What follows is a draft of an article I’ve submitted to a journal. If two blind reviews are good, more must be better, right? Keep in mind this could get rejected or substantially altered from its final version.

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This paper outlines how agent-based modeling can be used as a laboratory for exploring aspects of ancient economic life. Bang (2006; 2008) has put forth a model of the Roman economy developed from the insights of Clifford Geertz (1979) as an ‘imperial bazaar’. A significant portion of Bang’s model hinges on social networks. Particular network topologies have implications for the flows of materials or ideas through them, and so knowing the kind of network shapes that the ‘bazaar’ might generate should be explored. We can develop an agent based simulation of Bang’s model which as a by-product of its functioning generates social networks. We can then look at under what conditions the generated social network matches social networks known archaeologically from the extractive economy of Roman brick and tile. The simulation thus represents a way of bridging economic theory with the archaeological evidence. Suggestions for extending the model to explore multiple kinds of products and adapting it are presented.

Keywords

Agent based modeling; Roman economic history; simulation; trade, natural resources

Introduction

This paper explores what the economist Lea Tesfatsion calls ‘agent-based computational economics’ (2012). It uses the Netlogo (Wilensky, 1999) agent based modeling platform to implement a (necessarily) simplified Roman economy. The model generates social networks which can then be measured against known archaeological networks; where there is a degree of congruence, I argue that the model has generated new knowledge. In this regard, what I am building is a ‘computational laboratory’ that takes place in an explicitly spatial environment (Dibble, 2006). In the spirit of open access, I make the model and its code available for experimentation and extension and so the results presented here should be seen as necessarily preliminary.

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). In such states, trade and markets remained locally and regionally fragmented (though there could be overlapping ‘regions’ of different sizes, depending on the product; cf Horden and Purcell 2000: 123-72 on ‘connectivity of microregions’). This was a ‘stable’ economic state, with its own characteristics and patterns. 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 was notorious as a place of high risk and uncertainty where bottlenecks, asymmetries and imbalances were endemic… Bazaar can be used to denote a stable and complex business environment characterised by uncertainty, unpredictability and local segmentation of markets.” (79)

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 concludes, “…the set of strategies outlined here provided a complex and resistant foundation for trade. But the result was to consolidate tendencies towards market segmentation where economic flows seem to run in separate, compartmentalised channels and networks… The bazaar, to conclude, is the model of agrarian markets we have been looking for.” (84).

It is this last component on which I focus. ‘Networks’ as both a metaphor and a statistical, measurable feature of ancient society have recently begun to invade the literature. Brughmans 2012 gives an overview of the historiography of network approaches to archaeology. He draws attention to the work of Wasserman and Faust (1994: 4) that illustrates the social assumptions of network analysis:

-Actors and their actions are viewed as interdependent rather than independent, autonomous units.

– Relational ties (linkages) between actors are channels for transfer or “flow” of resources (either material or nonmaterial).

– Network models focusing on individuals view the network structural environment as providing opportunities for or constraints on individual action.

– Network models conceptualize structure (social, economic, political, and so forth) as lasting patterns of relations among actors.  (Brughamns 2012: An Introduction to SNA).

In a recent application of network theory to the problems of Greek colonization, Malkin (2011: 18-19) argues that since we can never know the exact, perfect ‘wiring’ of any ancient network, it is better to use ‘network analysis’ and its concepts metaphorically. This would miss an opportunity. A network approach should properly not stop at ‘network’ as metaphor. It should outline as fully as possible the connections relevant to the question we are asking, to understand the implications of the topology (pattern of connections) for what they might mean for history. A small-world, in network terms, is one where most connections are local and short, while a handful of individuals have connections that connect otherwise disparate parts of the network. This allows whatever flows through the network to reach all its parts quite quickly (Buchanan 2002; Milgram 1967; Watts and Strogatz 1998; Watts 1999). Consequently, as Brughmans points out, a social network with this pattern of connections would have implications for our understanding of the processes underlying its formation, such as the spread of religious ideas or the establishment of social norms or political power (2010).

