Mappings between infinite sets can always be completed, such that at least one of the sets is exhausted. (2) The real numbers can be well…

General Mathematics · Mathematics 2007-05-23 W. Mueckenheim

We study infinite asymptotic games in Banach spaces with an F.D.D. and prove that analytic games are determined by characterising precisely the conditions for the players to have winning strategies. These results are applied to characterise…

Functional Analysis · Mathematics 2008-10-24 Christian Rosendal

We compare games under delayed control and delay games, two types of infinite games modelling asynchronicity in reactive synthesis. Our main result, the interreducibility of the existence of sure winning strategies for the protagonist,…

Computer Science and Game Theory · Computer Science 2023-10-03 Martin Fränzle , Sarah Winter , Martin Zimmermann

We introduce the game of Cops and Eternal Robbers played on graphs, where there are infinitely many robbers that appear sequentially over distinct plays of the game. A positive integer $t$ is fixed, and the cops are required to capture the…

Discrete Mathematics · Computer Science 2020-03-11 Anthony Bonato , Melissa Huggan , Trent Marbach , Fionn Mc Inerney

We show that under some general conditions the finite memory determinacy of a class of two-player win/lose games played on finite graphs implies the existence of a Nash equilibrium built from finite memory strategies for the corresponding…

Computer Science and Game Theory · Computer Science 2016-07-13 Stéphane Le Roux , Arno Pauly

In this paper we introduce and study the domination game on hypergraphs. This is played on a hypergraph $\mathcal{H}$ by two players, namely Dominator and Staller, who alternately select vertices such that each selected vertex enlarges the…

Combinatorics · Mathematics 2017-10-03 Csilla Bujtás , Balázs Patkós , Zsolt Tuza , Máté vizer

We analyze a coin-based game with two players where, before starting the game, each player selects a string of length $n$ comprised of coin tosses. They alternate turns, choosing the outcome of a coin toss according to specific rules. As a…

We consider perfect-information reachability stochastic games for 2 players on infinite graphs. We identify a subclass of such games, and prove two interesting properties of it: first, Player Max always has optimal strategies in games from…

Computer Science and Game Theory · Computer Science 2011-06-10 Václav Brožek

Various voting rules are based on ranking the candidates by scores induced by aggregating voter preferences. A winner (respectively, unique winner) is a candidate who receives a score not smaller than (respectively, strictly greater than)…

Computer Science and Game Theory · Computer Science 2021-02-01 Aviram Imber , Benny Kimelfeld

We consider a zero-sum continuous time stopping game in which the pay-off is revealed in the maximum of the two stopping times instead of the minimum, which is the case in Dynkin games.

Probability · Mathematics 2015-07-28 Erhan Bayraktar , Zhou Zhou