The 2-party political system defines a natural partition of a network of individuals into 2 teams. One can view these individuals as players in a network-sized game, and the utility (or equivalently cost) functions for each player can be realized as wanting to be connected to individuals on the same political party and distanced from those in the opposing political party. When considered from a game theoretic point of view, the ``greedy'' (or myopic/optimal) strategies can be examined. Thus, the game turns into a dynamical system, which can be investigated to understand when each political party will become totally connected. When the original network is sampled from an Erdos-Renyi graph G(n, q), we find a one-sided threshold of when a political party will become completely connected.