Real-world economies exhibit five essential properties. First, they consist of heterogeneous interacting participants characterized by distinct local states (data, attributes, methods) at each given time. Second, they are open-ended dynamic systems whose dynamics are driven by the successive interactions of their participants. Third, human participants are strategic decision-makers whose decision processes take into account past actions and potential future actions of other participants. Fourth, all participants are locally constructive, i.e., constrained to act on the basis of their own local states at each given time. Fifth, the actions taken by participants at any given time affect future local states and hence induce system reflexivity.
Taken together, these five essential properties imply that real-world economies are locally-constructive sequential games.
This website discusses a modeling approach, Agent-based Computational Economics (ACE), that permits the
modeling of economic systems as locally-constructive sequential games.
Roughly defined, ACE is the computational modeling of economic processes (including whole economies) as open-ended dynamic systems of interacting agents. Below are seven basic modeling principles that characterize the ACE modeling approach. These principles reflect the fundamental goal of many agent-based modelers: namely, to be able to study real-world dynamic systems as historical processes unfolding through time.
(MP1)Agent Definition: An agent is a software entity within a computationally constructed world capable of acting over time on the basis of its own state, i.e., its own internal data, attributes, and methods.
(MP2)Agent Scope: Agents can represent individuals, social groupings, institutions, biological entities, and/or physical entities.
(MP3)Agent Local Constructivity: The action of an agent at any given time is determined as a function of the agent's own state at that time.
(MP4)Agent Autonomy: Coordination of agent interactions cannot be externally imposed by means of free-floating restrictions, i.e., restrictions not embodied within agent states.
(MP5)System Constructivity: The state of the modeled system at any given time is determined by the ensemble of agent states at that time.
(MP6)System Historicity: Given initial agent states, all subsequent events in the modeled system are determined solely by agent interactions.
(MP7)Modeler as Culture-Dish Experimenter: The role of the modeler is limited to the setting of initial agent states and to the non-perturbational observation, analysis, and reporting of model outcomes.
Considered as a collective whole, modeling principles (MP1)--(MP7) embody the idea that ACE models are computational laboratories permitting users to explore how changes in initial conditions affect outcomes in a modeled dynamic system over time. This exploration process is analogous to biological experimentation with cultures in petri dishes. A user sets initial conditions for a modeled dynamic system in accordance with some purpose at hand. The user then steps back, and the modeled dynamic system thereafter runs forward through time as a virtual world whose dynamics are determined by the interactions of its constituent agents.
From a mathematical point of view, (MP1)--(MP7) imply that ACE models are state-space models in initial value form. Specifically, an ACE model specifies how an ensemble of agent states varies over time, starting from a given ensemble of agent states at an initial time.
However, modeling principles (MP3)--(MP7), which require agent autonomy conditional on initial agent states, sharply differentiate ACE models from standard state-space models within economics. The latter models incorporate modeler-imposed rationality, optimality, and equilibrium conditions that are not locally constructive; that is, these conditions could not (or would not) be met by agents acting purely on the basis of their own local states at each successive point in time.
For example, rational expectations assumptions require ex ante agent expectations to be consistent with ex post model outcomes. Consequently, the derivation of rational expectations solutions is a global fix-point problem requiring the simultaneous consideration of all time periods.
For ACE researchers, as for economists in general, the modeling of decision-making agents is a primary concern. Here is it important to correct a major misconception still being expressed by some commentators uninformed about the powerful capabilities of modern software: namely, the misconception that ACE decision-making agents cannot be as rational (or irrational) as real people.
To the contrary, the constraints on agent decision-making implied by modeling principles (MP1)-(MP7) are constraints inherent in every real-world dynamic system. As demonstrated concretely in
the decision methods used by ACE agents can range from simple behavioral rules to sophisticated anticipatory learning algorithms for the approximate achievement of intertemporal objectives. Extensive annotated pointers to reference materials on the implementation of decision methods for ACE agents can be accessed at the following site:
ACE Research Area: Learning and the Embodied Mind.
A second common misconception is the incorrect belief that (MP1)--(MP7) rule out any consideration of stochasticity. To the contrary, stochastic aspects can easily be represented within ACE models. Agent data can include recorded realizations for random events, agent attributes can include beliefs based on probabilistic assessments, and agent methods can include
pseudo-random number generators (PRNGs). A PRNG is an algorithm, initialized by a seed value, that is able to generate a number sequence whose properties mimic the properties of a random number sequence.
PRNGs can be included among the methods of decision-making agents, thus permitting these agents to "randomize" their behaviors. For example, a decision-making agent can use PRNGs to choose among equally preferred actions or action delays, to construct mixed strategies in game situations to avoid exploitable predictability, and/or to induce perturbations in action routines in order to explore new action possibilities.
