Nuts such as almonds, pecans, walnuts, and pistachios are available in the U.S. market in different forms and brands. There are well-known national brands as well as not-so well-known private label and store brands. Nut producing firms compete for market share and strategically price, brand, advertise and position products in the market. Conventional brand-level analysis of such markets is achieved through calculation of market power and price cost margins assuming the presence of pure strategy Bertrand-Nash Equilibrium in prices. This is supported by a set of prior assumptions with regards to the structure of the market and oftentimes these are too restrictive, because pricing decisions are made in a complex multivariate situation with numerous interactions between variables that determine the prices and prices themselves. In this study, using 2015 Nielsen scanner data for nut products, complex causal relationships among brand level prices are estimated using cutting-edge machine learning algorithms. Also within this method, the concept of Markov Blankets is used to identify specific brands that are immediately important for a given brand. Several national brands were identified as a direct cause of the price of store brands. Even though store brands were associated with the highest market share, they had no influence on any other brands’ pricing decision and strategy.