On Simulation of the Nash Equilibrium in the Stock Exchange Contest

A simple Stock Exchange Game Model (SEGM) was introduced in Mockus (2003), to simulate the behavior of several stockholders using fixed buying-selling margins at fixed bank yield. In this paper, an extended model USEGM is proposed. The advantage of USEGM is application of the Nash Equilibrium (NE) to strategies that define buying-selling margins and bank haircuts dynamically. This enables us to simulate market illiquidity that is an important feature of the present financial crisis (Allen, 2008). In addition, USEGM includes the transaction costs to reflect the reality better. To represent users that prefer linear utility functions, USEGM adds the AR-ABS(p) autoregressive model, minimizing the absolute values, to the traditional AR(p) model minimizing least square deviations. A formal application of NE to simulate the behavior of market participants is a new feature of these models. In the well-known works Allen (2008), Brunnermeier (2009), Brunnermeier and Yogo (2009) equilibrium ideas were applied to supply-demand balance concepts, as usual. The objective of USEGM is not forecasting, but simulation of financial time series that are affected by predictions of the participants. The “virtual” stock exchange can help in testing the assumption of rational investor behavior vs the recent theories that explain financial markets by irrational responses of major market participants (Krugman, 2000, 2008, 2009). The model helps comparing expected profits of different prediction models using the virtual and historical data. The model has been compared with eighteen actual financial time series and found the results to be close in many cases.