Towards the computational study of the Roman economy: draft

I’m contributing to a volume on  ‘Land and Natural Resources in the Roman World’. Below is my draft, on which I welcome comments and questions.

Towards the computational study of the Roman economy

Shawn Graham, Carleton University, Ottawa Canada

“Economies are complicated systems encompassing micro behaviours, interaction patterns, and global regularities. Whether partial or general in scope, studies of economic systems must consider how to handle difficult real-world aspects such as asymmetric information, imperfect competition, strategic interaction, collective learning, and the possibility of multiple equilibria. Recent advances in analytical and computational tools are permitting new approaches to the quantitative study of these aspects. One such approach is Agent-based Computational Economics (ACE), the computational study of economic processes modelled as dynamic systems of interacting agents.”[1]

Most models of the Roman economy do not take into account this idea that micro-behaviours, feedback, and local interaction provide the circumstances out of which emerge those larger issues about which we are typically concerned.[2]  Before we can ask questions about growth, or market integration, or the degree to which Rome was ‘primitive’ versus ‘modern’, we have to focus on individual decision making. In this paper, I outline an agenda for how we might be able to do this. It comes down to this: we have to draw out and understand networks of individuals at all geographical scales and then use those networks as the substrate for computationally simulating individuals’ economic activities. Thus, archaeology and ancient literature become united through computation.

It is not necessary, I think, to rehash the historiography of studies of the Roman economy; the broad outlines of the debate are well known.[3] What I find exciting though is the emergence of the New Institutional Economics of Douglass North[4]. These works all draw attention to ideas around the consequences of individual decision making from incomplete knowledge, of how ‘good enough’ or satisficing decisions push actors and economics towards path-dependence (where because of past decisions one is locked into a particular mode).[5] The idea that network relationships (and the institutions that emerge to promote these) are the mechanism through which ancient economies deal with incomplete knowledge[6]  is a powerful one because we can find and outline the traces of these networks through archaeology.

Bang takes this idea further and through cross-cultural comparison with Mughal India pushes our attention to the bazaar: “a stable and complex business environment characterised by uncertainty, unpredictability and local segmentation of markets’.[7] Bang shows how the bazaar helped shield the individual from (while at the same time encouraging) fragmented information and instability. For Bang, one of the key mechanisms for exploring and understanding a bazaar-like economy is social networks, the way they form, and how information flows through them.[8] We need to focus on the social differences between actors in a market situation.[9]

Even the Emperor can be incorporated into such a perspective. In considering the Emperor as both the embodiment of the state and a private person intervening in its economy as one more player amongst other private citizens, Lo Cascio draws attention to the interplay between the Emperor’s euergetism and private markets, that he solved the problem of feeding Rome “by leaving unchanged the market mechanisms at work” and by “establishing and enforcing the rules of the game”.[10] He does so to ensure that individuals neither engage in rampant speculation to force up prices, but also to ensure that prices do not become set to low, that is, to ensure an adequate profit.[11] The success or failure of the Emperor to do this should depend on his position in the network.[12]

This is a very complex view, too complex for any one individual to hold in one’s head and to be able to understand the non-linear outcomes of so many interacting parts.[13] We need the computer. To understand the Roman economy, we need to simulate it. The best way to do this is to ground our simulation in what our evidence actually gives us: the actions of individuals in the past, whether we find that evidence in the archaeology or the ancient literature. We have to build up from individuals before we can begin to understand what ‘the Roman economy’ might actually mean.

Roman Economics Needs to be Networked

Networks and network analysis are currently in vogue in many areas of research. Tom Brughmans has neatly summarised the historiography and main issues surrounding networks and network analyses as applied to archaeological research.[14] In essence, he argues that all of the varied approaches to network analyses are united by the idea that networks are ubiquitous and influence decision making; through networks both tangible objects and intangible influences spread (and in turn, promote or hinder network growth). Through studying networks, we are able to bridge the study of parts through reductionism to the emergent whole.[15] The methodological advantages enumerated by Carl Knappett[16]  can be tied explicitly to the advantages that the New Institutional Economics bring. A network perspective forces one to consider relations between entities; they are spatial whether considered in social or physical terms; they work across scales; they can incorporate people, objects, and time.

