I’m presenting next week at the Society for American Archaeology Annual Meeting. I’m giving two papers. One argues for parsimonious models when we do agent based modeling.  The other reverses the flow of archaeological network analysis and instead of finding nets in the archaeology, I use agent based models to generate networks that help me understand the archaeology. (The session is ‘Connected Past’.) Here is the draft of my talk, with all the usual caveats that that entails. Parts of it have been drawn from an unpublished piece that discusses this methodology and the results in much greater detail. It will appear…. eventually.

Scott Weingart has been an enormous help in all of this. You should follow his work. 

My interests lie in the social networks surrounding primary resource extraction in the Roman world. The Roman epigraphy of stamped brick easily lends itself to network analysis. One string together, like pearls, individual landowners, estate names, individual brick makers, signa, brick fabrics, and locations. This leads to very complicated, multi-dimensional networks.

When I first started working with this material, I reduced this complexity by looking only at the humans, whom I tied together based on appearing in the same stamp type together. I called these ‘producer’ networks. I then looked at the ties implied by the shared use of fabrics, or the co-location of brick stamp types at various findspots, and called these ‘manufacturing’ networks.

I then sliced these networks up by reigning dynasty, and developed a story to account for their changing shapes over time.

This was in the late 1990s, and in terms of network theorists I had largely only Granovetter, Hanneman & Riddle, and Strogatz & Watts to go on. The story I told was little more than a just-so story, like how the Camel got its Hump.

I had the shape, I had points where I could hang the story, but I couldn’t account for how I got from the shape of the network in the Julio-Claudian period, to that of the Flavian, to that of the Antonines. I’ve done a lot of work on networks since then; now I want to know what generates these networks that we see archaeologically, in the first place.

In this talk today, I want to reverse the direction of my inquiry. We are all agreed that we can find networks in our archaeological materials. The problem, I think, for us, is to explain the network processes that produce these patterns, and then to use our understanding of those processes to narrow down the possible entangled human & thing interactions that could give rise to these possible processes.

We need to be able to understand the possible behaviour-spaces that could produce the networks we see, to tease out the inevitable from the contingent. We need to be able to rigorously explore the emergent or unintended consequences of the stories we tell. The only way I know how to do that systematically, is to encode those stories as computer code, to turn them from normal, archaeological storytelling rhetoric, to computational procedural rhetoric.

So this is what we did.

One story we tell about the Roman world, that might be useful for understanding things like the exploitation of land for building materials, is that its social economy functioned like a ‘bazaar’.

According to Peter Bang, the Roman economic system is best understood as a complex, agrarian tributary empire, of a kind similar to the Ottoman or Mughal (Bang 2006; 2008).  Bang (2006: 72-9) draws attention to the concept of the bazaar. The bazaar was a complete social system that incorporated the small peddler with larger merchants, long distance trade, with a smearing of categories of role and scale. The bazaar emerged from the interplay of instability and fragmentation. The mechanisms developed to cope with these reproduced that same instability and fragmentation. Bang identifies four key mechanisms that did this: small parcels of capital (to combat risk, cf Skydsgaard 1976); little homogenization of products (agricultural output and quality varied year by year, and region by region as Pliny discusses in Naturalis Historia 12 and 18); opportunism; and social networks (80-4). As Bang demonstrates, these characteristics correspond well with the archaeology of the Roman economy and the picture we know from legal and other text.

Bang’s model of the bazaar (2008; 2006), and the role of social networks within that model, can be simulated computationally. What follows is a speculative attempt to do so, and should be couched in all appropriate caveats and warnings. The model simulates the extraction of various natural resources, where social connections may emerge between individuals as a consequence of the interplay of the environment, transaction costs, and the agent’s knowledge of the world. If the networks generated from the computational simulation of our models for the ancient economy correspond to those we see in the ancient evidence , we have a powerful tool for exploring antiquity, for playing with different ideas about how the ancient world worked (cf. Dibble 2006). Computation might be able to bridge our models and our evidence. In particular, I mean, ‘agent based modeling’.

