Agent-based models

Agent-based models (ABMs) are simulations that represent each entity in a system as an independent and autonomous agent (Epstein and Axtell, 1996; Gilbert, 2007). An ABM consists of a set of rules that describe how the entities behave and, crucially, how they interact with other entities. Agent-based modelling is a framework well-suited to model complex systems: systems in which interactions between entities, for exam- ple between individuals, can produce emergent, or unexpected phenomena (Newman, 2011). Regularities in the spatio-temporal patterns associated with civil violence is an example of one such emergent phenomenon and ABMs can be constructed that attempt to replicate such patterns. Overcoming limitations associated with a lack of data at appropriate resolutions, ABMs have been employed as a means of understanding how different forms of individual behaviour might aggregate to system-wide outputs that may be empirically observed.

In many early applications of agent-based modelling, the behaviours proposed for the agents were somewhat simple, and the models were used largely to demonstrate that unanticipated emergent phenomena can be the result of individual autonomous ad- herence to simple rules. For example, in the model of neighbourhood segregation by Schelling (1971), agents’ slight preference for similar neighbours can result in com-

plete neighbourhood segregation. The emphasis of this model was not to successfully replicate real-world individual behaviours, but to demonstrate that simple rules, when combined into a system with many interacting components, can produce unexpected results. The translation of this finding into the real-world provides support for the argu- ment that observed segregation in urban areas is the result of inherent system properties, rather than any systematic prejudices in the population.

In another early example, Granovetter (1978) formulates a model of riot partic- ipation in which individuals can either choose to join a riot, or choose not to join, depending on the size of the riot and their perceived probability of being arrested. Each individual has associated to them a threshold that indicates the likelihood that they will join the riot given the number of rioters already engaged in the disorder. Thus, a safety in numbers effect is emphasised, with rioters who are more risk averse requiring a larger riot before they participate themselves. This model demonstrates how even with a range of risk averse people, it is possible for a cascading effect to result in widespread riot- ing. Furthermore, the model demonstrates sensitive dependence on initial conditions. Widespread rioting or a peaceful system state can depend on the presence of so-called ‘instigators’ to start the rioting, those with little to no risk aversion. Instigators enable others who are slightly risk averse to join who, in turn, enable even more risk averse individuals to participate.

Epstein (2002) presents an ABM of civil violence, which again incorporates rel- atively simplistic individual behaviours in order to capture interesting or unexpected dynamics at the overall system level. In this model, agents have heterogeneous lev- els of grievance and risk aversion, both of which influence the likelihood that any given agent engages in violence and becomes ‘active’ via a threshold model similar to the one employed in Granovetter (1978). The model also contains police agents which arrest active agents, who are then jailed before returning to the system in a passive state. The agents are free to move randomly on a simplified lattice and change their state based on their local environment. The model is explored in a variety of scenarios, including the occurrence of decentralised rebellion and ethnic violence, and results are interpreted in the context of the real-world. Given the wide range of empirical studies that investigate the causes of civil violence, Epstein’s model of individual behaviour is certainly overly simplistic; however, Epstein argues that since the model exhibits outbursts and conta-

gion reminiscent of real-world rebellions, the model can be valuable in understanding how simple local behaviours can aggregate to global outcomes.

As the use of agent-based modelling has become more widespread, the range of behaviours available to agents have become increasingly complex, and more in line with extant theories of individual behaviour. There are a number of ABMs that, for example, employ criminological theory and robust empirical observations—such as the phenomenon of repeat victimisation in residential burglary in which houses who have recently been burgled are most likely to experience further burglary—to model a system containing offenders, opportunities to offend, and police response (Short et al., 2008; Johnson, 2008; Malleson et al., 2010; Bosse and Gerritsen, 2010; Birks et al., 2012) (see also Johnson and Groff (2014)).