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. Networks can be discerned and drawn out from archaeology, prosopography, and historical sources (e.g., Brughmans 2010; Manning 2010; Ruffini 2008; Graham and Ruffini 2007; Graham 2006a). If the networks we see in the ancient evidence correspond to networks generated from the computational simulation of our models for the ancient economy, 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 this paper, I develop a simple simulation that represents a starting point for bringing this agenda about, and explore some of its consequences.

The Bazaar and the New Institutional Economics

The idea of the Roman economy as a kind of bazaar puts the emphasis on the trading institutions of the Roman world. This is a trend that fits into the ‘New Institutional Economics’ (NIE) of Douglass North (1990) and his followers (especially for antiquity as formulated by Frier and Kehoe’s 2007 chapter in the Cambridge Economic History of the Greco-Roman World; cf also Bang’s 2009 review). What North proposed in his NIE was not a rejection of neoclassical economics, but rather a re-assessment of what rationality could mean, especially over time. Over time, what is most costly in any transaction is information. Working out these costs and measuring them are the roots of institutions (Lo Cascio 2006: 219, citing North 1990: 27).

NIE assumes that knowledge is costly to acquire, which limits actors in their ability (or their will) to act. Thus, individuals tend to make ‘good enough’ decisions, that is, ones that are ‘satisficing’. They account for incomplete knowledge through guess work, reliance on social relationships, values and judgements that are necessarily incomplete (Frier and Kehoe 2007: 121-122). Once a particular choice is made, further choices in the same direction are easier (less immediately costly) than perhaps superior alternatives. This is called ‘path dependence’ (Fier and Kehoe 2007: 137, citing North 1990). The development of the slave-based villa economy is an example, where the immediate profits from the system forestalled the development of a more sustainable system that promoted longer-term growth.

Institutions help to regularize and promote the flow of knowledge; it was a strategy to cope with uncertainty. In the ancient world, the institution of the market or fair helped to overcome the problems of asymmetrical knowledge not through some ‘invisible hand’ setting a ‘correct’ price, but through the formation of personal networks. “[more important than bringing buyers and sellers together is] the network of long-term personal relationships that arise within regular markets: patterns of trust and reliance based upon prior experience… cultivating these long-term “relational” contracts is often of more importance than obtaining the lowest price” (Frier and Kehoe 2007: 119)

According to Bang, the key characteristics of a bazaar-type economy lie in poor information, fragmented organization, and little standardisation. Personal connections were used to obtain information and bridge the gaps (2008: 198). The participants in a bazaar market actively sought to minimize uncertainty by establishing a clientele. By trading with a preferred partner, the marketer is sheltered from some risk and uncertainty, but only by fostering particular relationships. Other possibilities might exist, but are not open to the market trader, since he is limited to what can be known through his own network of contacts (5). More generally, Bang finds it telling for instance that transport amphorae never lost their regional characteristics, that despite entering trading networks of long or mid range, they never evolved to a standard type or size. He argues that the world of Roman trade should therefore be modelled not as a ‘generalized market sphere’, but as a patchy, weakly integrated space where trading ‘circuits’ are segmented at different scales: “It was a high-risk, high transaction-cost environment” (194-5).

Despite market irregularities, imperfect knowledge, and differences in social power, the trader should not be seen as passive. Rather, what the NIE suggests is that despite high transaction costs creating so-called ‘market imperfections’, they also create different approaches, different strategies to cope with uncertainty. For Bang, the key is to explore social differences between actors in a market. “[The differences] show the existence of a hierarchy and thus of a particular social system replete with institutionalised forms of behaviour and specialisation of functions. The markets of traditional trade should not be seen in terms only of one of its players, the pedlar, they constituted an entre social universe – the bazaar’. For Bang, ‘the bazaar’ is not the quaint tourist trap of labyrinthine shops and traders, but rather a ‘system and hierarchy’ that includes fairs and markets, stretching from rural hinterlands to inter-urban exchange networks (Bang 2008: 197).