Schortman and Ashmore make the argument that a by-product of social networks is the emergence of power, through collaborative or cooperative action.[17]  Debates around structure and agency in the social sciences revolve around questions related to the concentration of power and the generation of hierarchies across multiple spatial scales. It is from this contending for assets that politics becomes necessary and structures for the same emerge. [18]

Achieving power over others involves monopolizing some aspect of the production, distribution or use of materials. On the other hand, others can contest this by using their own social networks to gather resources (whether material or social). In this way, action through social networks results in political structures which are themselves the aggregate of flows of materials and ideas through social networks.[19]

Perhaps the most well-known term in network studies is the idea of the ‘small-world’, first coined by Stanley Milgram.[20] A small-world is not just a metaphor, but rather a precise concept in network terms, where a randomly connected network with mostly local connections has a few long distance connections which allow the entire network to be spanned in only a few steps.[21] This is a crucial concept and one we should look for archaeologically or as a by-product of our models. Brughmans writes

“   …   Such a specific topology has direct implications for the processes underlying it, like the transportation of materials, the spread of religious ideas or the enforcement of political power. These processes would largely take place between the highly connected nodes [actors of whatever kind] and they would only reach the larger number of less connected nodes through these [linkages]. In a small-world network, on the other hand, nodes within the same small-world are more often directly connected to each other, while only processes involving other small-worlds (e.g. long-distance trade) would go over the bridging nodes.”[22]

How can we draw out networks from archaeological materials?  Objects carry the resonances of who make them. They mark out membership and social identity. “Exchanging these items thereby manifests and extends crucial social linkages… Networks, therefore, come alive, in part, through the transfer of items that partake of their members’ social essences”.[23] Objects therefore could be taken as proxies for social actors.[24] Artefacts are the result of human, individual, decisions. They influenced other individuals at the time through their complex resonances of thing and place and object life-history. By considering artefacts and their relationships explicitly in terms of social network analysis, we reconnect with the individual in the past, and we obtain a perspective that allows us to see what kinds of actions were possible in the past, patterns of agency and structure, that those actors themselves could not see.

Anytime one can discern a relationship, a network is possible. Fiona Coward reminds us that the archaeological record is not a passive by-product but rather is in fact social relationships: “The patterning of material culture is a direct result of the social relationships between individuals and groups in which these objects were caught up. A network perspective provides a much more realistic picture, not only of objective sociality, but also potentially of individuals’ subjective experience of their worlds”.[25]

But as Scott Weingart warns us, we also have to take into account the dangers of methodology appropriation.[26] Network analysis comes to us from graph theory, from statistics, from computer science. The methods, philosophies and concerns of those disciplines are not necessarily congruent with archaeology. Brughman’s recent work will go a long way to addressing the potentials and perils of drawing out networks from archaeological materials.[27]

Economic Simulation

If we can draw out networks from the ancient literature or the archaeological record, what then?  We re-animate these networks using agent based (or ‘individual based’) modelling. This is a technique where a population of autonomous, heterogeneous ‘agents’ are created within a computerized environment. They are given rules of behaviour which they implement given a particular situation (whether when interacting with other agents, or with the environment). They are goal-oriented and to a degree, self-aware. That is, if we are interested in something called ‘the Roman economy’, we simulate the agents that compose that economy and their behaviours: not the economy itself (in contrast to traditional economic models with their equations and ‘rationalizing’ assumptions; we simulate at one level of complexity below our ‘target’.[28]

Lea Tesfatsion discusses a number of ways in which ‘agent-based computational economics’ can be used, and classifies different studies according to their objectives. The one which should concern us here is what she calls, ‘qualitative insight and theory generation’: “how can economic systems be more fully understood through a systematic examination of their potential dynamical behaviours under alternatively specified initial conditions?”[29]  A key feature of agent modelling that differentiates it from other approaches is that once the starting conditions are specified, all subsequent events are driven by agent interactions. The researcher then is not so concerned with the final results of the simulation as its evolution over time, its history. Thus, the focus is on the process.[30] That is to say, we study the model’s history to generate insight into real history.

