This paper investigates the structure of bilateral oligopolies – a simple version of Shapley Shubik games with two types of traders and two commodities. It shows that interior equilibria exist, studies the example of CES utility functions to uncover the relation between the complementarity of products in the utility functions and the shape of the reaction functions of the traders, and proves that the number of trading posts is irrelevant. Even if traders can split their offers on different markets, they never choose to specialize and all equilibria are equivalent to an equilibrium where all agents trade on a single market.