Planar Learning to Forecast Market Games

Abstract

In a system where expectations and realisations of a price feed back to each other, it has been found that the sign and strength of this feedback is an important predictor of the market stability. In this paper we contribute to the generalisation of this result to a two dimensional system, where the expectations and realisations of two prices affect each other. We conduct a Learning to Forecast Experiment and show that eigenvalues can be used as predictors of stability in such a higher dimensional framework. We investigate eigenvalues of positive real part, and found that complex eigenvalues with a polar angle of 45◦ lead to more stable dynamics than real eigenvalues with the same absolute value. For the real eigenvalues we find a change from stable to unstable dynamics inside the unit circle, which is in line with the findings from the one dimensional case. In order to reproduce the decisions being made in individual time steps, simple models like an adaptive rule are often sufficient. In order to reproduce long run dynamics, we develop a two dimensional Heuristic Switching Model. We use this model to predict the stability of systems with eigenvalues which we did not test experimentally.