Research into agent based models of economies has found that the topology of interactions matters. It is not just the pattern of social ties that matters,[31] but also the environment in which these actions take place.[32] We can explore the environmental aspect by setting the simulation on top of a cellular-automaton, a chess-board like arrangement of squares, where each square represents a unit of land and its holdings, and which responds to rules about growth, climate, geology, and so on. In many ways, a cellular automaton represents a dynamic geographic information system and which could obviously be drawn from archaeological GIS. Combined with an agent-based model representing the decision making agents, we then have a powerful tool.

A number of researchers have applied ABM and cellular automata to studying problems of structural change in agricultural societies, exploring everything from government intervention,[33] to the diffusion of innovation in agriculture,[34] to the beginning of European-style agriculture in Indiana in the early 1800s.[35] These studies point to ways in which economic path-dependence emerges, under what circumstances innovation may diffuse, and decision making processes at different spatial scales.

Archaeology and Simulation

Simulation has a long history in archaeology.[36] Agent based modelling is an outgrowth from several different fields, primarily game theory and complex systems studies.[37] John Barret, in considering the relationship between agents and society, drew attention to how agents both form and are constrained by, the social structures that emerge from their interactions. He argued therefore that the level of ‘society’ should not form the basic unit of archaeological analysis, but rather the individual.[38] It is social learning that creates a society (or an economy, for that matter).

There are now many agent-based models of past societies.[39] Many of these are quite complicated, with many moving parts, which can make it difficult to understand what the model results may actually be telling us. I advocate instead for extremely simple models, exploring only a limited aspect of the phenomena in which we are interested in. After building a series of these, we can consider their results in aggregate.

Building a Simulation

How do we translate our arguments over the Roman economy into an agent framework? Tesfatsion suggests a four-step method for recasting that understanding in a way that can be modelled and explored:

“• Select as your benchmark case an equilibrium modelling of an economy from the economic literature that is clearly and completely presented and that addresses some issue you care about.

• Remove from this economic model every assumption that entails the external imposition of an equilibrium condition (e.g., market clearing assumptions, correct expectations assumptions, and so forth).

• Dynamically complete the economic model by the introduction of production, pricing, and trade processes driven solely by interactions among the agents actually residing within the model. These procurement processes should be both feasible for the agents to carry out under realistic information limitations and appropriate for the types of goods, services, and financial assets that the agents produce and exchange.

• Define an “equilibrium” for the resulting dynamically complete economic model.”[40]

Tesfatsion remarks that when she tries this exercise with economics students, they find it difficult to understand the economy at this level working with individual agents. The challenge of this method is that it foregrounds survival: that the needs of subsistence, of surviving over time (death is always a possibility in these models) are the bedrock on which everything else is based.

Thus, we build our rule-sets that our computational agents will follow from our understanding of how an individual [Roman; collegium; military unit; family; city] acts in particular situations. While every agent might have the same suite of variables, each agent is heterogeneous. Its particular combination of variables is unique. We might all be playing basketball by the same rules, but my abilities are different than yours. We model the appropriate underlying environment. We specify the initial starting conditions, and then set the simulation in motion. We run the simulation over and over again to explore the complete behaviour space for all of the particular starting conditions, to see what emerges when and how.

