This work considers the issue of distributing contents to vehicles through roadside communication infrastructure. Within this scenario, this work studies the dynamics of infrastructure deployment by using game theoretic tools. A strategic game is used to model the case in which the operators perform their deployment decisions concurrently, whereas an extensive game is used to study the dynamics in case one operator is the deployment leader and moves first. The equilibria of the aforementioned games are then assessed as a function of several parameters (nominal infrastructure capacity, interference, vehicle flows). Simulations are used to validate the analytical findings.