The global trade system can be viewed as a dynamic ecosystem in which exporters struggle for resources: The markets in which they export. We can think that the aim of an exporter is to gain the entirety of a market share (say, car imports from the United States). This is similar to the objective of an organism in its attempt to monopolize a given subset of resources in an ecosystem. In this paper, we adopt a multilayer network approach to describe this struggle. We use longitudinal, multiplex data on trade relations, spanning several decades. We connect two countries with a directed link if the source country's appearance in a market correlates with the target country's disappearing, where a market is defined as a countryproduct combination in a given decade. Each market is a layer in the network. We show that, by analyzing the countries' network roles in each layer, we are able to classify them as out-competing, transitioning or displaced. This classification is a meaningful one: When testing the future export patterns of these countries, we show that out-competing countries have distinctly stronger growth rates than the other two classes.