We study here the effect of concurrent greedy moves of players in atomic congestion games where n selfish agents (players) wish to select a re- source each (out of m resources) so that her selfish delay there is not much. The problem of maintaining global progress while allowing concurrent play is ex- actly what is examined and answered here. We examine two orthogonal settings : (i) A game where the players decide their moves without global information, each acting freely by sampling resources randomly and locally deciding to migrate (if the new resource is better) via a random experiment. Here, the resources can have quite arbitrary latency that is load dependent. (ii) An organised setting where the players are pre-partitioned into selfish groups (coalitions) and where each coalition does an improving coalitional move. Our work considers concur- rent selfish play for arbitrary latencies for the first time. Also, this is the first time where fast coalitional convergence to an approximate equilibrium is shown.