I understand what an equilibrium is. The question is: who are the players who are in equilibrium? Apple dictates the terms of the iOS app store. It's clear that Apple has a set of moves it can choose from. What moves do other players have, really, even if they were suboptimal?
It doesn't seem there really are any, other than to leave the app store entirely, which most would consider pretty extreme to the point where it's really hypotehtical. That's why I questioned whether the language of equilibria is appropriate in the first place: it just doesn't seem to be a pretty misleading framing of the situation.
Players: Apple, developers, user; playing a finite iterated game of uncertain time horizon.
Game order: Apple chooses a policy burden \omega ~ [0, 1] which stands in for the restrictions they place on developers or the cut of purchases they take. Apple takes \omega \beta in profit and incurs no costs.
Let's take you at your word that a developer's only choice is to leave or stay -- Developers choose whether to develop exclusively on Apple [reward (1 - \omega) \beta], on all platforms (1 - \omega) \beta + \theta, or not on Apple [reward \theta]. \beta and \theta are both constrained to be non-negative. Developers pay a cost of development -c where c is constrained to be non-negative. Developers all decide simultaneously.
You could model this as one developer choosing a fraction of effort. You could make costs variable. You could make developers decide sequentially. You could model Google, who is not an actor in this scenario. etc. etc.
Users observe the fraction of developers who opted in ||d||. Each user has a type [0, 1] which determines the threshold amount of developer support it will require for them to choose Apple over another platform. \beta and \theta both update to be higher or lower depending on user choices according to some update function you prefer.
Let each player have either an individual or shared discount parameter \delta.
This is clearly a well-specified game. I am not going to solve it for the equilibriums; it may well be the case for any practice \beta, \theta, c, etc. that Apple's incentive is to choose a very high \omega and developers best response is to choose "develop for Apple anyway". That would still be an equilibrium. Most games have degenerate equilibria.
It seems to me that if you adjust developers to be sequential rather than simultaneous this is very nearly the Chain Store Game; if you make it a single developer this probably gets close to something like divide the dollar; if you want to model the lawsuit, it's a costly signalling game (Epic burning cash to establish type)
All of this is very traditional game theory. I get that your point is that Apple is mean and the government should do something about it, but there's nothing wrong with me describing the current arrangement of winners and losers as an equilibrium, or to describe the shock a lawsuit could induce via policy change as something that will establish a new equilibrium by exogenously changing or constraining parameters. I left all this out because I didn't think anyone would require this effort to accept the use of a very uncontroversial term.
It doesn't seem there really are any, other than to leave the app store entirely, which most would consider pretty extreme to the point where it's really hypotehtical. That's why I questioned whether the language of equilibria is appropriate in the first place: it just doesn't seem to be a pretty misleading framing of the situation.