To know that we have found something new about the Roman economy from such a process, I would suggest that we ground one of the model’s behaviours in social networks. There are various ways this might be accomplished. We might draw from an understanding of how patronage worked in the Roman world.[41] Or, we could draw from Bang’s arguments about Rome-as-bazaar.[42] Then, when the simulation has run its course, we can measure the emergent network and compare its features to real networks known from the archaeology. When the two correspond, then the model settings for that particular run have something important to tell us about ancient society. Alternatively, we could reverse that and specify networks found in the archaeology as our starting point. Do the model outcomes, when set from a starting point known archaeologically, make any sense according to what we believe to have been true about the Roman economy? If not, then perhaps our rule sets are flawed.

Doran  underlines some of the main impediments to simulation building amongst archaeologists,  limitations in computing power, and the disciplinary boundaries that create barriers to knowledge building.[43] As Doran points out, the computing power issue is largely no longer an issue. Quite complicated simulations may be built on a desktop computer without too much trouble in terms of hardware. The second problem is more difficult. One way we can break those boundaries down may lie in the choice of simulation environment: the simpler and more intuitive the framework, the easier to use, develop, and communicate results. In my own work, I use the open-source Netlogo modelling environment, which I recommend to anyone interested in exploring the possibilities of this approach.[44] While Netlogo has its genesis in efforts to educated school children in complex systems thinking, it is now in its fifth major release and is quite powerful. The learning curve is not overly steep, and much can be accomplished through tweaking the many models that come pre-packaged with the software (more on this below).

A simulation is an argument in computer code about the way the world works, and so represents a kind of ‘procedural rhetoric’.[45] It is object-oriented, meaning that each individual behaviour exists as its own object. One then arranges the objects (which can be conditional) in the order the agents should carry them out, given a particular position in the environment or social position vis-à-vis other agents. One can have quite sophisticated simulations running after a day of working through the included tutorials. This should not be taken as a sign that Netlogo is simplistic. Quite powerful models have been built in it, including modelling the emergence of cities in the third millennium BC.[46]

An excellent place to begin is with the included model, ‘Wealth Distribution’.[47] In this model, a ‘world’ is simulated where grain is distributed randomly. In some places it grows thick on the ground; in other places it is sparse. A population of agents are introduced to this world. Their goal is to find enough grain to keep living, and to reproduce when conditions are right. The agents have ‘vision’ or knowledge of the world, to differing degrees. They have ‘metabolism’, or a preset amount of food they must consume with each time-step or they shall die (which again varies by individual). The amount of food collected above this metabolic rate becomes ‘wealth’. When this simulation is run, it becomes apparent that the differential distribution of resources in this world is sufficient in itself to create a partition of the world into classes where there are a few extremely wealthy individuals and a vast mass of others who are in constant danger of ‘dying’ from not having enough food.

We could then extend this model to represent something of the Roman world. We could give the agents a way of looking for help, of becoming a client of someone a bit wealthier than themselves. In return we could imagine that these ‘clients’ could offer support to their patron in turn. Perhaps the number of followers, and their relative ‘wealth’, could be translated into a score for ‘prestige’ which in turn affects the ‘patron’s’ ability to extract wealth from the world. What kind of artificial society results? In my ‘Patronworld’ model,[48] which had its inspiration in the Wealth Distribution model, chains of connected individuals (that is, networks) do emerge from this dynamic, but they are fragile. One result seems to be that extremely high levels of gift-giving seem to go hand in hand with network collapse. It seems to do this by destabilizing the networks: too many people outside particular chains of patrons-clients are shut out of the system.[49] Given the competitive building that characterizes the late Republic, this result is intriguing.[50] It is a very simple model, to be sure, but one that foregrounds an important element of new models of the Roman economy: networks and social life. This kind of modelling also has the virtue that if one disagrees with the assumptions of the model, the code can be easily modified and adapted. In this way, model building is not an end point of research but rather a first step of a larger conversation (my own models may be found at the digital data repository Figshare.com and I welcome their use, adaptation, and improvement).