Agent based modelling is an approach to simulation that focuses on the individual. In an agent based model, the agents or individuals are autonomous computing objects. They are their own programmes. They are allowed to interact within an environment (which frequently represents some real-world physical environment). Every agent has the same suite of variables but each agent’s individual combination of variables is unique (if it was a simulation of an ice-hockey game, every agent would have a ‘speed’ variable, and an ‘ability’ variable, and so the nature of every game would be unique). Agents can be aware of each other and the state of the world (or their location within it), depending on the needs of the simulation. It is a tool to simulate how we believe a particular phenomenon worked in the past. When we simulate, we are interrogating our own understandings and beliefs.

The model imagines a ‘world’ (‘gameboard’ would not be an inappropriate term) in which help is necessary to find and consume resources. The agents do not know when or where resources will appear or become exhausted. By accumulating resources, and ‘investing’ in improvements to make extraction easier, agents can accrue prestige. When agents get into ‘trouble’ (they run out of resources) they can examine their local area and become a ‘client’ of someone with more prestige than themselves.  It is an exceedingly simple simulation, and a necessary simplification of Bang’s ‘Bazaar’ model, but one that captures the essence and exhibits subtle complexity in its results. The resulting networks can be imported into social network analysis software like Gephi.

It is always better to start with a simple simulation, even at the expense of fidelity to the phenomenon under consideration, on the grounds that it is easier to understand and interpret outputs. A simple model can always be made more complex when we understand what it is doing and why; a complex model is rather the inverse, its outcomes difficult to isolate and understand.

A criticism of computational simulation is that one only gets out of it what one puts in; that its results are tautological. This is to misunderstand what an agent based simulation does.  In the model developed here, I put no information into the model about the ‘real world’, the archaeological information against which I measure the results. The model is meant to simulate my understanding of key elements of Bang’s formulation of the ‘Imperial Bazaar’. We measure whether or not this formulation is useful by matching its results against archaeological information which was never incorporated into the agents’ rules, procedures, or starting points. I never pre-specify the shape of the social networks that the agents will employ; rather, I allow them to generate their own social networks which I then measure against those known from archaeology. In this way, I start with the dynamic to produce static snapshots.

We sweep the ‘parameter space’ to understand how the simulation behaves; ie, the simulation is set to run multiple times with different variable settings. In this case, there are only two agent variables that we are interested in (having already pre-set the environment to reflect different kinds of resources), ‘transaction costs’ and ‘knowledge of the world’. Because we are ultimately interested in comparing the social networks produced by the model against a known network, the number of agents is set at 235, a number that reflects the networks known from archaeometric and epigraphic analysis of the South Etruria Collection of stamped Roman bricks (Graham 2006a).

What is particularly exciting about this kind of approach, to my mind, is that if you disagree with it, with my assumptions, with my encoded representation of how we as archaeologists believed the ancient world to have worked, you can simply download the code, make your own changes, and see for yourself. If you are presented with the results of a simulation that you cannot open the hood and examine its inner workings for yourself, you have no reason to believe those findings. Thus agent based modeling plays into open access issues as well.

So let us consider then some of the results of this model, this computational petri dish for generating social networks.For my archaeological networks, I looked at clustering coefficient and average path length as indicator metrics, (key elements of Watts’ small world formulation).  We can tentatively identify a small-world then as one with a short average path length and a strong clustering coefficient, compared to a randomly connected network with the same number of actors and connections. Watts suggests that a small-world exists when the path lengths are similar but the clustering coefficient is an order of magnitude greater than in the equivalent random network (Watts 1999: 114).

In Roman economic history, discussions of the degree of market integration within and across the regions of the Empire could usefully be recast as a discussion of small-worlds. If small-worlds could be identified in the archaeology (or emerge as a consequence of a simulation of the economy), then we would have a powerful tool for exploring flows of power, information, and materials. Perhaps Rome’s structural growth – or lack thereof – could be understood in terms of the degree to which the imperial economy resembles a small-world (cf the papers in Manning and Morris 2005)?

