At a certain point game sessions become a puzzle that everyone is trying to solve, players and GM both.
Having created these problems, having put our heroes and other innocents in dire straits, having set up the villains and terrible hazards, how do we resolve everything in a way that is both dramatic and satisfactory to everyone? Victory alone is not the goal, since too easy a victory will not be appreciated.
It's four in the morning and tunnel vision sets in. Plans have already gone awry and there are more loose threads than solutions. How can the heroes exonerate the framed prince and overthrow his treacherous uncle when their only shred of evidence just got burned to a crisp? Or save the eastern seaboard from the death ray when they're already shrunken down and trapped in test tubes in the villain's lab? The urge to end the game in a way that makes sense starts to compete with the urge to just go home. Deus ex machina starts to look good.
So who steers the game to a satisfactorily conclusion, the players or the GM? It seems it should be the players, given that the concept is that the GM creates the problems and the players solve them. But often it is the GM who leaves a window open, or sees a place where a window must be to prevent the situation from becoming a stalemate, an impossible scenario, or one where the most likely solution is bad, dull or just unattractive. Or (sadly) the GM has scripted in that single solution, the only solution that will resolve the conflict, but that's a design flaw.
The real answer is that whoever is the best at forging a resolution will be the one to do it, regardless of what seat they're in. If a player is better at it, that player will do it. If the GM is better at it, the GM will do it. It can be a conscious or unconscious process, a subtle case of leading by example or a blatant vote to decide how to wrap things up. Other players (and the GM) will go along if the solution works for them.
