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We prove PSPACE-hardness for fifteen games in the Super Mario Bros. 2D platforming video game series. Previously, only the original Super Mario Bros. was known to be PSPACE-hard (FUN 2016), though several of the games we study were known to…

Computational Complexity · Computer Science 2024-04-17 MIT Hardness Group , Hayashi Ani , Erik D. Demaine , Holden Hall , Matias Korman

The Taxman game has proven to be hard to solve optimally, so efforts have been made to find heuristic strategies that do well in practice. We present results on the NP-hardness of a variant of the game via an equivalence to a particular…

Combinatorics · Mathematics 2022-11-02 Atli Fannar Franklín , Robert K. Moniot

We study the computational complexity of controlling the result of an election by breaking ties strategically. This problem is equivalent to the problem of deciding the winner of an election under parallel universes tie-breaking. When the…

Artificial Intelligence · Computer Science 2014-05-30 Nicholas Mattei , Nina Narodytska , Toby Walsh

Something is definitely wrong. If the game has a linear winning strategy, then it is tractable. What's going on? Well, we describe a two-person game which has a definite winner, that is, a player who can force a win in a finite number of…

Combinatorics · Mathematics 2016-09-07 Aviezri S. Fraenkel

The strong Ramsey game $R(\mathcal{B}, H)$ is a two-player game played on a graph $\mathcal{B}$, referred to as the board, with a target graph $H$. In this game, two players, $P_1$ and $P_2$, alternately claim unclaimed edges of…

Combinatorics · Mathematics 2025-01-28 Jiangdong Ai , Jun Gao , Zixiang Xu , Xin Yan

We revisit the game in which each of several players chooses a pattern and then a coin is flipped repeatedly until one of these patterns is generated. In particular, we demonstrate how to compute the probability of any one player winning…

Probability · Mathematics 2015-07-07 Jan Vrbik , Paul Vrbik

In this paper we study a cooperative card game called Hanabi from the viewpoint of algorithmic combinatorial game theory. In Hanabi, each card has one among $c$ colors and a number between $1$ and $n$. The aim is to make, for each color, a…

Discrete Mathematics · Computer Science 2017-03-09 Jean-Francois Baffier , Man-Kwun Chiu , Yago Diez , Matias Korman , Valia Mitsou , André van Renssen , Marcel Roeloffzen , Yushi Uno

Pebble games were extensively studied in the 1970s and 1980s in a number of different contexts. The last decade has seen a revival of interest in pebble games coming from the field of proof complexity. Pebbling has proven to be a useful…

Computational Complexity · Computer Science 2015-07-01 Jakob Nordstrom

We prove that deciding whether the Runner can win this turn (mate-in-1) in the Netrunner card game generalized to allow decks to contain an arbitrary number of copies of a card is weakly NP-hard. We also prove that deciding whether the Corp…

Computational Complexity · Computer Science 2017-10-17 Jeffrey Bosboom , Michael Hoffmann

This paper discusses the complexity of graph pebbling, dealing with both traditional pebbling and the recently introduced game of cover pebbling. Determining whether a configuration is solvable according to either the traditional definition…

Combinatorics · Mathematics 2007-05-23 Nathaniel G. Watson

In this paper we introduce polytopal stochastic games, an extension of two-player, zero-sum, turn-based stochastic games, in which we may have uncertainty over the transition probabilities. In these games the uncertainty over the…

Logic in Computer Science · Computer Science 2025-02-26 Pablo F. Castro , Pedro D'Argenio

We continue the investigation of finite-duration variants of infinite-duration games by extending known results for games played on finite graphs to those played on infinite ones. In particular, we establish an equivalence between pushdown…

Computer Science and Game Theory · Computer Science 2012-10-10 Wladimir Fridman , Martin Zimmermann

The Possible-Winner problem asks, given an election where the voters' preferences over the set of candidates is partially specified, whether a distinguished candidate can become a winner. In this work, we consider the computational…

Computer Science and Game Theory · Computer Science 2018-02-27 Batya Kenig

We consider imperfect information stochastic games where we require the players to use pure (i.e. non randomised) strategies. We consider reachability, safety, B\"uchi and co-B\"uchi objectives, and investigate the existence of…

Formal Languages and Automata Theory · Computer Science 2018-03-28 Arnaud Carayol , Christof Löding , Olivier Serre

Wythoff's Game is a game for two players playing alternately on two stacks of tiles. On her turn, a player can either remove a positive number of tiles from one stack, or remove an equal positive number of tiles from both stacks. The last…

Combinatorics · Mathematics 2016-06-23 Alex Meadows , Brad Putman

Infinite games where several players seek to coordinate under imperfect information are known to be intractable, unless the information flow is severely restricted. Examples of undecidable cases typically feature a situation where players…

Logic in Computer Science · Computer Science 2014-05-01 Dietmar Berwanger , Anup Basil Mathew

Positions of chess players in intransitive (rock-paper-scissors) relations are considered. Namely, position A of White is preferable (it should be chosen if choice is possible) to position B of Black, position B of Black is preferable to…

History and Overview · Mathematics 2022-12-22 Alexander Poddiakov

The Maker-Maker convention of positional games is played on a hypergraph whose edges are interpreted as winning sets. Two players take turns picking a previously unpicked vertex, aiming at being first to pick all the vertices of some edge.…

Discrete Mathematics · Computer Science 2025-04-22 Florian Galliot , Jonas Sénizergues

In the paper it is proven that the two-players turn-based stochastic game "Risk or Safety" has a unique solution. Both players need to play the same strategy if they want to maximize their winning chances. An analytical method based on the…

Combinatorics · Mathematics 2026-03-03 Rüdiger Jehn

We settle two long-standing complexity-theoretical questions-open since 1981 and 1993-in combinatorial game theory (CGT). We prove that the Grundy value (a.k.a. nim-value, or nimber) of Undirected Geography is PSPACE-complete to compute.…

Computational Complexity · Computer Science 2021-06-07 Kyle Burke , Matthew Ferland , Shanghua Teng