Adva Mond

Maker-Breaker percolation games on a random board

The (m,b) Maker-Breaker percolation game on an infinite graph G is played in the following way. Maker starts by choosing a vertex and naming it the origin. Maker and Breaker then alternately claim m and b unclaimed edges of G, respectively. Breaker wins if the component containing the origin becomes finite when his edges are deleted from G. Maker wins if she can indefinitely avoid a win of Breaker.

We will discuss the state of the art for this game, with special attention to the case where G is the result of bond percolation on the square lattice. In particular, we will show how this game can be analyzed using tools from bootstrap percolation.

This is joint work with Vojtěch Dvořák and Victor Souza.