PRNGs can also be included among the methods of other types of agents, such as physical or biological agents, in order to model stochastic processes external to decision-making agents. For example, a Weather agent might use a PRNG to generate a weather pattern for its computational world during each simulated year that in turn affects the actions of decision-making agents.
However, a key point with regard to stochasticity is that the modeling principles (MP1)-(MP7) require ACE models to be dynamically complete virtual worlds. Consequently, ACE modelers must explicitly identify the source of any stochastic shocks affecting events within their modeled worlds, not simply their impact points, because all such shocks must come from agents actually residing within these worlds. This requirement encourages ACE modelers to think carefully about the intended empirical referents for any included stochastic shock terms.
Current ACE research divides roughly into four strands differentiated by objective.
One primary objective is empirical understanding: What explains the appearance and persistence of empirical regularities? Examples of such regularities include social norms, socially accepted monies, market protocols, business cycles, persistent wealth inequality, and the common adoption of technological innovations. ACE researchers seek possible causal mechanisms grounded in the successive interactions of agents operating within computationally-rendered virtual worlds. A virtual world capable of generating an empirical regularity of interest provides a candidate explanation for this regularity.
A second primary objective is normative design:
How can ACE models be used as computational laboratories to facilitate the design of structures, institutions, and regulations resulting in desirable system performance over time? The ACE approach to normative design is akin to filling a bucket with water to determine if it leaks. A researcher constructs a virtual world that captures salient aspects of a system operating under a proposed design. The researcher identifies a range of initial agent state specifications of interest, including seed values for agent PRNG methods. For each such specification the researcher permits the virtual world to develop over time driven solely by agent interactions. Recorded outcomes are then used to evaluate design performance.
One key issue for ACE normative design is the extent to which resulting outcomes are efficient, fair, and orderly, despite possible attempts by strategic decision-making agents to game the design for personal advantage. A second key issue is a cautionary concern for adverse unintended consequences.
Optimal design might not always be a realistic goal, especially for large complex systems; but ACE models can facilitate robust design for increased system resiliency, a goal that is both feasible and highly desirable.
A third primary objective is qualitative insight and theory generation: How can ACE models be used to study the
potential behaviors of dynamic systems over time? Ideally, what is needed is a dynamic system's phase portrait, i.e., a representation of its potential state trajectories starting from all feasible initial states. Phase portraits reveal not only the possible existence of equilibria but also the basins of attraction for any such equilibria. Phase portraits thus help to clarify which regions of a system's state space are credibly reachable, hence of empirical interest, and which are not. An ACE modeling of a dynamic system can be used to conduct batched runs starting from multiple initial agent states, thus providing a rough approximation of the system's phase portrait.
A quintessential example of this line of research is an old but still unresolved concern of economists such as Adam Smith (1723-1790), Ludwig von Mises (1881-1973), John Maynard Keynes (1883-1946), Joseph Schumpeter (1883-1950), and Friedrich von Hayek (1899-1992): namely, what are the self-organizing capabilities of decentralized market economies?
A fourth primary objective is methodological advancement: How best to provide ACE researchers with the methods and tools they need to undertake theoretical studies of dynamic economic systems through systematic sensitivity studies, and to examine the compatibility of sensitivity-generated theories with real-world data? ACE researchers are exploring a variety of ways to address this objective ranging from careful consideration of methodological principles to the practical development of programming, visualization, and empirical validation tools.
ACE Website Management
Linked below are materials of possible interest to ACE researchers as well as to researchers who wish to explore the potential usefulness of agent-based modeling for social science purposes more generally. These materials are updated on a regular basis, and suggestions for additional materials to include are welcome.
As time permits, ACE news notes are posted both to the Social Simulation (SimSoc) mailing list and to the Society for Computational Economics (SCE) mailing list to let people know which ACE website pages have been most heavily updated since the last news notes posting. If you would like to subscribe to either of these mailing lists, please visit
Please contact me at
tesfatsi AT iastate.edu
if you have ACE-related news items that you would like included at the ACE website. To keep website maintenance manageable, only items of a more persistent nature (e.g., journal articles) can be considered for the ACE website. However, you can post items of a more temporary nature (e.g., conference announcements) at the SimSoc and SCE mailing lists.
Materials Linked to Date
"Economic Systems as Constructively Rational Games: Oh, the Places We Could Go!"
On-line guide for newcomers to agent-based modeling
in the social sciences,
with links to demonstration
software (R. Axelrod and L. Tesfatsion)
Annotated pointers to ACE introductory materials
"ACE: A Constructive Approach to Economic Theory"
ACE Handbook (L. Tesfatsion and K. L. Judd), Elsevier/North Holland, 2006