On the Efficient-Market Hypothesis and stock exchange game model

The Efficient-Market Hypothesis (EMH) asserts that the market is efficient and whenever new information comes up the market absorbs it by correcting itself. The corresponding prediction model is the Random Walk (RW) (the Wiener process, in mathematical terms). The Nash Equilibrium (NE) conditions define N-person game strategies that provide no incentives for changes. The aim of this paper is to explain EMH as the Nash equilibrium. We consider a model where it is assumed that the future asset prices depend on the predictions of N major stockholders. Then the stock exchange can be represented as an N-person game. Simulations indicate that NE could be achieved when all major players are using the RW model. The simulations of N-person game are compared with predictions of real world financial data when Artificial Neural Network and Autoregressive by Absolute Errors were used. Under some conditions the RW model provides next-day predictions reasonably well and approximately reflects the behavior of longer time trends. This approach provides some theoretical basis for explanation of EMH and can be useful for analyzing simulation results obtained by exploration of prediction models of the financial time series when asset prices depend on predictions.