We approach a two-echelon supply chain optimisation problem, specifically, a retailer’s replenishment problem, which faces stochastic demand. The retailer has to coordinate, beforehand, with his/her supplier on the amount purchased in order to satisfy their demanded quantity and, at the same time, minimise costs due to storage and penalty costs. To solve this problem, a Markov state game was designed and fictitious play, a learning methodology used in game theory, was applied and programmed in Borland C++ Builder 6.0 Enterprise Edition, where software known as ‘UN Tech Supply Chain Optimiser’ was generated and produced at a 95% confidence level, better results than those already found in literature for this same problem.