Euergetism or other investments in ‘social capital’ by merchants was ‘sound business’. These investments helped to maintain or improve the fides of the individual, thus proving or signalling the honour and thus credit-worthiness of the individual (260). This idea accords well with the ideas of Shennan (2002: 224-7) on costly signalling, an evolutionary idea where one gains prestige and status, by putting energy into conspicuous display. Game theory experiments suggest that individuals are prepared to accept lower returns from individuals with a perceived higher status (Shennan 225, citing Boone and Kessler 1999:271); the experiments also seem to suggest that individuals who invest in costly signalling also end up at the head of the queue for resources in times of crisis (Shennan 225, citing Boone and Kessler 1999: 262-5). Shennan also draws attention to the fact that individuals who engage in costly signalling also must be able to ‘back up’ the display by providing benefits to the larger social group as a whole. He argues that their display achieves this end also by making it too expensive for other individuals to compete in the same game, thus cementing their role (Shennan 2002: 225). Thus, market activities of merchants taken as a communal whole turn the bazaar into a social system; for Bang, a market was also a “social universe fostering a sense of hierarchy and promoting norms of proper conduct between individual traders” (Bang 2008: 260).

The Piazzale delle Corporazione in Ostia, the collegiae of traders in Lugdunum, the Palmyrene merchants in Palmyra – all of these are evidence, for Bang, of the ways traders banded together into social groups in attempts to mitigate the imperfect knowledge and regional vagaries of the Roman world (Bang 2008: 251-3). Information uncertainty and unpredictability of supply and demand are the ‘ideal-typical’ characteristics of the bazaar (Bang 2008: 4). Building networks was one response to this situation. These then are the economic characteristics and social behaviours that we will seek to model in our computational simulation of the bazaar. Can such a simulation generate social differences between actors? What kinds of hierarchies can emerge? Under what conditions does this computational world resemble the one we see in the archaeology – and what can that tell us about the Roman economy?

Agent Based Modelling

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 (cf Gilbert and Troitzsch 2005:17 on the logic of simulation; Macal and North 2010). When we simulate, we are interrogating our own understandings and beliefs. What is particularly valuable then is that we can build a simulation, and when the agents begin to interact along the patterns of behavior that we have specified (drawn from our understanding of how various processes worked), we have a way of exploring the non-linear, non-intuitive, emergent consequences of those beliefs.

What is more, in order to code a particular behavior, we have to be clear about what we think about that behavior. We have to make our assumptions explicit in order to translate an historical argument into code. A second investigator then can examine the code, critique these assumptions and biases (or indeed, errors) and modify the simulation towards a ‘better’ state. The model is built using the open-source Netlogo modeling environment and language (Wilensky 1999). Examples of agent based models used for archaeological questions include Wilkinson et al.(2007); Graham (2009, 2006b); Graham and Steiner (2008); Kohler et al.(2005).

The Model Setup and Rules

This 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, but one that exhibits subtle complexity in its results. (It is an extension of Wilensky’s Wealth Distribution model, 1998). 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.

In this simple world, only one kind of resource is simulated at a time – forest, coppicing, clay, and mining/quarrying. These resources are chosen because of the probable use of broadly similar kinds of strategies to organize the trade (Graham 2005: 111-115, the use of stamps on the product to organize extraction and distribution). There was of course a great deal of difference between these resources in terms of the scale of the organization by the Imperial period (cf Meiggs, 1982:325-370; Hirt 2010: 357-369; for an agent-based simulation of mining in Bronze Age Halstatt see Kowarik et al. 2012). The model takes account of scale and variability by giving each point in the world a chance of holding a certain amount of whatever resource is being simulated (with mines being the least likely, and forests the most). In the model, forest and coppicing regenerate after a set amount of time, while clay pits and mines do not. Each location keeps track of how often it has been ‘harvested’, allowing for exhaustion or depletion of the resource and thus taking it out of play.