Moving forward

We need more and better networks drawn from historical and archaeological data. It is not enough, in contrast to Malkin,[51] to use ‘networks’ as simple metaphor. Particular network topologies have different implications for the actors which make them up. If we are to make progress on the Roman economy, we need to explore the multiple networks of individuals and objects at multiple social and spatial scales. We need to turn our archaeological geographic information systems into computing environments in which agents can interact: at a stroke, we will have unified landscape archaeology, ancient history, and the study of ancient economics. Once we have this data, we can take our current understandings of the ancient economy, whether ’consumer city’, ‘primitive’; ‘modernising’, ‘bazaar’, NIE, or something else and translate them into an agent based simulation. If we can generate analogous networks to the ones we know archaeologically, then we might just have the wherewithal to argue that we have a model that tells us something useful, something new, about the past.

References

Agar, M. (2003).  ‘My kingdom for a function: modelling misadventures of the innumerate’, Journal of Artificial Societies and Social Simulation 6.3. http://jasss.soc.surrey.ac.uk/6/3/8.html (accessed 28/05/2012).

Bang, P. (2006). ‘Imperial Bazaar:  towards a comparative understanding of markets in the Roman Empire’, in P. Bang, M. Ikeguchi, H. Ziche (eds.), Ancient Economies, Modern Methodologies: Archaeology, Comparative History, Models and Institutions. Bari, 51-88.

Bang, P. (2009). ‘The ancient economy and New Institutional Economics’, Journal of Roman Studies 99: 194-206.

Barabási, A.-L. and R. Albert. (1999). ‘Emergence of scaling in random networks’, Science 268: 509-12.

Barrett, J. (2000). ‘A thesis on agency’, in M. Dobres and J. Robb (eds.), Agency in Archaeology. New York, 61-8.

Barrett, J. (2001). ‘Agency, the duality of structure, and the problem of the archaeological record’, in I. Hodder (ed.), Archaeological Theory Today. Cambridge, 141-64.

Bentley, R. and H. Maschner (2003). ‘Preface: considering complexity theory in archaeology’, in R. Bentley and H. Maschner (eds.), Complex Systems and Archaeology. Salt Lake City, 1-8.

Berger, T. (2001). ‘Agent-based spatial models applied to agriculture: a simulation tool for technology diffusion, resource use changes, and policy analysis’, Agricultural Economics 25: 245-260.

Bogost, I. (2007). Persuasive Games. Cambridge, MA.

Bourdieu, P. (1977). Outline of a theory of practice (trans. R. Nice). Cambridge.

Brughmans, T. (2010). ‘Connecting the dots: towards archaeological network analysis’, Oxford Journal of Archaeology 29.3: 277-303.

Brughmans, T. (2012). ‘Thinking through networks: a review of formal network methods in archaeology’, Journal of Archaeological Method and Theory 19.2 Online version: DOI: 10.1007/s10816-012-9133-8 http://www.springerlink.com/index/10.1007/s10816-012-9133-8 (accessed 28/05/12).

Buchanan, M. (2002). Nexus: Small Worlds and the Groundbreaking Science of Networks. New York.

Clarke, D. (1968). Analytical Archaeology. London.

Clarke, D. (1972). Models in Archaeology. London.

Costopoulos, A and M. Lake. (2010). (eds.), Simulating Change: Archaeology Into the Twenty-First Century. Salt Lake City.

Coward, F. (2010). ‘Small worlds, material culture and Near Eastern social networks’, Proceedings of the British Academy 158, 449-479. http://www.fcoward.co.uk/Cowardsmallworlds.pdf (accessed 28/05/12).

Davis, J. (1998). ‘Ancient economies: models and muddles’, in H. Parkins and C. Smith (eds.), Trade, Traders and the Ancient City. London, 225-56.

Davis, J. (2005) ‘Linear and non-linear flow models for ancient economies’, in J. Manning and I. Morris (eds.), The Ancient Economy: Evidence and Models. Stanford, 127-56.

