Global trade agreements in agriculture have been unsuccessful. Current explanations argue that this outcome reflects the fact that governments have motivations other than maximising social welfare. At the current state of the knowledge, there is not a suitable framework that can be used either to assess the veracity of these explanations or determine how these biases influence the international trade structure. The objective of this article is to fill this gap by proposing a formal international trade network adapted to study the issue of global agreements in agriculture. The network approach outlined here accounts for the bias of government policies towards farmers or consumers; but we also allow for intermediaries in agricultural markets that have the potential to exercise market power are largely ignored in current approaches to modelling agricultural trade. We show that accommodating these features of agricultural markets offers important insights in understanding why promoting free trade in agricultural markets has proved to be so elusive.