The economic structure of a one-period security market

We present an analytical model of a one-period financial market for one asset. All traders learn by least squares regression, and interlocking expectations drive price towards return. The explicit specification of the information processing mechanism allows the derivation of mathematical expressions for market characteristics including price dynamics, efficiency, the impact of news and the market share of each trading strategy at economic equilibrium. We find that efficiency is a property generated by the market itself rather than a property inherited from informed traders. Market efficiency is not complete, and the residual discrepancy between price and return provides the return to the trading agents and resolves the Grossman-Stiglitz paradox. Traders are rewarded according to the scarcity and salience of their information. Outside economic equilibrium, the reward takes the form of profit; at economic equilibrium, the reward is market share. The model extends to a theory of market formation - as the amount of natural business increases, the market passes through four regimes: no market, price making only, price and data analysis, and full efficiency.

The model exhibits many themes from complexity theory, starting with its basis in learning by adaptive agents and proceeding to a demonstration that a financial market can organise itself sustainably although information is distributed. It is shown algebraically that least squares learning by heterogenous agents is isomorphic to natural selection in a biological system, as modelled by the Fisher fundamental theorem of natural selection. On this basis we argue that prediction is fundamentally the same process as adaptation. The organisation of the market can be explained by interpreting price as an object in the sense in which that term is used in computing, an entity with defined properties and methods. The price stores information, makes it available to the agents, and is updated by the agents. Market efficiency emerges as a property of the price object.