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Winners-take-all situations introduce an incentive for agents to diversify their behavior, since doing so will result in splitting an eventual price with fewer people. At the same time, when the payoff of a process depends on a parameter…

Computer Science and Game Theory · Computer Science 2019-06-11 Abel Molina

We generalize the results and conjectures of Tam\'{a}s Lengyel, showing that the \textsc{nim}-values of a large class of two-dimensional subtraction-transfer games are periodic. These are impartial, normal-play games with two piles of…

Combinatorics · Mathematics 2026-05-25 Alon Danai , Paul Ellis , Thotsaporn Aek Thanatipanonda

When normal and mis\`{e}re games are played on bi-type binary Galton-Watson trees (with vertices coloured blue or red and each having either no child or precisely $2$ children), with one player allowed to move along monochromatic edges and…

Probability · Mathematics 2021-03-31 Moumanti Podder

Promoting behavioural diversity is critical for solving games with non-transitive dynamics where strategic cycles exist, and there is no consistent winner (e.g., Rock-Paper-Scissors). Yet, there is a lack of rigorous treatment for defining…

Artificial Intelligence · Computer Science 2021-06-11 Nicolas Perez Nieves , Yaodong Yang , Oliver Slumbers , David Henry Mguni , Ying Wen , Jun Wang

We study the class of word-building games, where two players pick letters from a finite alphabet to construct a finite or infinite word. The outcome is determined by whether the resulting word lies in a prescribed set (a win for player $A$)…

Dynamical Systems · Mathematics 2015-01-19 Ville Salo , Ilkka Törmä

In numerous positional games the identity of the winner is easily determined. In this case one of the more interesting questions is not {\em who} wins but rather {\em how fast} can one win. These type of problems were studied earlier for…

Combinatorics · Mathematics 2008-06-03 Dan Hefetz , Michael Krivelevich , Miloš Stojaković , Tibor Szabó

This paper introduces a novel algorithm for two-player deterministic games with perfect information, which we call PROBS (Predict Results of Beam Search). Unlike existing methods that predominantly rely on Monte Carlo Tree Search (MCTS) for…

Artificial Intelligence · Computer Science 2024-04-26 Sergey Pastukhov

This paper considers a reach-avoid differential game in three-dimensional space with four equal-speed players. A plane divides the game space into a play subspace and a goal subspace. The evader aims at entering the goal subspace while…

Optimization and Control · Mathematics 2019-04-08 Rui Yan , Zongying Shi , Yisheng Zhong

We study biased {\em orientation games}, in which the board is the complete graph $K_n$, and Maker and Breaker take turns in directing previously undirected edges of $K_n$. At the end of the game, the obtained graph is a tournament. Maker…

Combinatorics · Mathematics 2011-07-12 Ido Ben-Eliezer , Michael Krivelevich , Benny Sudakov

We give operational meaning to wave-particle duality in terms of discrimination games. Duality arises as a constraint on the probability of winning these games. The games are played with the aid of an n-port interferometer, and involve 3…

Quantum Physics · Physics 2018-02-07 Emilio Bagan , John Calsamiglia , Janos A. Bergou , Mark Hillery

We study zero-sum (combinatorial) games, within the framework of so-called Richman auctions (Lazarus et al. 1996) namely, we modify the alternating play scoring ruleset Cumulative Subtraction (CS) (Cohensius et al. 2019), to a discrete…

Computer Science and Game Theory · Computer Science 2020-03-13 Urban Larsson , Neel Patel , Ravi Kant Rai

We study a spatial two-strategy (cooperation and defection) Prisoner's Dilemma game with two types ($A$ and $B$) of players located on the sites of a square lattice. The evolution of strategy distribution is governed by iterated strategy…

Physics and Society · Physics 2009-01-15 Gyorgy Szabo , Attila Szolnoki

We introduce a simple one-parameter game derived from a model describing the properties of a directed polymer in a random medium. At his turn, each of the two players picks a move among two alternatives in order to maximize his final score,…

Statistical Mechanics · Physics 2008-12-08 Clément Sire

We study two-player games of infinite duration that are played on finite or infinite game graphs. A winning strategy for such a game is positional if it only depends on the current position, and not on the history of the play. A game is…

Logic in Computer Science · Computer Science 2012-08-29 Erich Graedel , Igor Walukiewicz

We study 2-player impartial games of the form take-away which produce P-positions (second player winning positions) corresponding to complementary Beatty sequences, given by the continued fractions (1;k,1,k,1,...) and (k+1;k,1,k,1,...). Our…

Combinatorics · Mathematics 2013-02-04 Urban Larsson , Mike Weimerskirch

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

Computer Science and Game Theory · Computer Science 2020-01-28 Guy Avni , Thomas A. Henzinger , Rasmus Ibsen-Jensen

The second author introduced with I. T\"orm\"a a two-player word-building game [Playing with Subshifts, Fund. Inform. 132 (2014), 131--152]. The game has a predetermined (possibly finite) choice sequence $\alpha_1$, $\alpha_2$, $\ldots$ of…

Formal Languages and Automata Theory · Computer Science 2019-09-17 Jarkko Peltomäki , Ville Salo

We study the Maker-Maker version of the domination game introduced in 2018 by Duch\^ene et al. Given a graph, two players alternately claim vertices. The first player to claim a dominating set of the graph wins. As the Maker-Breaker…

Combinatorics · Mathematics 2023-06-12 Eric Duchêne , Arthur Dumas , Nacim Oijid , Aline Parreau , Eric Rémila

We present constructions regarding the general behaviour of biased positional games, and amongst others show that the outcome of such a game can differ in an arbitrary way depending on which player starts the game, and that fair biased…

Combinatorics · Mathematics 2025-09-08 Ali Deniz Bagdas , Dennis Clemens , Fabian Hamann , Yannick Mogge

We introduce the following variant of the Gale-Berlekamp switching game. Let $P$ be a set of n noncollinear points in the plane, each of them having weight $+1$ or $-1$. At each step, we pick a line $\ell$ passing through at least two…

Computational Geometry · Computer Science 2025-08-19 Adrian Dumitrescu , Jeck Lim , János Pach , Ji Zeng