The Maker–Breaker percolation game on a random board
Abstract
The (m,b) Maker–Breaker percolation game on (Z2)p, introduced by Day and Falgas-Ravry, is played in the following way. Before the game starts, each edge of Z2 is removed independently with probability 1−p. After that, Maker chooses a vertex v0 to protect. Then in each round Maker and Breaker claim, respectively, m and b unclaimed edges of Z2. Breaker wins if after the removal of the edges claimed by him the component of v0 becomes finite, and Maker wins if she can indefinitely prevent Breaker from winning. We show that for any p0.9402, while almost surely Breaker has a winning strategy whenever p
Fields of Study & Subjects
Game Theory and Applications
Artificial Intelligence in Games
Publication details
- Journal / source
- The Annals of Probability
- Volume
- 54
- Issue
- 3
- Publication date
- 21 April 2026
- Language
- EN