The trade networks of the Roman Empire are among the most intensively researched large-scale market systems in antiquity, yet there is no consensus on the economic structure behind this vast network. The difficulty arises from data fragmentation and the lack of formal analytical methods. Here, the authors present a Bayesian analysis quantifying the extent to which four previously proposed hypotheses match the evidence for the market system in Roman olive oil. Results suggest that the size of economic agents involved in this network followed a power-law distribution, strongly indicating the presence of free market structures supplying olive oil to Rome. This new analysis offers an important tool to researchers exploring the impact of trade on the dynamics of past societies.

XRC and MCS were funded by the European Research Council Advanced Grant EPNet (340828). We would like to thank the two anonymous reviewers for their comments on previous versions of the manuscript. We would also like to thank Enrico Crema, Albert Díaz-Guilera, Luce Prignano, Ignacio Morer, Jean-Marc Montanier, Simon Carrignon, Joan Rodríguez, Víctor Revilla, Maria Yubero, Jonàs Alcaina, Pau Valdés, Alessandra Pecci and Tom Brughmans for advice on the analysis, access to unpublished data and productive discussions on the methods and results of this work. The dataset is distributed under the terms of a Creative Commons Attribution-Share Alike 4.0 International Licence. The source code of the model is licensed under a GNU General Public Licence; both can be downloaded from https://github.com/xrubio/bayesRome (accessed 9 June 2017).

Peer Reviewed