New paper shows markets are just backprop in disguise

A new paper from the MATS program (under Richard Ngo’s research stream) presents a groundbreaking formalization: markets are mathematically equivalent to backpropagation in neural networks, reinforcement learning algorithms, and continuous Bayesian inference. The core insight is 'price recursion'—a recursive update rule where market prices act as gradients (specifically, gradients on activations, not weights) that propagate information through the system without vanishing at equilibrium. This unifies previously vague intuitions about market dynamics and machine learning, such as the Efficient Market Hypothesis and bounded rationality, under a single mathematical framework. The paper demonstrates how markets can be modeled as Markov Decision Processes (MDPs) or Markov Logic Programs (MLPs), with price dynamics serving as a computational mechanism for intelligence emerging from decentralized agents—much like how neural networks learn from sub-optimally performing neurons.

The author, building on prior work like Caspar Oesterheld’s BRIA and Hayek Machine (inspired by Holland and Schmidhuber’s classifier systems), extends the analogy by factoring the 'right to act' into discrete 'goods' axes, mirroring real-world markets. This approach resolves long-standing questions about arbitrage as inconsistency, Godelian limitations in prediction markets (e.g., markets cannot efficiently price questions like 'This market will resolve below 50%'), and the computational nature of market equilibria. The 40-page paper includes a proof that markets rationalize reward and identity, drawing parallels to Bayesian belief updates and replicator dynamics. It also highlights caveats, such as the conditional nature of rationality given computational constraints—a concept deeply relevant to both economics and AI.