I was recently just scrolling my life away on this app called TikTok on this miniature computer called my phone, and recently came accross a trend of people playing a game on a filter. The game is quite simple, it's just a graph and two entities, a zombie and a guy. The goal is for the guy to get from one side to the other side of the graph without being touched by the zombie.
My questions are, what areas of math would this concern? Obviously graph theory but I don't really know what area of graph theory would work with the two players. Is there an optimal strategy? If there is, can this strategy be generalised to n higher dimensions? Maybe this has some overlap with random walks, just the walks not being random for an optimal strategy?
Here is a link to the game being played : https://www.tiktok.com/@shawndasheep96/video/7260503333100719402