Computational Model Library

MERCURY extension: transport-cost (version 1.0.0)

This is extended version of the MERCRUY model (Brughmans 2015) incorporates a ‘transport-cost’ variable, and is otherwise unchanged. This extended model is described in this publication: Brughmans, T., 2019. Evaluating the potential of computational modelling for informing debates on Roman economic integration, in: Verboven, K., Poblome, J. (Eds.), Structural Determinants in the Roman World.

Brughmans, T., 2015. MERCURY: an ABM of tableware trade in the Roman East. CoMSES Comput. Model Libr. URL

Release Notes


This extended version of the model incorporates a ‘transport-cost’ variable, and is otherwise unchanged. This extended model is described in this publication:
Brughmans, T., 2019. Evaluating the potential of computational modelling for informing debates on Roman economic integration, in: Verboven, K., Poblome, J. (Eds.), Structural Determinants in the Roman World.

This agent-based model aims to represent and explore two descriptive models of the functioning of the Roman trade system that explain the observed strong differences in the wideness of distributions of Roman tableware.

A detailed technical description of the model is published as:
Brughmans, T., & Poblome, J. (in review). MERCURY: an agent-based model of tableware trade in the Roman East. Journal of Artificial Societies and Social Simulation.

The archaeological research context and interpretation of experiments’ results are published as:
Brughmans, T., & Poblome, J. (in press). Roman bazaar or market economy? Explaining tableware distributions in the Roman East through computational modelling. Antiquity.

The tablewares (fine thin-walled ceramics with shapes including bowls, plates, cups, and goblets; each ware has a distinct production centre or region) produced in the Eastern Mediterranean between 25BC and 150AD show an intriguing distribution pattern. Some wares like Eastern Sigillata A (ESA) were distributed very widely all accross the Mediterranean, whilst others (ESB, ESC, ESD) had a more limited regional distribution. Archaeologists and historians have suggested many aspects of the Roman trade system as the key to explaining tableware distribution patterns: physical transport mechanisms, tributary political systems, military supply systems, connectivity. In this model we focus on exploring the potential role of social networks as a driving force. The concept of social networks is here used as an abstraction of the commercial opportunities of traders, acting as a medium for the flow of information and the trade in tableware vessels between traders. We aim to formalise and evaluate two very different hypotheses of the Roman trade system in which such social networks are key: Peter Bang’s ‘The Roman Bazaar’ (2008) and Peter Temin’s ‘The Roman Market Economy’ (2013). In his model, Bang considers three factors crucial to understanding trade and markets in Roman Imperial times: bazaar-style markets, the tributary nature of the Roman Empire, and the agrarianate nature of ancient societies. The engine of the model, however, is clearly the concept of the bazaar: local markets distinguished by a high uncertainty of information, relative unpredictability of supply and demand, leading to poorly integrated markets throughout the empire. Bang argues that different circuits for the flow of goods could emerge as the result of different circuits for the flow of information. In other words, the observed distribution patterns of tablewares and different workshops’ products (when these can be identified) are at least in part a reflection of the structure and functioning of past social networks as defined above. Temin agrees with Bang that the information available to individuals was limited and that local markets are structuring factors. However, contrary to Bang he believes that the Roman economy was a well-functioning integrated market where prices are determined by supply and demand. Temin’s model can be considered to offer an alternative approach, where the structure of social networks as a channel for the flow of information must have allowed for integrated markets.

This model is designed to illustrate that certain aspects of Bang’s and Temin’s hypotheses can be tested through computational modelling.



The transport cost variable can be set in experiments to any value between 0 and 1, where 1 is the maximum price of an item of tableware in the model. The procedure to determine whether to add this transport cost to a transaction is as follows: when a seller wishes to sell an item to one of his contacts in the social network, these contacts (potential buyers) will determine the price they believe an item of tableware is worth (by drawing on the commercial information available to them), and will reduce this price by the amount of the transport costs if and only if they are located on a different market than the seller (i.e. if transport of the item from one market to another is required, then a constant transport cost will be applied to the transaction). After this extension with a transport cost procedure, MERCURY’s trade procedure works as follows in every time step of the simulation:

