In this paper, we study a wireless multicast cost sharing game where the population of users is dynamically changing due to random arrivals and departures. Each user can either subscribe to a dedicated (wired or wireless) connection of fixed cost or join a multicast session served by a wireless Base Station (BS). In the latter case, the instantaneous cost of transmission at any time is shared among the users that are present in the multicast session at that time. Each user, being selfish, chooses one of the two options so as to minimize its own share of cost. We characterize the symmetric equilibria with several information availability structures. With only distributional information, we obtain the probability with which a random user would join the multicast session under the Highest Cost Allocation (HCA), the Incremental Cost Allocation (ICA) and the Shapley Value Allocation (SVA) schemes. We observe that, if the the number of users in the session is made available to the users, then the equilibrium strategy of the users is to join the multicast session when at least one other user is already present and to randomize only when there is none.