Dean, J. S., Gumerman, G. J., Epstein, J. M., Axtell, R. L., Swedlund, A. C., Parker, M. T., and McCarroll, S. (2006) ‘Understanding Anasazi culture change through agent-based modeling.’ in Epstein, J. (ed.), Generative Social Science: Studies in Agent-Based Computational Modeling  Princeton, 90–116.

Deffuant, G., S. Huet, J.P. Bousset, J. Henriot, G. Amon, G. Weisbuch. (2002). ‘Agent based simulation of organic farming conversion in Allier Département’, in M. Janssen (ed.), Complexity and Ecosystem Management: The Theory and Practice of Multi-Agent Systems. Cheltenham, 158–187.

DeLaine, J. (2002). ‘Building Activity in Ostia in the Second Century AD’ in C. Bruun and A. Gallina Zevi (eds.). Ostia e Portus Nelle Loro Relzaioni con Roma (Acta Instituti Romanae Finlandiae 27). Rome, 41-101.

Dibble, C. (2006). ‘Computational laboratories for spatial agent-based models’, in L. Tesfatsion and K. Judd (eds.), Handbook of Computational Economics, Vol. 2: Agent-Based Computational Economics. Amsterdam, 1511-1550.

Dobres, M. and J. Robb (2000). Agency in Archaeology. New York.

Doran, J. (2011). Review of A. Costopoulos and M. Lake, Simulating Change: Archaeology into the Twenty-First Century Salt Lake City. http://jasss.soc.surrey.ac.uk/14/4/reviews/2.html

Dornan, J. (2002). ‘Agency and archaeology: past, present, and future directions’, Journal of Archaeological Method and Theory 9: 303-29.

Evans, T.P., and H. Kelley. (2004). ‘Multiscale analysis of a household level agent-based model of land-cover change’,  Journal of Environmental Management 72.1, 57–72.

Frier, B. and D. Kehoe. (2007). ‘Law and economic institutions’, in W. Scheidel, I. Morris, R. Saller (eds.), The Cambridge Economic History of the Greco-Roman World. Cambridge, 113-143.

Gardner, A. (2007). An archaeology of identity: soldiers and society in late Roman Britain. Walnut Creek.

Giddens, A. (1984). The constitution of society: outline of the theory of structuration. Berkeley.

Gilbert, N., and K. Troitzsch. (2005). Simulation for the Social Scientist. Second edition. Maidenhead, Berkshire.

Graham, S. (2006a). ‘Networks, Agent-Based Modeling, and the Antonine Itineraries’, The Journal of Mediterranean Archaeology 19.1: 45-64.

Graham, S. (2006b). Ex Figlinis: The Complex Dynamics of the Roman Brick Industry in the TiberValley during the 1st to 3rd Centuries AD. British Archaeological Reports, International Series 1486: Oxford.

Graham, S. (2009). ‘BehaviourSpace: Simulating Roman Social Life and Civil Violence’, Digital Studies/ Le champ numérique, 1(2). http://www.digitalstudies.org/ojs/index.php/digital_studies/article/view/172/214 (accessed 29/5/12)

Graham, S. and G. Ruffini. (2007). ‘Network Analysis and Greco-Roman Prosopography’, in K.S.B. Keats-Rohan (ed.), Prosopography Approaches and Applications: A Handbook. Oxford: 325-36.

Graham, S. and J. Steiner. (2008). ‘Travellersim: Growing Settlement Structures and Territories with Agent-Based Modelling’, in J. Clark and E. Hagemeister (eds.), Digital Discovery: Exploring New Frontiers in Human Heritage. CAA 2006. Computer Applications and Quantitative Methods in Archaeology. Proceedings of the 34th Conference, Fargo, United States, April 2006. Budapest: 57-67.

Hoffmann, M., H. Kelley, and T. Evans. (2002). ‘Simulating land-cover change in south-central Indiana: an agent-based model of deforestation and afforestation’, in M. Janssen (ed.), Complexity and Ecosystem Management: The Theory and Practice of Multi-Agent Systems. Cheltenham, 218–247.

