Traveling Traders’ Exchange Problem: Stochastic Modeling Framework and Two-Layer Model Identification Strategy

The Traveling Traders’ Exchange Problem (TTEP) is formalized, aiming at studying the collision–exchange systems found in various research areas. As an example of the TTEP models, a 1-D model is developed and characterized in detail. The computational stochastic simulation of the 1-D TTEP model relies on a stochastic simulation algorithm implemented on the basis of the Monte Carlo method. A model identification framework is proposed where the money distribution in the system obtained from the stochastic model is characterized in terms of (a) standard deviation of the money redistribution; (b) its probability density function. Results indicate that the expressions of the estimated functions for terms (a) and (b) are tightly related to the system input conditions. The example of curve fitting on the probability density function shows how the variation of money redistribution in the system in time is driven by different values of the parameters describing the interaction mechanism.