Economics

A basic way to imagine “microscopically” modeling an economic system is to have a Token-Event Graph in which the tokens are something like “configurations of agents”, and the events are possible transactions between them.

Much like the relations between atoms of space that are the tokens (represented by hyperedges) in our models of fundamental physics, the tokens we’re describing here as “configurations of agents” can more accurately be thought of as relations between elements that, say, represent economic agents, objects, goods, services, currency, etc. In a transaction we’re imagining that an “interaction” between such “relations” leads to new “relations”—say representing the act of exchanging something, making something, doing something, buying something, etc. At the outset, we’re not saying which transactions happen, and which don’t. And in fact we can imagine a setup (essentially a rulial token-event graph) where every conceivable transaction can in principle happen. The result will be a very complicated structure—though with certain inexorable features. But now consider how we would “observe” this system. Maybe there’d be a “from-the-outside” way to do this, but we could also just “be in the system” getting data through transactions that we’re involved in. But then we’re in a situation that’s pretty closely analogous to fundamental physics. And to make sense of what we observe, we’ll basically inevitably end up sampling the system by setting up some kind of reference frame. But if this reference frame has typical “generalized human” characteristics such as computational boundedness it’ll end up weaving through all possible transactions to pick out slices that are “computationally simple to describe”. And this seems likely to be related to the origin of “value” in economics (or perhaps more so to the notion of a numéraire). Much like in physics, a reference frame can allow coordinates to be assigned. But the question is what reference frames will lead to coordinates that are somehow stable under the time evolution of the system. And in effect this is what general relativity tells us. And quite possibly there’s an analog of this in economic systems. Why isn’t there just an immediate value for everything? In the model we’re discussing, all that’s defined is the network of transactions. But just seeing particular local transactions only tells us about things like “local value equivalences”. To say something more global requires the whole knitting together of “economic space” achieved by all the local transactions in the network. It’s very much like in the emergence of physical space. Underneath, there’s all sorts of complicated and computationally irreducible behavior. But if we look at the right things, we see computational reducibility, and something we can describe in the limit as continuum space. In economic systems, low-level transactions may show complicated and computationally irreducible behavior. But the point is that if we look at the right things, we again see something like continuum behavior, but now it corresponds to money and value. (And, yes, it is ironic that computational irreducibility is the basic phenomenon that seems to lead to a robust notion of value—even as it’s also what proof-of-work cryptocurrencies use to “mine” value.) Like a changing metric etc. in spacetime, “value” can vary with position and time. And we can expect that there will be some general-relativity-like principles about how this works (perhaps with “curvature in economic space” allowing arbitrage etc.). There also might be analogs of quantum effects—in which a value depends on a bundle of alternate paths in the multiway graph. (In “quant finance”—which, yes, coincidentally sounds a bit like “quantum”—it’s for example common to estimate prices from looking at the effects of all possible paths, say approximated by Monte Carlo.) At the outset, it’s not obvious that one can make any “economics-level” conclusion just based on thinking about what amount to arbitrary token-event graphs. But the remarkable thing about multicomputational models is that just from their general structure there are often inexorable quantitative laws that can be derived. And it’s conceivable that at least in the limit of a large economic system, it may finally be possible to do this.

⇒ Machine Learning