First place is absolutely certain: Alert or Terminate

[DanielOakfield]

I need to clarify my idea, I didn't mean that once one has mathematically won the nuke should start automatically, I suggested that once there's a winner (doesn't matter how many players) it should be notified in the match, then it's up to the players what to do with that information... maybe it could just show a small icon somewhere, happy to study possible UI solutions if that's something Simon would like to implement.

[namida]

I definitely think an alert in such cases is a good idea. This could even be on a per-player basis - one icon for "you can no longer improve beyond your current standing", and maybe another for "no player behind you can overtake you" (as there may be a situation where a player can no longer improve beyond their current ranking, but is still under threat of someone overtaking them so thus needs to defend their 2nd or 3rd etc place instead of just ending the match right there).