Each individual agent represents a single individual who works in this world. Their sole task is to locate and ‘harvest’ the resource. Each agent consumes a portion of whatever is harvested in order to remain active. The amount consumed is set randomly per agent, to a user preset maximum; every individual is different in their abilities. The original simulation calls this ‘metabolism’; we can think of it as representing ‘transaction cost’. Individual agents also have knowledge of the world (which is called ‘vision’ in the model, representing how ‘far’ they can ‘see’ within the environment), to differing degrees (again, to a user preset maximum). We can think of this as representing Bang’s informational uncertainty. These two variables allow the user to simulate worlds of differing economic conditions.

An agent searches the environment within its field of vision, looking for a resource. If it finds some, it may harvest it. If its costs to move are greater than the amount of the resource it has on hand, it is removed from the simulation. A new agent takes its place, representing a generational change-over. If the agent has now consumed all of its resources, it may ask for help (and thus stave off removal). Each agent keeps track of who has given it help and to whom it has given help in turn, which generates a network structure that we may analyse at the conclusion of the simulation.

When an agent asks for help, it examines its local neighbourhood (within its range of vision, ie, knowledge-of-the-world) for a possible patron. A possible patron is one whose prestige is equal to or greater than its own (initially, all agents have the same prestige value; exact values are not as important as having appropriately conceived processes, cf Agar 2003). If a potential patron can be found, and the potential patron accepts the other agent as client (determined by a roll of the die), then the patron gives the client some of its resource. This gift increases the patron’s prestige, and puts the client in its debt. Patrons, in the model, invest some of their resources in improving the yield from a location, thus representing the investment in fides.

At the end of each cycle, the agents compare their resource amount against others whom they ‘know’ (who may be found within the agent’s ‘vision’). The simulation makes the same comparison for the population of all agents as a whole at the same time. The agents set their ‘prestige’ to reflect their local status into top middle, and bottom thirds. Each ‘patron’ (an agent with at least two other agents in its debt) selects another patron to compete against at the same rank (thus local elites compete against other local). Elites compare both the quality and number of their followers against each other. A patron with a few wealthy clients might beat a patron with several poor ones. Winning the game increases prestige, losing reduces prestige. The winner then calls on its clients to support it through gifts of resources (while simplistic, this modeling of ‘patronage’ does not stray from the broad outlines suggested by scholars collected in Wallace-Hadrill, 1989a).

At the end of the simulation, each agent writes its patrons and clients into a single file for network analysis. The network analysis is performed using the Gephi network analysis program (Bastian et al.2009; Kuchar 2011). Data on the state of the model at each time step is written to a spreadsheet, counting the number of agents who are patrons, clients, their degree of prestige, and their classification into high-middle-low status both locally and globally. [Insert Endnote 1 here] What goes in, and what comes out, of an agent based model

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. As Box and Draper put it, ‘all models are wrong, but some are useful’ (1987: 424). 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 correct 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. Social networks can be discerned in archaeological materials since artefacts are the direct result of social relationships (Knappett 2011; Coward 2010; Graham and Ruffini 2007: 325-331).

Our archaeological base line for the networks comes primarily from epigraphy. Clay and timber carried explicit messages on them, in the form of stamps (Graham 2005; Graham 2006a). Other classes of raw materials in the Roman world similarly carried explicit messages on them (such as masons’ marks on marble in the quarries). These messages ranged from the simple name of the maker, to the name of the estate whence they came, to the year in which they were made/cut down/quarried. In essence, the right to extract or use the resource was arranged through locatio-conductio contracts, whether or not the landowner took an active stake in production, which the language of the stamps reflects (Steinby 1993; Setälä 1977; Helen 1975; Aubert 1994). Meiggs supposes that the same system used for letting out public contracts was used in managing the public forests (1982: 329). Hirt discusses the differences between private and public mines/quarries, in much the same terms (2010: 84-93).

