Explaining the Law of Supply and Demand via Online Learning

The law of supply and demand asserts that in a perfectly competitive market, the price of a good adjusts to a market clearing price . In a market clearing price p ⋆ the number of sellers willing to sell the good at p ⋆ equals the number of sellers willing to buy the good at price p ⋆ . In this work, we provide a mathematical foundation on the law of supply and demand through the lens of online learning. Specifically, we demonstrate that if each seller employs a no-swap regret algorithm to set their individual selling price—aiming to maximize its individual revenue—the collective pricing dynamics converge to the market-clearing price p ⋆ . Our findings offer a novel perspective on the law of supply and demand, framing it as the emergent outcome of an adaptive learning processes among sellers.