Jansenn, M. and E. Ostrom (2006). ‘Governing Social-Ecological Systems’ in L. Tesfatsion and K. Judd (eds.), Handbook of Computational Economics, Vol. 2: Agent-Based Computational Economics. Amsterdam, 1466-1510.

Knappett, C. (2011). An archaeology of interaction. Network perspectives on material culture and society. Oxford.

Kohler, T., G. Gumerman, and R. Reynolds. (2005). ‘Simulating Ancient Societies’, Scientific American 293.1: 76-84.

Lehner, M. (2000). ‘Fractal house of pharaoh: ancient Egypt as a complex adaptive system, a trial formulation’ in Kohler, T. A. and Gumerman, G. J. (eds.), Dynamics in Human and Primate Societies: Agent-Based Modeling of Social and Spatial Processes . Oxford, 275–353.

Lo Cascio, E. (2006). ‘The role of the state in the Roman economy: making use of the New Institutional Economics’, in P. Bang, M. Ikeguchi, H. Ziche (eds.), Ancient Economies, Modern Methodologies: Archaeology, Comparative History, Models and Institutions. Bari, 215-236.

Malkin, I. (2011). A Small Greek World: Networks in the Ancient Mediterranean. Oxford.

Manning, J. And I. Morris. (2005). The Ancient Economy: Evidence and Models. Stanford.

Milgram, S. (1967). ‘The small world problem’, Psychology Today. 2:60–67.

North, D. (1990). Institutions, Institutional Change and Economic Performance. Cambridge.

Ourednik, A. and P. Dessemontet. (2007). ‘Interaction maximization and the observed distribution of urban populations: an agent based model of humanity’s metric condition’. http://ourednik.info/urbanization_mc (accessed 28/5/12).

Premo, L. S. (2006) Agent-based models as behavioral laboratories for evolutionary anthropological research. Arizona Anthropologist 17:91-113.

Scheidel, W. (2010). ‘Approaching the Roman economy’ version 1.0. http://www.princeton.edu/~pswpc/pdfs/scheidel/091007.pdf (accessed 28/5/12).

Scheidel, W. and S. von Reden (2002). The Ancient Economy. Edinburgh Readings on the Ancient World. New York.

Schortman, E. and W. Ashmore. (2012). ‘History, networks, and the quest for power: ancient political competition in the Lower Motagua Valley, Guatemala’, Journal of the Royal Anthropological Institute 18.1: 1-21.

Symons, S. and D. Raine. (2008) ‘Agent-Based Models Of Ancient Egypt’, in N. Strudwick (ed.), Proceedings of Informatique et Égyptologie. Piscataway, NJ. http://www.physics.le.ac.uk/ComplexSystems/papers/AgentBasedModelsEgypt2008.pdf (accessed 28/5/12).

Tesfatsion, L. (2006). ‘Agent-based computational economics: a constructive approach to economic theory’, in L. Tesfatsion and K. Judd (eds.), Handbook of Computational Economics, Vol. 2: Agent-Based Computational Economics. Amsterdam, 831-880.

Vriend, N. (2006). ‘ACE models of endogenous interactions’, in L. Tesfatsion and K. Judd (eds.), Handbook of Computational Economics, Vol. 2: Agent-Based Computational Economics. Amsterdam, 1047-1080.

Wallace-Hadrill, A. (1989) (ed.) Patronage in Ancient Society. London.

Watts, D. (1999). Small Worlds. The Dynamics of Network Between Order and Randomness Princeton.

Watts , D., and S. Strogatz. (1998). ‘Collective dynamics of ‘small-world’ networks’, Nature 393: 440-42.

Weingart, S. (2012). ‘Demystifying networks’, the scottbot irregular http://www.scottbot.net/HIAL/?p=6279 (accessed 28/5/12).

