Equilibria in Nonantagonistic Positional Games on Graphs and Searching for Them

2018 ◽  
Vol 79 (2) ◽  
pp. 360-365
Author(s):  
I. A. Bashlaeva
Keyword(s):  
Games On Graphs ◽  
Positional Games

scholarly journals A metric for positional games

2000 ◽  
Vol 230 (1-2) ◽  
pp. 207-219 ◽  
Author(s):  
J.Mark Ettinger
Keyword(s):  
Positional Games

scholarly journals On the Chvátal-Erdős Triangle Game

10.37236/559 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
József Balogh ◽  
Wojciech Samotij
Keyword(s):  
Complete Graph ◽  
Winning Strategy ◽  
Seminal Paper ◽  
Positional Games ◽  
Positive Integers

Given a graph $G$ and positive integers $n$ and $q$, let ${\bf G}(G;n,q)$ be the game played on the edges of the complete graph $K_n$ in which the two players, Maker and Breaker, alternately claim $1$ and $q$ edges, respectively. Maker's goal is to occupy all edges in some copy of $G$; Breaker tries to prevent it. In their seminal paper on positional games, Chvátal and Erdős proved that in the game ${\bf G}(K_3;n,q)$, Maker has a winning strategy if $q < \sqrt{2n+2}-5/2$, and if $q \geq 2\sqrt{n}$, then Breaker has a winning strategy. In this note, we improve the latter of these bounds by describing a randomized strategy that allows Breaker to win the game ${\bf G}(K_3;n,q)$ whenever $q \geq (2-1/24)\sqrt{n}$. Moreover, we provide additional evidence supporting the belief that this bound can be further improved to $(\sqrt{2}+o(1))\sqrt{n}$.

Related Games on Graphs and Hypergraphs

2021 ◽  
pp. 83-108
Author(s):  
Boštjan Brešar ◽  
Michael A. Henning ◽  
Sandi Klavžar ◽  
Douglas F. Rall
Keyword(s):  
Games On Graphs

Fugitive-search games on graphs and related parameters

1995 ◽  
pp. 331-342 ◽  
Author(s):  
Nick D. Dendris ◽  
Lefteris M. Kirousis ◽  
Dimitris M. Thilikos
Keyword(s):  
Search Games ◽  
Games On Graphs

scholarly journals The complexity of flood-filling games on graphs

2012 ◽  
Vol 160 (7-8) ◽  
pp. 959-969 ◽  
Author(s):  
Kitty Meeks ◽  
Alexander Scott
Keyword(s):  
Games On Graphs
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