The networks generated from the study of brick stamps are of course a proxy indicator at best. Not everyone (presumably) who made brick stamped it. That said, there are some combinations of settings that produce results broadly similar to those observed in stamp networks, in terms of their internal structure and the average path length between any two agents.

One such mimics a world where transaction costs are significant (but not prohibitive), and knowledge of the world is limited . The clustering coefficient and average path length observed for stamped bricks during the second century fall within the range of results for multiple runs with these settings. In the simulation, the rate at which individuals linked together into a network suggests that there was a constant demand for help and support. The world described by the model doesn’t sound quite like the world of the second century, the height of Rome’s power, that we think we know, suggesting something isn’t quite right, in either the model or our understandings. But how much of the world did brickmakers actually know, remembering that ‘knowledge of the world’ in the model is here limited to the location of new resources to exploit?

Agent based modeling also allow us to explore the consequences of things that didn’t happen. There were a number of simulated worlds that did not produce any clustering at all (and very little social network growth). Most of those runs occurred when the resource being simulated was coppiced woodland. This would suggest that the nature of the resource is such that social networks do not need to emerge to any great degree (for the most part, they are all dyadic pairs, as small groups of agents exploit the same patch of land over and over again). The implication is that some kinds of resources do not need to be tied into social networks to any great degree in order for them to be exploited successfully (these were also some of the longest model runs, another indicator of stability).

What are some of the implications of computationally searching for the networks characteristic of the Roman economy-as-bazaar? If, despite its flaws, this model correctly encapsulates something of the way the Roman economy worked, we have an idea of, and the ability to explore, some of the circumstances that promoted economic stability. It depends on the nature of the resource and the interplay with the degree of transaction costs and the agents’ knowledge of the world. In some situations, ‘patronage’ (as instantiated in the model) serves as a system for enabling continual extraction; in other situations, patronage does not seem to be a factor.

However, with that said, none of the model runs produced networks that had the classical signals of a small-world. This is rather interesting. If we have correctly modeled the way patronage works in the Roman world, and patronage is the key to understanding Rome (cf Verboven 2002), we should have expected that small-worlds would naturally emerge. This suggests that something is missing from the model – or our thinking about patronage is incorrect. We can begin to explore the conundrum by examining the argument made in the code of the simulation, especially in the way agents search for patrons. In the model, it is a local search. There is no way of creating those occasionally long-distance ties. We had initially imagined that the differences in the individual agents’ ‘vision’ would allow some agents to have a greater ability to know more about the world and thus choose from a wider range. In practice, those with greater ‘vision’ were able to find the best patches of resources, indeed, the variability in the distribution of resources allowed these individuals to squat on what was locally best. My ‘competition’ and prestige mechanisms seem to have promoted a kind of path dependence. Perhaps we should have instead included something like a ‘salutatio’, a way for the agents to assess patrons’ fitness or change patrons (cf Graham 2009; Garnsey and Woolf 1989: 154; Drummond 1989: 101; Wallace-Hadrill 1989b: 72-3). Even when models fail, their failures still throw useful light. This failure of my model suggests that we should focus on markets and fairs as not just economic mechanisms, but as social mechanisms that allow individuals to make the long distance links. A subsequent iteration of the model will include just this.

This model will come into its own once there is more and better network data drawn from archaeological, epigraphic, historical sources. This will allow the refining of both the set-up of the model and comparanda for the results. The model presented here is a very simple model, with obvious faults and limitations. Nevertheless, it does have the virtue of forcing us to think about how patronage, resource extraction, and social networks intersected in the Roman economy. It produces output that can be directly measured against archaeological data, unlike most models of the Roman economy. When one finds fault with the model (since every model is a simplification), and with the assumptions coded therein, he or she is invited to download the model and to modify it to better reflect his or her understandings. In this way, we develop a laboratory, a petri-dish, to test our beliefs about the Roman economy. We offer this model in that spirit.

[edited April 4th to make it less clumsy, and to fit in the 15 minute time frame]