Wilensky, U., and M. Resnick. (1998). ‘Thinking in Levels: A Dynamic Systems Approach to Making Sense of the World’ Journal of Science Education and Technology 8.1: 3-18.

Wilensky, U. (1999). Netlogo . Evanston, IL. http://ccl.northwestern.edu/netlogo (accessed 28/5/12).

Wilhite, A. (2006). ‘Economic activity on fixed networks’, in L. Tesfatsion and K. Judd (eds.), Handbook of Computational Economics, Vol. 2: Agent-Based Computational Economics. Amsterdam, 1013-1046.


[1] Tesfatsion 2006: 832.

[2] Indeed, many economic models fail to recognize that the spatial context of economic action undermines many of the basic assumptions of economic theory, Dibble 2006: 1515.

[3] The discussion is usefully treated in for example Scheidel 2010, Manning and Morris 2005, and Scheidel and von Reden 2002.

[4] North 1990, and its application to the ancient world in Frier and Kehoe 2007; Bang 2009; the various papers in Manning and Morris 2005; Scheidel’s forthcoming Cambridge Companion to the Roman Economy

[5] Frier and Kehoe 2007.

[6] Frier and Kehoe 2007: 119.

[7] Bang 2006: 79.

[8] Bang 2006: 80-4.

[9] Bang 2008: 197.

[10] Lo Cascio 2006: 225.

[11] Lo Cascio 2006: 231.

[12] Graham 2006b: 111-113.

[13] cf.  Davis’ diagrams in 2005; 1998.

[14] Brughmans 2012; 2010.

[15] Brughmans 2012; Bentley and Maschner 2003:1.

[16] Knappett 2011: 10.

[17] Schortman and Ashmore 2012: 3.

[18] Schortman and Ashmore 2012: 2-3 citing Barrett 2000, Bourdieu 1977, Dobres and Robb 2000; Dornan 2002; Garnder 2007; Giddens 1984.

[19] Schortman and Ashmore 2012: 3-4.

[20] Milgram 1967.

[21] Buchanan 2002; Watts and Strogatz 1998; Watts 1999.

[22] Brughmans 2010.

[23] Shortman and Ashmore 2012: 4.

[24] Graham and Ruffini 2007: 325-331.

[25] Coward 2010.

[26] Weingart 2012.

[27] Brughmans 2012; 2010.

[28] cf.  Wilensky and Resnick 1998: 4; Agar 2003; Gilbert and Troitzsch 2005: 199-202. Gilbert and Troitzsch is an excellent resource for learning how to build simulations.

[29] Tesfatsion 2006: 840.

[30] Tesfatsion 2006:843.

[31] Watts and Strogatz 1998; Barabasi and Albert 1999.

[32] Janssen and Ostrom 2005: 1496 citing Dibble 2006; Wilhite 2006; Vriend 2006.

[33] Berger 2001.

[34] Deffuant et al., 2002.

[35] Hoffmann et al 2002; Evans and Kelley 2004.

[36] Some of the earliest work being in Clarke 1968, 1972; see Graham 2006a: 53-4.

[37] The premier journal is the Journal of Artificial Societies and Social Simulation, jasss.soc.surrey.ac.uk.

[38] Barrett 2001:155.

[39] for instance Lehner 2000; Kohler, Gumerman and Reynolds 2005; Dean et al 2006; Graham 2006a; Premo 2006; Graham and Steiner 2008; Symons and Raine 2008; Graham 2009; Costopoulos and Lake 2010.

[40] Tesfatsion 2006: 852-3.

[41] cf. Wallace-Hadrill 1989.

[42] Bang 2006; 2008

[43] Doran 2011.

[44] Wilensky 1999.

[45] Bogost, 2007: 28-44.

[46] Ourednik and Dessemontet 2007.

[47] Wilensky, 1998.

[48] Published in Graham 2009.

[49] Graham 2009: 11.

[50]  cf.  DeLaine 2002 on patronage in building projects at Ostia.

[51] Malkin 2011: 18-9.