In the case of civil violence, there have been several studies that extend the model of Epstein (2002), attempting to incorporate more realistic mechanisms into each agent’s individual decision-making, their interactions, and the environment in which the model is simulated. For example, Fonoberova et al. (2012) explore a range of agent risk propensity functions that extend on Epstein’s implicit linear relationship between the likelihood of engaging in violence and the ratio of police to rioters. The authors explore the effect of lattice size on the modelled police and crime numbers in compar- ison to empirical data. Torrens and McDaniel (2013) also extend the Epstein model by incorporating more realistic spatial information and agent decision-making when studying the onset of rioting.

Taking the perspective that insights can be obtained from simple models, Bennett (2008) proposes an ABM of an insurgency in which civilians can choose to commit attacks if their level of anger at the state or counterinsurgents exceeds their level of fear. Bennett uses this model to explore the tradeoff between effectiveness and accuracy of counterinsurgent forces. Although emphasising that the model is simplistic and therefore cannot capture a wide range of behaviours that have been observed in the literature, the model generates policy-level considerations for counterinsurgent forces, such as the comparative advantages of being highly accurate with counterinsurgent measures during the early stages of an insurgency.

As well as incorporating theories regarding individual behaviour, there is an in- creasing trend for ABMs of social systems to explicitly consider how the environment

in which the agents move impacts their decision-making and their interactions (Tor- rens and McDaniel, 2013; Heppenstall et al., 2012). A number of sophisticated ABMs with empirically driven modelling and validation procedures have explored the role of individual migration and the resulting spatial distributions of ethnic groups in the oc- currence of violent events (Lim et al., 2007; Bhavnani and Choi, 2012; Weidmann and Salehyan, 2013; Bhavnani et al., 2014; Rutherford et al., 2014). By constructing mod- els of specific examples of civil violence, and by calibrating outputs so that they are empirical consistent, as these studies do, the policy relevance of such models becomes immediately apparent. Bhavnani et al. (2014), for example, use their model of segrega- tion and violence in Jerusalem to explore a number of counterfactuals that result from different policy decisions.

While agent-based modelling began as a conceptual tool to consider emergence in hypothetical and largely simplified systems, another simulation technique, microsimu- lation, began with the explicit aim of being data-driven and empirical. Microsimulation aims to overcome the ecological fallacy—which refers to problems brought about by assuming that characteristics of individuals within a given population can be assumed to be equal to the averaged statistics of that population—by modelling individuals us- ing data from a population that includes those individuals. This requires a model that describes the variance within a population, and which therefore disaggregates the pop- ulation statistics over each individual. Many of these models are typically based on the calculation of conditional probabilities for the underlying population, and are often explicitly spatial (Ballas et al., 2005). Such models simulate probabilities for the un- known attributes of an individual based on what is known about them (e.g. where they live, and what are the overall characteristics of the location in which they live). The aim is to construct realistic representation of the population that matches the overall statistics for a particular area.

The two model frameworks referred to as agent-based modelling and microsim- ulation are becoming indistinguishable: data-driven and explicitly spatial ABMs have begun to incorporate statistics of underlying populations to investigate the interactions of individuals (Heppenstall et al., 2012), whilst dynamic microsimulation models are becoming versatile enough to incorporate the changing behaviours of individuals and are therefore capable of exploring the emergent behaviour of populations (Birkin and

Wu, 2012).

With regards to such simulations of civil violence, on the one hand, some ABMs can be criticised for being overly simplistic and not incorporating extant theories re- garding human behaviour; however, on the other, some models may appear to be overly complicated, with modelling decisions taken without proper justification. As a research tool, agent-based models have also been criticised as they can be difficult to reproduce and write code in a standardised way. More recently, empirical agent-based modelling, in which model outputs are compared against real-world data, has been demonstrated as a valuable tool in studying individual behaviours, and how these behaviours result in aggregate observed outcomes during civil violence. The development of agent-based models is becoming more established as a research tool (Grimm et al., 2010), and it is a method that looks set to play an increasing role in future research.