FOR EVERY item of tableware
SELECT at random one of the traders with an item (the seller)
IF there are NO network neighbours of the seller that have a positive demand OR are willing to stock items for redistribution (i.e. potential buyers)
ADD the item to the seller’s stock
IF there ARE potential buyers
Potential buyers determine whether a transport cost applies to the transaction
Seller identifies the potential buyer that offers the highest profit where: Transaction price = buyer price + transport cost
IF the seller can make a profit or break-even
Seller sells item to buyer
Buyer stores the item in stock for redistribution if this promises a higher profit
If not, the buyer sells the item to a consumer who deposits it at their site
IF the seller CANNOT make a profit or break-even
ADD the item to the seller’s stock


Traders are located at different sites and within sites connected in a social network with a ‘small-world’ structure (Watts and Strogatz 1998). A variable proportion of pairs of traders located on different sites are also connected. Four products are produced at four different sites, and are distributed through commercial transactions between pairs of traders connected in the social network. Two variables represent the availability of information and reflect key differences between Bang’s and Temin’s hypotheses: ‘random-inter-site-links’ and ‘local-knowledge’.

Setup procedures:
The model is initialised by creating sites and traders, and distributing the traders among the sites. Four sites which are equally spaced along a circular layout are selected to become tableware production sites. A fixed number of traders determined by the variable ‘traders-production-site’ is moved to each of the four production sites. The remaining traders are distributed on these sites following an exponential or uniform frequency distribution, determined by the variable ‘traders-distribution’.

Traders are subsequently connected to each other to form a social network. In our model the social networks between traders at each site have a ‘small-world’ structure, with a high clustering coefficient and a low average shortest-path-length. This is suitable since a feature of ‘small-world’ networks is the efficient spread of information within clusters whilst few intermediary traders will allow information to flow between clusters. These clusters represent the ‘communities’ of traders in Bang’s model who are more likely to limit commercial information to their members. We further ensure that at least one pair of traders is connected between every pair of adjacent sites along the circular layout (this ensures that in experiments with a value of 0 for ‘random-inter-site-links’ each site is connected through pairs of traders to only two other sites) and that the network consists of one connected component (this guarantees that each trader can theoretically obtain an item of each product). This results in a high average shortest-path-length between traders at different sites. The average shortest-path-length is reduced in the experiments by the variable ‘random-inter-site-links’, which determines the proportion of randomly selected pairs of traders located at different sites to be connected. This variable therefore increases the ability for commercial information to be shared between communities at different sites: increasing this variable relaxes Bang’s extreme hypothesis. The procedure to create a network with a ‘small-world’ structure is inspired by the model for the growth of social networks by Jin, Girvan and Newman (2001), previously applied in an archaeological model of exchange by Bentley, Lake and Shennan (2005).

Distribution procedures:
In every time step traders perform the following tasks in sequence: they determine their demand, discard part of their stock (due to broken or unfashionable items), traders on tableware production sites obtain new items if their current possession is less than their demand, traders obtain commercial information from their neighbours in the network, they determine what they believe to be the current price of an item using this commercial information, and then all items owned by all traders in that turn are considered for trade once.

Every time step each trader will only have commercial information available from a proportion of its link neighbours. This proportion is determined by the variable ‘local-knowledge’. The trader then calculates the average demand and average supply of this proportion of neighbours, including his own supply and demand. Using this commercial information available to him he then determines what he believes is the price of one item of any product as follows:
price= (average-demand)/(average-supply+average-demand). A seller will only agree to sell an item if the buyer’s price is equal to or higher than this price.
Each item is considered for trade once per time step. An item is put in a trader’s stock if he cannot make a profit or if none of his neighbours in the network requires an item (i.e. their demand = 0). Items in stock can be redistributed in the next time step. An item is sold to a buyer if the buyer’s price promises a profit or break-even for the seller. The buyer either places the obtained item in stock for redistribution if the average-demand is higher than his demand (i.e. if redistribution holds the promise of a higher profit), or if this is not the case he sells it to a consumer (the buyer’s demand is decreased by 1, the item is taken out of the trade system, and the volume of the product in question deposited on the buyer’s site is increased by 1).


A list of all variables and their tested settings are available for download from OpenABM as a tab delimited text file.

The model runs slowly due to a large number of reporters, counters, and graphs in this version. These can be removed to make the model much faster. Please refer to the list of all variables to identify which reporters and counters can be removed.

