Epidemiography. II: Games with a dozing yet winning player
type: Item
instance of: scholarly article
title: Epidemiography. II: Games with a dozing yet winning player
zbMATH Open document ID: 0649.90110
DOI: 10.1016/0097-3165(88)90030-1
author: Aviezri S. Fraenkel
author: Martin Loebl
author: J. Nešetřil
published in: Journal of Combinatorial Theory. Series A
publication date: 1988-01-01T00:00:00Z
review text: [For part I see the first and third author, Pac. J. Math. 118, 369-381 (1985; Zbl 0574.90110).] Epidemiography designates a class of games played on directed graphs. At step k of the game, the move made on a digraph G is replicated onto f(k) isomorphic copies of G. The player first unable to move is the loser; his opponent the winner. We show that if G is finite and acyclic, then the game terminates for every function \(f: Z^ k\to Z^ 0\), and we construct classes of digraphs and functions f for which the first (second) player can win. Many epidemiography games are robust: the outcome depends only on the ``foliage'' of G, and the winner can play randomly during much of the time. Play is very long even if f grows only linearly. Bounds on the length of play are provided.
Mathematics Subject Classification ID: 91A24
zbMATH DE Number: 4061030
zbMATH Keywords: perfect information game
zbMATH Keywords: dancing mania
zbMATH Keywords: Epidemiography
zbMATH Keywords: games played on directed graphs
MaRDI profile type: Publication
full work available at URL: 0097-3165(88)90030-1
OpenAlex ID: W2015620656
cites work: Q3941433
cites work: Q3944542
cites work: Q4099541
cites work: Loopy Games
cites work: Complexities of winning strategies in diophantine games
cites work: Epidemiography
cites work: Strategies for compounds of partizan games
cites work: The generalized Sprague-Grundy function and its invariance under certain mappings
cites work: Some undecidable determined games
cites work: Sums of Zuchswang games
cites work: Q3680651
cites work: Q3989710
cites work: Linearity and Unprovability of Set Union Problem Strategies
cites work: Q3772201
cites work: Q3245637
cites work: Algebraic solutions of partizan games with cycles
Recommended article: An SIS epidemiology game with two subpopulations
Recommended article: Spontaneous divergence of disease status in an economic epidemiological game
Recommended article: Epidemic population games and evolutionary dynamics
Recommended article: On the outcome of epidemics with detections
Recommended article: An epidemic with individual infectivities and susceptibilities
Recommended article: Game-theoretic frameworks for epidemic spreading and human decision-making: a review
Recommended article: The ``deterministic simple epidemic'' unmasked
Recommended article: Game theoretic modeling of infectious disease transmission with delayed emergence of symptoms
Recommended article: Games of age-dependent prevention of chronic infections by social distancing
Recommended article: Infection Spreading and Source Identification: A Hide and Seek Game
description: scientific article; zbMATH DE number 4061030