In The Kingdom and the Glory, Agamben tries to demonstrate that the concept of oikonomia links together the Trinity and notions of divine governance/providence, but he doesn’t really talk about the Trinity as such, as a theological problem in its own right. He’s basically doing a word study on oikonomia (and its subsequent translation into Latin as dispositio).
Thinking about how you would fill in Trinity-specific stuff in his argument, I’m thinking of the early patristic characterization of the Son and Spirit as God’s “hands,” then the subsequent division of power in the governmental apparatus (spiritual and secular), and finally the return of the hand metaphor with the “Invisible Hand” (of which there is presumably only one). I wonder what’s at stake politically in the dispute between binatarianism and trinitarianism, which from this perspective may be the more salient difference between Arianism and orthodoxy — and why, for instance, Arianism would so often suggest itself to emperors as the better way to go. Maybe it’s all just arbitrary, but that doesn’t seem satisfying.
I also wonder how we fit this into the prophetic and apocalyptic frameworks. We know that God’s providential plan for pagan rulers and kingdoms is guided by something like an “invisible hand” — a logic that is only discernable to those who have eyes to see and that otherwise just looks like the dispiriting tedium of power politics. We also know that God plans a more direct intervention and/or self-revelation in something like the messiah. Could we map these two positions onto the shadowy and vague Holy Spirit and the more concrete Son?
Further, could the early victory of Trinitarian orthodoxy be trying to reluctantly include the Empire in God’s plan via the curt inclusion of the Holy Spirit (the vague and indirect “hand”) alongside the Son (representing the Church as the real source of legitimate earthly authority)? Then the dispute could play out over which of the two powers is the vague HS and which is the more concrete Son — in the West, it seems that the papacy claims the Son, while in the East, the emperor becomes more like the Son, relegating the Church to the Holy Spirit role.
If this theory has any weight, we could see why emperors would find the Arian position appealling because there’s only one power working in the created realm.
(Idle thoughts that I have not substantiated by any means.)