Players Ruby and Bob are given an undirected graph and a number $N$. First Ruby colors $N$ vertices red, then Bob colors $N$ vertices blue (they must be distinct from Ruby's choices). Afterward, all other points on the graph are given the color of whichever color they are closest to (shortest path) with ties left blank. The player with more of their color on the resulting graph wins.
Can the first player always win (or tie)?
Some context: This problem arose for me out of a mobile puzzle game. My knowledge in graph theory is pretty minimal, so I don't have much machinery to solve it (but I have spent a while with small graphs, always able to find an unbeatable strategy for the first player). My thoughts so far are to mark points as having an advantage in comparison to their neighbors, the maximum of which I'd guess provides a win with N=1. For higher N though the dynamics get much more challenging for me to express. There seems to be an aspect of even-spacing which I'm not sure how to formalize (perhaps it's picking vertices which minimize their shortest distance to any point).
Also if anyone has heard of a similar problem before (specifically related to coloring a graph based on the shortest path to a colored vertex) or has references I'd be happy to read them, but was unable to find much since I'm not certain what to search for.