by : Marco A. Janssen

1. Introduction
Agent-based modelling (ABM) is the computational study of social agents as evolving systems of autonomous interacting agents. ABM is a tool for the study of social systems from the complex adaptive system perspective. From this perspective, the researcher is interested in how macro phenomena are emerging from micro level behaviour among a heterogeneous set of interacting agents (Holland, 1992). By using ABM as computational laboratories, one may test in a systematic way different hypotheses related to attributes of the agents, their behavioural rules, and the types of interactions, and their effect on macro level stylized facts of the system.
Since the early 1990s ABM has increasingly been used in most of the social sciences. I shall focus on the applications of ABM related to ecological economics (Janssen, 2002, 2005; Janssen and Ostrom, 2005). ABM of ecological economic systems can be defined as systems that are populated with heterogeneous population of agents, who determine their interactions with other agents and with their environment, on the basis of internalized social norms and mental models, internal behavioural rules and cognitive abilities, formal and informal institutional rules that affect how agents interact, individual and social learning, etc.
2. Motivations for Agent-based Modelling
Some readers may question why we need complex approaches such as ABM. Are equation-based models not sufficient? Other readers may argue that ABM is not new. My response to these queries is that it all depends on the type of questions one is interested in. For many problems, equation-based models are excellent tools to study the problem of concern. However, for a problem like coordination or strategic interaction, multiple agents need to be distinguished.
Traditional game theory has been very successful in addressing strategic interaction by a small number (mainly two) (types of) players, using equation-based models. Unfortunately, traditional game theory is rather restrictive: Agents are required to have high cognitive abilities, the rules of the game are fixed, and the structure of the interactions is on a rigid lattice or fully random. But from empirical studies it is known that humans are boundedly rational, the rules of the
game change, and social interactions have complex social structures (e.g.,Gigerenzer and Selten, 2001; Janssen and Ostrom, in press). It is no surprise that ABM has been widely applied to games since the early 1980s (e.g., Axelrod, 1984).
Indeed, models of individual units were developed long ago, such as statistical mechanics and micro-simulations. But these methods assume no interaction, or random interaction, between the agents. A key element in ABM is the possibility of complex structures of social interactions. In some systems, the macroscale properties are sensitive to the structure of interactions between agents and social
networks. In equation-based models, the agents are frequently, implicitly, assumed to be well mixed, the mean-field assumption, and thus these approaches miss the opportunity to investigate the sensitivities of the structure of interactions.
Finally, within integrated modelling of ecological economic systems, one of the key problems is how to match the scale of social and ecological dynamics (Levin, 1992; Gibson et al., 2000). By the use of agents, we derive tools that make it possible to integrate processes and interactions at different levels of scale, for agent-agent and agent-environment interactions.
3. ABM Methodology
Most ABMs applied within ecological economics consist of two elements:
cellular automata and agents. I will now discuss briefly both elements.
Cellular Automata
Originally, the cellular automata (CA) approach was introduced by John von
Neumann and Stanislaw Ulam at the end of the 1940s. Since the early 1970s,
CA have been used by many disciplines to study complex dynamic behaviour of
systems. The essential properties of a CA are:
• a regular n-dimensional lattice (n is in most cases of one or two dimensions),
where each cell of this lattice has a discrete state,
• a dynamical behaviour, described by so called rules. These rules describe the
state of a cell for the next time step, depending on the states of the cells in the
neighbourhood of the cell.
The basic element of a CA is the cell that is represented by states. In the
simplest case, each cell can have the binary states 1 or 0. In more complex
simulations, the cells can have more different states. These cells are arranged in
a lattice. The most common CAs are built in one or two dimensions. The cells
can change state by transition rules, which determine the state of the cells for the
next time step. In cellular automata, a rule defines the state of a cell in
dependence of the neighbourhood of the cell.
With regard to our interest for ecological economics, the application of CA can
be rather straightforward. In fact, CA can be used to produce a dynamic
Geographical Information System (GIS). The lattice represents a map of a certain
area, with each possible state of a cell representing a possible land use. Due to
physical restrictions, cells on some locations may be restricted to a limited
number of states; for example, a secondary forest cannot turn back into a
primary forest. Transition rules determine when a certain land use of a cell
changes into another land use. Cell changes can be influenced by local rules; for
example, if the cell is a forest-cell, and if one of the neighbour cells is on fire,
then the cell turns to fire. However, global rules are also possible, since land use
changes can be influenced by demand for certain land on a higher level of scale.
For example, demand for extra agricultural land can be translated as changing
those cells to agriculture that are the most suitable.
A drawback of using CA for representing social agents is its simplicity. For
example, social networks are more complex than the local neighbours on a
lattice. The number of possible states in which a social agent can be might be too
large to be efficiently represented as a CA. Within land use models, landowners
may own multiple cells and make decisions on the land use of their cells. Thus a
cell-based rule that ignores parcel boundaries is inadequate. The study of agents
has been a topic of research for a long time in computer science, which has
developed its own tools and frameworks.
Agents
The architecture of agents in ABM has been much influenced by work on multi-
agent systems in Artificial Intelligence (AI). Multi-agent systems research studies
the behaviour of adaptive autonomous agents in the physical world (robots) or in
cyberspace (software agents). Wooldridge (2002) argues that intelligent agents
are able to act flexibly and autonomously. By flexibility we mean that agents are
goal-directed (satisfying or maximizing their utility), reactive (responding to
changes in the environment) and capable of interacting with other agents. One of
the difficulties is in balancing reactive and goal-directed behaviour. Developing
models with agents who have only reactive behaviour is relatively simple, and
individual-based ecological modelling addresses problems by simulating non-
human agents as reactive objects (e.g., DeAngelis and Gross, 1992).
However, humans combine reactive and goal-directed behaviour.
Conventional economics assumes the selfish rational actor to describe individual
behaviour. Although this agent model provides a good description of human
behaviour in highly competitive markets, as is confirmed in experimental studies,
it is not satisfactory for the description of behaviour in various decision situations
of importance for ecological economics (Gintis, 2000). For decision situations
such as economic valuation and collective action, motivation, fairness and
preferences play an important role, and the characteristics may vary within the
population of human agents. Furthermore, decision problems related to
environmental management are often so complex that it is not likely that one has
full information and understanding of the problem and is able to evaluate all
possible options. Models of bounded rationality have been used as an alternative
in economics (Simon, 1955). Furthermore, using concepts from psychology, we
are able to include dimensions of economic agents such as emotions,
motivations, and perceptions. A problem is that loosening the tight framework of
the selfish rational actor leads to many possible frameworks. Within behavioural
economics, there is mainly attention to models of learning that explain observed
behaviour in experiments (Camerer, 2003). Others focus on fast and frugal
heuristics, of how individuals make a choice in simple problems under time
pressure (Gigerenzer et al., 1999).
A scheme of a simple model of two agents interacting with each other and
their environment is given in Figure 1, which provides the simplest description of
ABM applied to ecological economics. Agents derive information from the
environment that informs the perception they have about the state of the
environment. Based on the goals and attributes of the agents they make
decisions on actions to perform and these actions affect the environment. The
agents can interact indirectly, for example by affecting the common resource, or
directly by communication. This communication might be used to exchange
information about possible strategies, knowledge about the resource and
agreements how to solve collective action problems.