It is possible to reconstruct something of the social networks surrounding the exploitation of materials from this epigraphic material. (Additionally, we can see these networks in the archeometry of brick, tile, and other objects, Graham 2006a: 92-113; Malkin et al.2007; for criticism of the approach see Brughmans 2010). The named individuals in brick stamps can be knitted together into a social network. I use network statistics generated from a study of the patterning of co-occurrence of names of individuals, estates, and workshops, as well as patterns of co-exploitation of clay bodies as the control in this study. I set the simulation to run through all combinations of its variables, and then match the shape of the resulting generated social networks against the archaeological ones to identify simulation runs of interest.

If the simulations processes match our understandings of the phenomenon under consideration, then its outputs (the emergent, unpredictable outcomes) must have some validity. If they do not match, it may mean that our understanding we sought to model is incorrect. It is worth noting that this too is an important result.

Simulation Results

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). 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).

Nine different combinations of variables are used to sweep the entire space, twice for each of the four resources, making for 72 different runs over nearly 60 000 iterations of the model. The simulation is set to stop at the arbitrary point of 50 generations (the question of when to halt an experiment is not at all obvious when it comes to simulation. The reader may wish to experiment with changing this; cf Weingart 2012).

Table 1. Combinations of variables in the ‘sweep’ of the model’s behaviour space.

We should expect some basic trends to emerge. We could expect that:

• increasing the transaction costs should make it much more difficult for agents to survive (i.e., make the simulation reach its arbitrary end-conditions, a point where the average number of generations per agent equals 50) relatively quickly).
• increasing ‘vision’ (we reduce information uncertainty by increasing the amount of the world it is possible to ‘know’) should make it much easier for agents to survive; that the simulation takes a relatively long time to reach its arbitrary end point.

This is in fact what we see (Figure 1). A world where fifty generations are reached quickly might be characterised as unstable, while one that takes some time could be called stable. Combinations 3, 6, and 9 lead to the greatest peaks in stability. If one were to map these against the economic development of the Roman world, one could argue that combinations 9 and 6 would agree with a situation or area where many transport or communications links have still to be developed, though the general lay of the land is well known. Combination 3 would agree with a situation where the transportation or communications networks were at the most developed and secure. Either way, these combinations point to a degree of integration (and the differing circumstances under which integration could be produced, in the simulation).

Combinations 4 and 7, the greatest dips in the graph (and thus worlds of instability), are suggestive of a situation where transaction costs are high and communications are poor. The question is, which of these situations corresponds with the ‘real’ world? We turn to the generated social networks and their comparison with archaeological data.

 

Social Networks Analysis

Table 2. Network characteristics of stamped Tiber Valley bricks, based on the epigraphy of the stamps. Shading suggests that small-world conditions might be in evidence (same average path length as in a random graph although the clustering is of an order of magnitude or more higher, Watts: 1999:114). After Graham 2006: 102, Table 6.1

The way individuals are connected carries implications for the ways in which information or other materials flow through that network. Network structure carries implication for the ability to act, and the ways individuals embedded in a network can leverage the information/material that flows through that network. Individuals and their positioning matters. In a network, individual’s local situations give rise to a global network whose dynamics emerge from this local interplay (see for instance Brughmans 2012; Coward 2010; Mitchell 2009: 227-290; Christakis and Fowler 2009; Ruffini 2008; Graham 2006 whose in charge; Barabasi 2002; Watts 1999).

One can compute metrics to understand the implications of an individual’s positioning (such as the number of connections, or the number of paths through the network between every pair of individuals on which this particular individual sits). I use the Gephi network visualization suite (Bastian et al. 2009). Here, since we are not interested in actual individual historic actors, we are more concerned with global metrics. Two in particular allow us to compare the behavior of the generated networks with the ones known from archaeology and epigraphy (Brughmans 2012 gives an excellent overview of the statistical properties of networks and their archaeological implications).

• Clustering coefficient. This is a measurement that looks at how dense the connections are amongst the neighbors of each individual in the network (neighbors are those to whom the individual is connected at ‘one degree’ remove). The coefficient is the average of all the ‘neighborhoods’ (Hanneman and Riddle 2005 Chapter 8).
• Average Path Length. This is a measurement that takes the mean of the number of links between every pair of actor.

