A Phase Transition in Large Network Games

In this paper, we use a model of large random network game where the agents plays selfishly and are affected by their neighbors, to explore conditions under which Nash equilibrium (NE) is perturbation in network. We phase transition phenomenon observed finite rank deformations matrices, study how NE changes on crossing critical threshold points. Our main contribution as follows: when strength greater than point, it impacts game, whereas below remains independent parameter. This demonstrates alludes that perturbations can affect behavior society only if above threshold. provide numerical examples for result present scenarios could potentially occur real world applications.