The experiments this model was designed for were run with the following default independent variable settings:

Num-traders: 1000 (computationally doable)
Num-sites: 100 (similar to average number of sites in archaeological database)
Maximum-degree: 5 (adopted from Jin etal. 2001)
Proportion-intra-site-links: 0.0005 (adopted from Jin etal. 2001)
Proportion-mutual-neighbors: 2 (adopted from Jin etal. 2001)

In experiments the following variables are modified to explore their effect on the distribution of the four products:


Click the setup button to initialise the model (this takes a long time).
Click the go button to run the model.

The main pattern of interest is shown in the ‘distribution products’ graph which shows the number of sites at which each of the four products is deposited.


The model is designed to observe differences in the wideness of tableware distributions with different settings for the variables ‘random-inter-site-links’ and ‘local-knowledge’ in particular. Strong differences can be observed in the ‘distribution products’ graph when these variable settings are changed.

By increasing the proportion of random links between all pairs of traders on different sites, the average shortest-path-length becomes shorter. This enables products to spread throughout the network in a lower number of steps.

A higher ‘local-knowledge’ will give traders more accurate information of supply and demand of their potential transaction partners. Increasing this variable does not lead to strong differences in the wideness of products’ distributions, but it did have a strong impact on the proportion of failed and successful transactions.

In addition to these variables a number of other independent variables can be varied. Low values for ‘traders-production-site’ and ‘max-demand’ give rise to limited distributions of wares, whilst high values give rise to wide distributions. However, neither of these variables give rise to strong differences in the wideness of wares’ distributions.

Changing ‘traders-distribution’ to ‘uniform’ will give rise to more limited distributions.

Changing ‘network-structure’ to ‘random’ allows one to replace the hypothesised ‘small-world’ network structure with a Bernoulli random graph with the same number of edges as the hypothesised graph with the same variable settings would have. Random graphs give rise to more widely distributed wares but with very little difference between the wideness of different wares’ distributions.

When the variable ‘traders-production-site’ is excluded, all traders are distributed following an exponential distribution, and when the maximum demand of a trader equals the number of traders at its site, then the observed wideness and range of wares’ distributions can be reproduced.


In future work this model could be extended by considering different types of traders, evaluating possible correlations between prices with network distance away from the production centre and incorporating transport costs, considering different valuations for different products, and introduce ‘haggling’ and market-clearing mechanisms. Crucially, a comparison of this model with a significantly simplified mathematical model of the spread of objects over network structures would be of interest, although this mathematical model would not form the basis of future extensions of the current model that incorporate different types of traders.


The nw extension is used:

Bentley, R., M. Lake & S. Shennan. 2005. Specialisation and wealth inequality in a model of a clustered economic network Journal of Archaeological Science 32: 1346–56.

Graham, S., & Weingart, S. (2015). The Equifinality of Archaeological Networks: An Agent Based Exploratory Lab Approach. Journal of Archaeological Method and Theory, 22: 248–74.

Jin, E.M., M. Girvan & M.E. Newman. 2001. Structure of growing social networks. Physical review. E, Statistical, nonlinear, and soft matter physics 64: 046132.

Wilensky, U. 2005. NetLogo Small Worlds model. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.


Thanks to Jeroen Poblome, Iza Romanowska, Jan Christoph Athenstaedt, Benjamin Davies, Mereke Van Garderen, David Schoch, Arlind Nocaj, David O’Sullivan and Viviana Amati for extensive comments on earlier versions of this model. These colleagues are not responsible for the final version of this model.
The model was created by Tom Brughmans.

The clustering coefficient (cc) measure used here is based on the small-world model in the Netlogo library
For an alternative calculation see

Bang, P.F. 2008. The Roman bazaar, a comparative study of trade and markets in a tributary empire. Cambridge: Cambridge university press.

Bentley, R., M. Lake & S. Shennan. 2005. Specialisation and wealth inequality in a model of a clustered economic network Journal of Archaeological Science 32: 1346–56.

Jin, E.M., M. Girvan & M.E. Newman. 2001. Structure of growing social networks. Physical review. E, Statistical, nonlinear, and soft matter physics 64: 046132.

Temin, P. 2013. The Roman Market Economy. Princeton: Princeton University Press.

Watts, D.J. & S.H. Strogatz. 1998. Collective dynamics of “small-world” networks. Nature 393: 440–42.

Version Submitter First published Last modified Status
1.0.0 Tom Brughmans Mon Jul 23 11:08:11 2018 Mon Jul 23 11:08:11 2018 Published


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