Running away is a perfectly valid action while within combat.  It happens by moving zone by zone away from the combatants.

What you can then do to turn it into a concession is to first Create Advantage like Out Of Sight, Out Of Mind or some such, to indicate that they lost track of you in the ongoing melee, then the GM can compel that to sweeten the pot so the Concession is accepted.

Of course, if someone splits off from the fight to give chase, it'll be harder to put that aspect into place...

If the combat segues into a chase (contest), and the person who chose to flee gets away without further penalty, that would be a pretty weak-sauce concession. I think that you are right though that either side of a combat should be able to initiate the transition to a contest if it makes sense in the fiction. I just think it is wrong to think of such as a concession.

If the minion of the Big Bad is under such blood-chilling orders to defeat the PCs that fleeing would have dire consequences, then that minion might offer the concession "I want to flee, but when I return to my master I will be beaten and imprisoned and effectively removed from this scenario" might be a concession that the PC would take if removing this piece from the chessboard would severely handicap the Big Bad.

Are you asking about a scenario where a participant in a Conflict changes his goal in response to how the Conflict is going? That in itself sounds like a Concession. "I am giving up on goal X (other side wins) and trying to run away. Next scene is a chase (Contest)." Why would someone reject that concession? They win the Contest, and they might still catch the guy.

For me a concession is a period on the end of the sentence, same as taken out. If the concession includes the conceder being able to run away, then their success at running away is a given and there's no need to move to any other mode of resolution. A concession has happened; therefore, it is resolved.

Carried with this is the implicit notion that if running away DOES transition to something else, then that's just what it is: a transition. Things are not yet resolved. A concession has not occurred.

Right, and that's what started the thought - if you run away, you're out of the conflict.  You're Taken Out.

But if someone won't accept the concession, you'd still then flee by getting enough space (zones), possibly creating some aspects via Create Advantage, until at some nebulous point the GM decides it's some other kind of scene.

I guess the question is then what are they doing to avoid the de facto escape?  If the NPC is 6+ zones away and running unimpeded, are you somehow going to catch him?  Target him with a Create Advantage?  HOW?

In the end, the one stubborn won't give up person at the table has to be brought around...  What's done is done.  I'm willing to offer a fate point as a sweetener, but that's just because I'm generous... really, the facts in the narrative are pretty clear.

Taken Out includes the notion of being at the mercy of the victorious party. They get to decide your fate. You don't get to run away unless the fiction provides some reason to make your fleeing acceptable to the winner.

Well, being busy fighting someone more immediately important than you is a pretty good reason...

+Robert Hanz Just because you Run Away from a Conflict does not imply that you are Taken Out. Taken Out has a clear meaning during a conflict and running away does not meet that. Someone running from a Conflict is not subject to the other side's control.

You could run away as part of a concession you offer - it is probably pretty common. "Sure, I get away - but I dropped a map containing a valuable clue." If this concession is accepted then there is no transition - it happens when it is agreed upon.

You could also run away simply by zoning far enough from other people in the conflict that the table agrees that you are no longer part of the conflict. This may transition the Conflict into a Contest if someone is giving chase.

I think this is a matter of taste and taking it on a case by case basis.  Personally I would probably allow the Concession as well as award Fate Points, but if the chase is still on I would transition to a Contest and say that any Consequences taken in the Conflict stay and the bad guys still have their free invokes.

What I'm assuming here is that the goal of the bad guys was to capture the good guys and that the goal of the good guys was not only to get away, but to remove the possibility of pursuit as well.  A win for the bad guys is the capture of the good guys, a win for the good guys is a clean escape with no possibility of immediate pursuit.  The Concession means that they get away, but are immediately chased again with no scene for downtime and regrouping.

Does that make sense?

Yeah, you're Out of the combat, but not Taken Out (with the effect that the victor gets to decide).  So, poor choice of words there.

Again, that's why it kind of seems like a Concession - one way or the other, you're Out, and I agree that in most cases it will be.

Remember the backhanded thing about offering a Compel to sweeten a Concession...

It means a fate point has to be paid to veto that Compel.

So if you get into a game situation where a "Concession" (escape from the conflict on relaxed terms) is a natural result of the narrative, it either happens or the PCs pay fate point(s) to prevent it.

Darn the luck.

One trend I'm seeing in this discussion is that many (myself included) seem to assume that a Conflict can only end via Concession or Taken Out. There's also Consensus, not necessarily between the opposing sides but by the table in the metagame. That's when you transition as +Fred Hicks said earlier.

For my part, Consensus is easy to forget because it's not the result of a discrete action a player makes on his turn.

The key for me is cost. If nothing changes except a few personal consequences, the battle can end up being a waste of time. For escape (or anything) to satisfy me as a concession, the loser has to lose something, and the victor needs to gain something.

Are the players are trying to achieve something important in a limited amount of time? Escape can be a concession because they ruined their only chance.
Did the PCs escape the crucial flanking position, causing their allies to lose the battle? Concession.
Will the PCs be ostracized for their cowardice in battle? Kinda weak concession. Does it cause a trial for desertion, followers to abandon the party, or lands to be seized? That's much better.

Without that, I would say make it a contest, with the stakes being ending the conflict (no FP payout), or continuing the same conflict, without stress refresh.

As usual, great question +Robert Hanz!

+Brendan Dukes:  They lose the stakes of the conflict.  Generally, I try to make conflicts about more than personal injury to the PCs - I try to keep them answering some question.  If they concede (or run), then the answer to that question is whatever answer the PCs didn't want.

+Robert Hanz I suppose that's my point. If there is something gained and something lost by fleeing, that's a concession.
In the case of the PCs being hunted for capture, I would run the contest as I said above, because escape would become players' goal. If the stakes were high enough, letting the players get away could even be considered a concession from the antagonists. 

Yeah, if the question the conflict is answering is "do the PCs get captured?" then concession by fleeing doesn't work (unless the PCs offer up something seriously sweet in exchange).