Models of markets

When serious economic theory began in the 1700s arguments tended to be based purely on common sense. But with the work of Léon Walras in the 1870s mathematical models began to become popular. In the early 1900s, common sense again for a while became dominant. But particularly with the development of game theory in the 1940s the notion became established, at least in theoretical economics, that prices represent equilibrium points whose properties can be derived mathematically from requirements of optimality. In practical trading, partly as an outgrowth of theories of business cycles, there had emerged all sorts of elaborate so-called technical analysis in which patterns of price movements were supposed—often on the basis of almost mystical theories—to be indicators of future behavior. In the late 1970s, particularly after the work of Fischer Black and Myron Scholes on options pricing, new models of markets based on methods from statistical physics began to be used, but in these models randomness was taken purely as an assumption. In another direction, it was noticed that dynamic versions of game theory could yield iterated maps and ordinary differential equations which would lead to chaotic behavior in prices, but connections with randomness in actual markets were not established. By the mid-1980s, however, it began to be clear that the whole game-theoretical idea of thinking of markets as collections of rational entities that optimize their positions on the basis of complete information was quite inadequate. Some attempts were made to extend traditional mathematical models, and various highly theoretical analyses were done based on treating entities in the market as universal computers. But by the end of the 1980s, the idea had emerged of doing explicit computer simulations with entities in the market represented by practical programs. (See also page 1105.) Often these programs used fairly sophisticated algorithms intended to mimic human traders, but in competitions between programs simpler algorithms have never seemed to be at much of a disadvantage. The model in the main text is in a sense an ultimate idealization along these lines. It follows a sequence of efforts that I have made since the mid-1980s—though have never considered very satisfactory—to find minimal but accurate models of financial processes.