A Two-Armed Bandit Theory of Market

Economics lacks a good theory of how stores should set their prices when they do not know the demand functions of their customers. Traditional theory either assumes that firms know their demand curves, or that they can, if necessary, find them out easily and costlessly from market experience. The market will inform the perfectly competitive firm of its demand function with ruthless efficiency. A firm which charges more than the market price will, as a matter of definition, lose all its customers. If it charges less than the market price, it will have all the customers it can handle. It is not difficult to explain how a perfectly competitive firm discovers what the market price is and all it needs to know of its deman function. Conventional theories of monopoly and imperfect competition attribute to firms’ complete knowledge of all relevant parameters of their demand relationships. Recently developed theories of firm behavior under uncertainty (for example, Baron [2] or Leland [IO]) are not exceptions. The firm is typically supposed to face a stochastic demand function of the genera% form f) = D(#, 0), where 19 is a random variable and X3(., .) a known fnnction. The firm is assumed to maximize expected profits (or the expected utility of profits). The theory does not explain how the firm comes to know D(., *) nor is it concerned with explaining how the Grm might come to know its demand function more accurately and thus reduce the uncertainty it faces.l