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 $p^\star$ the number of sellers willing to sell the good at $p^\star$ equals the number of sellers willing to buy the good at price $p^\star$. 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 $p^\star$ . 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.