Markets As Automata, Theory Of Computation, Etc.

I do not expect this post to be well-posed. I suggest that the following researchers provide elements for an interesting approach to economics:

• Michel Callon: Applied Actor-Network Theory to financial markets. [I KNOW EVEN LESS ABOUT THIS.]
• Karin Knorr Cetina: the sociology of finance. Use of algorithms in financial markets.
• Donald MacKenzie: Edinburgh school for sociology of knowledge. Performativity and counter-performativity of financial markets.
• Philip Mirowski: Markets as automata. Parallels with Chomsky hierarchy. Economies as evoloving ecology of market automata.
• Kumaraswamy Vela Velupillai: Constructivism in economics, including in Sraffa's work.

The laws of supply and demand, as presented in neoclassical economics, are muddled and confused. Demand for consumer goods, for eample, is the result of households maximizing some non-existent utility subject to constraints. A market is an unanalyed entity, generally with no brokers who make markets, willing to trade on either side. Although not discussed, the market in neoclassical microeconomics is typically a posted price market, corresponding to the lowest level of the Chomsky hierarchy.

Those who specialize in finance might say they observe something like supply and demand in order books. But those curves are not the supply and demand curves presented in introductory economics and in neoclassical microeconomics. These financial markets are structured, with algorithmic rules for matching bids and offers. They often parallel future markets, capable of going into backwardation and contango.

A certain sort of mathematics is needed to fully analyze markets. I happen to be able to write computer code, in some languages to some extent. And I have been exposed to a perspective that computers should be designed to execute our algorithms, which are abstract mathematical entities independent of such implementation.

At one point, I was quite aware of IEEE 754-2019. IEEE Standard for Floating-Point Arithmetic. At one level of abstraction, I would think of my algorithms as applying to real numbers. I also worried about underflow and overflows and other details. (By the way, some editions of Numerical Recipes contain bugs. You have to read and think, not just copy the code.) I also worried about computational complexity. I probably did not worry about any more than whether or not an algorithm could be implemented in polynomial time and how a parallel implementation can provide speedup. From literature on algorithmetic game theory, I know that if P ≠ NP, complexity classes exist in-between.

So I do not adopt a constructivist approach to economics and mathematics. But I appreciate the provision of algorithms to solve economic problems. And I see that Sraffa does that. I do not know of any evidence that Sraffa and Wittgenstein talked about this, even given Wittgenstein's work on the foundations of mathematics.