In this study, we investigate the use of machine learning methods to predict a Nash equilibrium state of a dual-market economic system given limited access to market information. The study considers a system of two interconnected markets, where goods produced on the first market are used to produce other goods on the second one. Each participant seeks to maximize their profit, considering market conditions and the behavior of competitors. By using machine learning methods, it is possible to obtain accurate approximation of the interconnected markets equilibrium, interactions between players within a market and between markets in terms of pricing formation, based on the limited information available about the market state and the players. This study is particularly relevant since access to market information for any player is often limited, making standard methods for finding equilibrium ineffective. The results of experiments conducted under different scenarios regarding the availability of market state information have demonstrated the practical importance of the proposed solution that involves using machine learning models to predict the Nash equilibrium state of complex interconnected market systems.