What Do Trading Algorithms Know?

Abstract

Let us start with an intriguing puzzle at the heart of Epistemic Game Theory: Is it possible to have a configuration of beliefs such that, “Ram believes that Kali assumes that Ram believes that Kali’s assumption is wrong” (Brandenburger & Keisler, 2006)?[1] If Ram believes that Kali’s assumption is correct, then he believes that the italicized second half of the sentence – Ram believes that Kali’s assumption is wrong – holds. But that immediately leads to a paradox: we started with Ram believing that Kali’s assumption was correct! That we are able to conjure up such puzzles at will suggests that paradoxes like these are part and parcel of our thinking – tucked away deep in our minds and manifested in the many contradictory decisions that we seem to take in ordinary life. How troublesome are such impossible beliefs when we trade? Do trading algorithms, too, grapple with such paradoxical beliefs? Algorithmic trading, especially in advanced markets such as the US, is the first instance of large-scale, real-time, interactive, automated decision-making in an ecosystem outside of computer science. And the many fascinating questions the area has been throwing up, especially as algorithms mature, has left all parties – researchers, practitioners and market regulators alike – scratching their heads.