Wow.
You say this:
I don't understand what you mean by "the dice determine the outcome". Can you give an example?
And then you say this:
All the examples of RPG mechanics that I'm thinking of at the moment involve a player declaring an action for his/her PC and then using the dice to find out whether or not the action succeeds.
Which. Is. Exactly. What. I. Mean.
So, which is it? Do you understand? Do you not understand? Do you understand but you don't know you understand? If you're playing stupid, please stop; I know you're not stupid.
I'm asking how is that fiction authored? By whom? And how is that authored ficiton used in subsequent adjudicaitons of declared actions?
I, as DM, author the starting states, which are used as exactly that--starting states, as a large part of the framing for a given adventure. As the game is played, more fiction emerges, which is used as further framing for further adventures. From time to time, I author new starting states, which I endeavor to keep consistent with previous events. In prior conversations, I have referred to this as "instigating" and you have professed to understand what I meant, then.
But now you're just assuming that players dont have agency. From time-to-time I GM games that take place in the "real world" - Cthulhu Dark and most recently Wuthering Heights. The players as much as me get to express views over what can be done in the real world. Eg in one of our Cthulhu Dark sessions the PCs had taken control of a tug boat and the player who knew the most about tug boats told us what could be done with it.
I am not presuming the players won't have agency. Something being impossible doesn't negate player agency. The fact you have a player at your table who knows how tugboats operate kept that consistent with reality, but the fact that the operator couldn't (in the absurd) have the tugboat take off like a helicopter doesn't do change the options he has.
In my games set in non-real worlds - eg my 4e game - the players also help decide what can or can't be done. Eg in that game it was the player of the invoker/wizard who generally took the lead in deciding what was possible to be done with magical effects.
That sounds more like authorship than agency to me. It's cool that you're so flexible as a GM--I find it hard to maintain coherence in the game world when I allow players the ability to write much in it.
This is why - multiple times upthread now - I have emphasised that establishing constraints of genre and fictional positioning can be a matter of negotiation and consensus, in which the players exercise their agency as participants in that process. It need not be unilateral GM authority.
And the fact that it can be negotiated is a reason for distinguishing it from action resolution procedures which, in the traditional RPGs that I play, are not about negotiation but rather involve rolling dice to see whether or not the fiction unfolds as the player is hoping for his/her PC.
Sounds to me as though you're talking about being clear what the action is before resolving it. That's good play, I agree. Everyone should be clear on the stakes of an action.
[T]he definition of player agency that you posit here is uninteresting because in every RPG players have it. It's not something that varies.
Given that, in a traditional RPG, the way a player changes the shared fiction is by declaring actions for his/her PC and then having those resolve, the connection between player agency and action resolution procedures is not coincidental.
If a player can't change the shared fiction; if all s/he can do is prompt the GM to make such changes by describing what it is that his/her PC tries to do; then what is the role of the player in the game?
There are games wherein arguably the players have less agency in the sense of authority over their characters, in exchange for greater ability to re-write the world by Fiat; so, it actually does vary, and it's a different thing from narrative authority.
I don't believe I have said anything to the contrary about player agency and action resolution; I have said that some of the mechanics described don't touch player agency.
As to the last paragraph, the players are more authors of the emergent stories than I am as DM. Their characters are busy changing the world--the shared fiction. That is the role of the players and their characters in the game.