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We consider the following combinatorial two-player game: On the random tree arising from a branching process, each round one player (Breaker) deletes an edge and by that removes the descendant and all its progeny, while the other (Maker)…

Probability · Mathematics 2024-12-17 Timo Vilkas

We introduce a new two-player game on graphs, in which players alternate choosing vertices until the set of chosen vertices forms a dominating set. The last player to choose a vertex is the winner. The game fits into the scheme of several…

Combinatorics · Mathematics 2025-10-31 Sean Fiscus , Glenn Hurlbert , Eric Myzelev , Travis Pence

In two-player games on graphs, the players move a token through a graph to produce an infinite path, which determines the winner of the game. Such games are central in formal methods since they model the interaction between a…

Computer Science and Game Theory · Computer Science 2023-06-22 Milad Aghajohari , Guy Avni , Thomas A. Henzinger

Two players alternate tossing a biased coin where the probability of getting heads is p. The current player is awarded alpha points for tails and alpha+beta for heads. The first player reaching n points wins. For a completely unfair coin…

Probability · Mathematics 2011-12-15 Robert W. Chen , Burton Rosenberg

"Guess Who?" is a popular two player game where players ask "Yes"/"No" questions to search for their opponent's secret identity from a pool of possible candidates. This is modeled as a simple stochastic game. Using this model, the optimal…

Probability · Mathematics 2025-11-24 Mihai Nica

Two-player graph games are a fundamental model for reasoning about the interaction of agents. These games are played between two players who move a token along a graph. In bidding games, the players have some monetary budget, and at each…

Computer Science and Game Theory · Computer Science 2024-12-24 Shaull Almagor , Guy Avni , Neta Dafni

Graph games lie at the algorithmic core of many automated design problems in computer science. These are games usually played between two players on a given graph, where the players keep moving a token along the edges according to…

Computer Science and Game Theory · Computer Science 2024-07-10 Guy Avni , Ehsan Kafshdar Goharshady , Thomas A. Henzinger , Kaushik Mallik

In the tournament game two players, called Maker and Breaker, alternately take turns in claiming an unclaimed edge of the complete graph on n vertices and selecting one of the two possible orientations. Before the game starts, Breaker fixes…

Combinatorics · Mathematics 2019-02-20 Dennis Clemens , Heidi Gebauer , Anita Liebenau

We consider the following game. A deck with $m$ copies of each of $n$ distinct cards is shuffled in a perfectly random way. The Guesser sequentially guesses the card from top to bottom. After each guess, the Guesser is informed whether the…

Probability · Mathematics 2022-12-19 Zipei Nie

We study variants of a stochastic game inspired by backgammon where players may propose to double the stake, with the game state dictated by a one-dimensional random walk. Our variants allow for different numbers of proposals and different…

Optimization and Control · Mathematics 2024-10-28 Haoru Ju , Daniel Leifer , Steven J. Miller , Sooraj A. Padmanabhan , Chenyang Sun , Luke Tichi , Benjamin Tocher , Kiley Wallace

A decision maker observes the evolving state of the world while constantly trying to predict the next state given the history of past states. The ability to benefit from such predictions depends not only on the ability to recognize patters…

Computer Science and Game Theory · Computer Science 2014-09-17 Gilad Bavly , Ron Peretz

We introduce and study Maker/Breaker-type positional games on random graphs. Our main concern is to determine the threshold probability $p_{F}$ for the existence of Maker's strategy to claim a member of $F$ in the unbiased game played on…

Combinatorics · Mathematics 2007-05-23 Milos Stojakovic , Tibor Szabo

We investigate a game played between two players, Maker and Breaker, on a countably infinite complete graph where the vertices are the rational numbers. The players alternately claim unclaimed edges. It is Maker's goal to have after…

Combinatorics · Mathematics 2024-12-23 Nathan Bowler , Florian Gut

A card guessing game is played between two players, Guesser and Dealer. At the beginning of the game, the Dealer holds a deck of $n$ cards (labeled $1, ..., n$). For $n$ turns, the Dealer draws a card from the deck, the Guesser guesses…

Computational Complexity · Computer Science 2022-01-04 Boaz Menuhin , Moni Naor

The Maker-Breaker connectivity game and Hamilton cycle game belong to the best studied games in positional games theory, including results on biased games, games on random graphs and fast winning strategies. Recently, the Connector-Breaker…

Combinatorics · Mathematics 2023-06-02 Dennis Clemens , Pranshu Gupta , Yannick Mogge

Consider the following two-player game on the edges of $K_n$, the complete graph with $n$ vertices: Starting with an empty graph $G$ on the vertex set of $K_n$, in each round the first player chooses $b \in \mathbb{N}$ edges from $K_n$…

Combinatorics · Mathematics 2022-07-07 Rajko Nenadov

In this paper we introduce and study {\em all-pay bidding games}, a class of two player, zero-sum games on graphs. The game proceeds as follows. We place a token on some vertex in the graph and assign budgets to the two players. Each turn,…

Computer Science and Game Theory · Computer Science 2019-11-20 Guy Avni , Rasmus Ibsen-Jensen , Josef Tkadlec

Assume that letters (from a finite alphabet) in a text form a Markov chain. We track two distinct words, $U$ and $D$. A gambler gains 1 point for each occurrence of $U$ (including overlapping occurrences) and loses 1 point for each…

Probability · Mathematics 2025-06-03 Zhiyi Chi , Vladimir Pozdnyakov

We study a combinatorial coloring game between two players, Spoiler and Algorithm, who alternate turns. First, Spoiler places a new token at a vertex in $G$, and Algorithm responds by assigning a color to the new token. Algorithm must…

Combinatorics · Mathematics 2017-12-27 Kevin G. Milans , Michael C. Wigal

M\"uller games form a well-established class of games for model checking and verification. These games are played on directed graphs $\mathcal G$ where Player 0 and Player 1 play by generating an infinite path through the graph. The winner…

Computer Science and Game Theory · Computer Science 2023-11-09 Zihui Liang , Bakh Khoussainov , Mingyu Xiao