Assessing Empirical Support for Replicator Dynamics in Financial Markets: A Maximum Entropy Method Tested with America’s Largest Companies

Abstract

Abstract The replicator dynamics (RD) model provides important insights in the evolution of markets but lacks empirical support. A main difficulty is how to obtain the payoff matrix connecting the pairwise effects between interacting market entities. A procedure for estimating these pairwise payoffs, based on the Maximum Entropy (ME) principle, is proposed. The resulting method is thus called Replicator Dynamics Pairwise Maximum Entropy (RDPME). To test this method, daily market values from 2014 to 2019 of America’s top revenue companies are used. As it is customary in time series forecasting analysis, these series are divided into a training period, used to infer the RDPME parameters (intrinsic growth rates and payoff matrix), and a validation period, used to validate the model. Different partitions into training and validation periods are considered. The RDPME method outperforms the stochastic benchmark of the geometric random walk in predicting empirical shares for most of the companies along most choices of validation periods. JEL codes: C51, C52,C53, C55, C58, C63, G17