English
Related papers

Related papers: Avoidance games are PSPACE-Complete

200 papers

Impartial subtraction games on the nonnegative integers have been studied by many and discussed in detail in for example the remarkable work Winning Ways by Conway, Berlekamp and Guy. We describe how comply variations of these games,…

Number Theory · Mathematics 2012-09-11 Urban Larsson

We consider a biased version of Maker-Breaker domination games, which were recently introduced by Gledel, Ir{\v{s}}i{\v{c}}, and Klav{\v{z}}ar. Two players, Dominator and Staller, alternatingly claim vertices of a graph $G$ where Dominator…

Combinatorics · Mathematics 2024-08-02 Ali Deniz Bagdas , Dennis Clemens , Fabian Hamann , Yannick Mogge

We study pursuit-evasion in a polygonal environment with polygonal obstacles. In this turn based game, an evader $e$ is chased by pursuers $p_1, p_2, ..., p_{\ell}$. The players have full information about the environment and the location…

Computational Geometry · Computer Science 2014-10-21 Brendan Ames , Andrew Beveridge , Rosalie Carlson , Claire Djang , Volkan Isler , Stephen Ragain , Maxray Savage

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 establish the first hardness results for the problem of computing the value of one-round games played by a verifier and a team of provers who can share quantum entanglement. In particular, we show that it is NP-hard to approximate within…

Quantum Physics · Physics 2007-11-21 Julia Kempe , Hirotada Kobayashi , Keiji Matsumoto , Ben Toner , Thomas Vidick

The concept of nimbers--a.k.a. Grundy-values or nim-values--is fundamental to combinatorial game theory. Nimbers provide a complete characterization of strategic interactions among impartial games in their disjunctive sums as well as the…

Computational Complexity · Computer Science 2022-02-24 Kyle Burke , Matthew Ferland , Shanghua Teng

The Domination game is an impartial game on graphs, introduced in 2010, and proved PSPACE-complete in the normal variant in 2026. In this game, Alice and Bob alternately select playable vertices, where a vertex is playable if it dominates…

Combinatorics · Mathematics 2026-05-05 Rudini Sampaio , Edileudo Maciel M. Filho , Jefter G. Maciel Paz , João Marcos Brito

Patrolling Games were introduced by Alpern, Morton and Papadaki (2011) to model the adversarial problem where a mobile Patroller can thwart an attack at some location only by visiting it during the attack period, which has a prescribed…

Cryptography and Security · Computer Science 2020-12-08 Steve Alpern , Paul Chleboun , Stamatios Katsikas

Concurrent parameterized games involve a fixed yet arbitrary number of players. They are described by finite arenas in which the edges are labeled with languages that describe the possible move combinations leading from one vertex to…

Logic in Computer Science · Computer Science 2025-05-22 Nathalie Bertrand , Patricia Bouyer , Gaëtan Staquet

Simple games cover voting systems in which a single alternative, such as a bill or an amendment, is pitted against the status quo. A simple game or a yes-no voting system is a set of rules that specifies exactly which collections of ``yea''…

Computer Science and Game Theory · Computer Science 2008-03-05 Josep Freixas , Xavier Molinero , Martin Olsen , Maria Serna

Consider the following one-player game played on an initially empty graph with $n$ vertices. At each stage a randomly selected new edge is added and the player must immediately color the edge with one of $r$ available colors. Her objective…

Combinatorics · Mathematics 2016-03-25 Andreas Noever

We consider the mixed search game against an agile and visible fugitive. This is the variant of the classic fugitive search game on graphs where searchers may be placed to (or removed from) the vertices or slide along edges. Moreover, the…

Discrete Mathematics · Computer Science 2022-10-21 Guillaume Mescoff , Christophe Paul , Dimitrios M. Thilikos

We analyze the computational complexity of motion planning through local "input/output" gadgets with separate entrances and exits, and a subset of allowed traversals from entrances to exits, each of which changes the state of the gadget and…

Computational Complexity · Computer Science 2023-11-16 Hayashi Ani , Erik D. Demaine , Dylan H. Hendrickson , Jayson Lynch

Counter reachability games are played by two players on a graph with labelled edges. Each move consists in picking an edge from the current location and adding its label to a counter vector. The objective is to reach a given counter value…

Computer Science and Game Theory · Computer Science 2013-07-22 Julien Reichert

In recent years, there has been a growing interest in games on graphs within the research community, fueled by their relevance in applications such as economics, politics, and epidemiology. This paper aims to comprehensively detail the…

Computer Science and Game Theory · Computer Science 2024-06-11 Christian Giannetti

Algorithms for computing game-theoretic solutions have recently been applied to a number of security domains. However, many of the techniques developed for compact representations of security games do not extend to {\em Bayesian} security…

Computer Science and Game Theory · Computer Science 2016-04-19 Yuqian Li , Vincent Conitzer , Dmytro Korzhyk

The design of aircraft collision avoidance algorithms is a subtle but important challenge that merits the need for provable safety guarantees. Obtaining such guarantees is nontrivial given the unpredictability of the interplay of the…

Logic in Computer Science · Computer Science 2022-11-23 Rachel Cleaveland , Stefan Mitsch , André Platzer

We initiate the study of the phantom version of Maker-Breaker positional games. In a phantom game, the moves of one of the players are hidden from the other player, who still has the complete information. We look at the biased $(a:b)$…

Combinatorics · Mathematics 2025-07-31 Dennis Clemens , Fabian Hamann , Mirjana Mikalački , Yannick Mogge , Miloš Stojaković

Simulation and bisimulation metrics for stochastic systems provide a quantitative generalization of the classical simulation and bisimulation relations. These metrics capture the similarity of states with respect to quantitative…

Computer Science and Game Theory · Computer Science 2015-07-01 Krishnendu Chatterjee , Luca de Alfaro , Rupak Majumdar , Vishwanath Raman

This project investigates the potential of computers to solve complex tasks such as games. The paper proves that the complexity of a generalized version of spider solitaire is NP-Complete and uses much of structure of the proof that…

Computational Complexity · Computer Science 2011-10-06 Jesse Stern