On simulation of optimal strategies and Nash equilibrium in the financial market context

Unlike physical time series, stock market prices may be affected by the predictions made by market participants with conflicting interests. This is the domain of game theory. Therefore, we propose a Stock Exchange Game Model (SEGM) to model this phenomenon. In SEGM, player strategies are to set their buying and selling levels for the next iteration via the autoregressive model AR(p) of order p selected by minimizing deviations from Nash Equilibrium (NE). NE represents the assumption of optimal behavior by market participants. The objective of SEGM is to simulate financial and other time series that are affected by predictions of the participants and to test the assumption of optimal player behavior, using a ‘virtual’ stock exchange. The simulation of SEGM suggests that NE is close to the Wiener model. This is a new explanation of the Random Walk (RW) model of the efficient market theory. To compare the simulation results with real data, the efficient market hypothesis was also tested, using financial time series of eight assets. The SEGM software is implemented in Java applets and can be run using a browser with Java support.