Watts (1999) formally identified a network structure that appears in social (and other) systems of all kinds, which he called the ‘small-world’ phenomena. In a small-world, most individuals are tightly connected in small groups or neighborhoods; it is highly ordered. Normally, this means that it takes many links to get from one side of the network to the other. Yet, in a small-world occasionally some individuals have links that connect otherwise disparate parts of the network, a kind of short-circuit (thus an element of randomness). This has the effect of making the entire network much ‘closer’ than its clustering would suggest – it looks ordered but behaves randomly.  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)? Small-worlds also seem to be a pre-requisite for self-organization, where complex phenomena emerge from the interaction of the constituent parts (Granovetter 2002; Cilliers 1998).

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 two particular combination of settings that produce results similar to those observed in stamp networks, in terms of their internal structure and the average path length between any two agents. In run 21, the variable settings are those for combination 3, which corresponds to a world where transactions costs are significant (M = 10) and knowledge of the world is deep (V = 20); the resource is ‘forest’. The clustering coefficient and average path length observed for stamped bricks during the second century (Antonines) fall just outside the range of results for multiple runs with these settings (from 0 to 0.018 for the clustering coefficient; and 2 to 8 for the average path length). Small-world conditions do not seem to be fulfilled in the real-world network, which perhaps means that we are dealing with a form of economic activity that does not correspond to the bazaar, that is not emergent: some form of outside control is imposed.

In the second run which produces network statistics very similar to observed real-world brick networks (run 13), the variable settings are those for combination 4, a world where transaction costs are significant (but not prohibitive; M = 10), and knowledge of the world is limited (V = 2); the resource is ‘forest’. 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 (from 0 to 0.034 for the clustering coefficient; and 2 to 14 for the average path length). In the simulation, the rate at which individuals linked together into a network suggests that there was a constant demand for help and support.

There were a number of runs 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).

The strongest network cohesion occurred in runs 5 (forest), 28 (mine), and 23 (clay) (table 3). Run 5 occurred in a combination implying a world where transaction costs were low, and knowledge of the world was middling. Run 28 occurred in a combination implying a world where the transactions costs were great, and the knowledge of the world was limited. Run 23 shows a world where the transactions costs were middling, and knowledge of the world was deep. In each case, it is the nature of the resource that makes the difference, rather than the variable settings. The social network which emerges depends on the kind of resource or product involved.

Table 3. Network statistics for the greatest participation rates (number of agents tied into the networks)

Conclusion

What are some of the implications of thinking of the Roman economy as a kind of 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 characteristics of a small-world. The equivalent random graph in every case had similar clustering coefficients and similar path lengths. 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. I 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 I 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.

Finally, the model runs on a torus-shaped world (that is, the left and right sides of the environment are connected, as are the top and bottom. If an agent wanders off the top of the screen, it re-appears at the bottom). A more useful model would be instantiated on top of a GIS with the real locations of various resources (and associated infrastructure) known. Perhaps it could be made to work with the transport economics modeled by Scheidel and Meeks and the ORBIS project (this interactive mapping project allows the user to explore the differences in the economic geography of the Roman world depending on time of year, mode of transport, and routes through the Roman world).

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. I offer this model in that spirit.

Acknowledgements

The nucleus of this paper was presented at the Land and Natural Resources in the Roman World conference in Brussels, May 2011. I would like to thank Paul Erdkamp and Koen Verboven for inviting me to participate in that conference, and also the participants of that conference for their insight and criticism of these ideas. Various drafts have been seen by various people at various stages, and I thank them for their comments and patience, especially Mark Lawall. Errors of logic or understanding are of course my own.

Notes

1. For the full model code and the details of its routines, please download at http://figshare.com/authors/Shawn%20Graham/97736 , open with Netlogo 5, and click on the ‘information’ tab. The code itself is annotated with comments explaining what is happening in each procedure, and may be reviewed by clicking on the ‘Code’ button.

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