Real-world economies exhibit five essential properties.
First, real-world economies consist of heterogeneous interacting entities encapsulating distinct states (data, attributes, methods). Second, real-world economies are open-ended dynamic systems whose dynamics are driven by the successive interactions of their participant entities. Third, human decision-makers participating in real-world economies are strategic entities whose decision processes take into account remembered past actions and envisioned future actions of other entities. Fourth, all entities participating in real-world economies are locally constructive, i.e., constrained to act on the basis of their own states. Fifth, real-world economies are reflexive; the actions of a participant entity can affect its own state as well as the states of other participant entities.
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 researchers to
study economic systems from this point of view.
Roughly defined, ACE is the computational modeling of economic processes (including whole economies) as open-ended dynamic systems of interacting agents. The stress on open-ended dynamics fundamentally distinguishes ACE from all other currently mainstream economic modeling approaches.
More precisely, the ACE modeling approach is characterized by the seven modeling principles listed below. These principles reflect the primary goal of many agent-based modelers: namely, to be able to study real-world dynamic systems as historically unfolding sequences of events.
(MP1)Agent Definition: An agent is a software entity within a computationally constructed world capable of
acting 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 instant is determined as a function of the agent's own state at that instant.
(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 computationally constructed world at any given instant is determined by the ensemble of agent states at that instant.
(MP6)System Historicity: Given initial agent states, all subsequent events in the computationally constructed world are determined solely by agent interactions.
(MP7)Modeler as Culture-Dish Experimenter: The role of the modeler of the computationally constructed world is limited to the setting of initial agent states and to the non-perturbational observation, analysis, and reporting of world 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 resulting dynamic outcomes.
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 unfolds forward as a virtual world whose dynamics are entirely driven by the interactions of its constituent parts.
From a mathematical point of view, modeling principles
(MP1)--(MP7) imply that ACE models are state-space models in initial value form. More precisely, an ACE model specifies how an ensemble of agent states dynamically evolves, starting from an initially given ensemble of agent states. However, these modeling principles further require an ACE model to exhibit essential real-world characteristics: namely, agent local constructivity, agent autonomy, system constructivity, and system historicity.
Modern economic theory also relies heavily on state-space models. However, these models typically incorporate modeler-imposed rationality, optimality, and equilibrium conditions that could not (or would not) be met by locally constructive agents interacting within an historical process.
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 fixed-point problem that requires the simultaneous consideration of all modeled time periods without regard for local constructivity and historical process constraints.
A Mathematics for the Real World?
Scientists seeks to understand how real-world systems work.
Models devised for scientific purposes must always simplify reality. However, ideally, scientists should be permitted to tailor these simplifications to purposes at hand.
Scientists should not be forced to distort reality in specific predetermined ways in order to apply a modeling approach.
A key goal motivating the development of modeling principles (MP1)-(MP7) was to adhere to this modeling precept for the study of real-world economic systems. An interesting question is the extent to which modeling principles (MP1)-(MP7) achieve this goal for real-world systems in general, not simply for real-world economic systems.
Any model adhering to (MP1)-(MP7) is an open-ended dynamic system of interacting agents representing physical, biological, and/or social entities, each characterized by its own state (data, attributes, methods). The interactions of these agents drive the dynamics of the system, starting from modeler-configured initial conditions. As a result of agent interactions:
each agent experiences "time" locally, as an unfolding
sequence of events;
the dimension and content of agent states
agents can subsume other agents as components;
agents can break apart into smaller component agents;
new agents can be created; and
existing agents can be destroyed.
This modeling flexibility permits the representation of a universe capable of supporting the evolution of perceptive self-conscious life.
Examples of state-changes for real-world agents include:
changes in physical attributes;
changes in sensed surroundings;
belief changes; and belief-induced
changes in action rules.
Examples of real-world agent subsumption include:
the formation of molecules through atomic bonding;
the parasitism of one organism by another;
the transition from prokaryotic to eukaryotic forms of organisms; the hiring of employees by corporate firms;
the acquisition of new members by existing organizations;
and organization mergers.
Examples of real-world agent creation and destruction include: volcanic eruptions; natural birth and death; the invention and obsolescence of products; and the establishment and disbanding of organizations. Creation and destruction events for populations of agents can be computationally modeled by means of evolutionary algorithms taking various forms.
Note, in particular, that models adhering to (MP1)-(MP7) permit the study of real-world systems that evolve from modeler-configured initial conditions with:
no fixed "space" apart from persistent spatial
agents (if any) that a modeler initially configures;
no fixed "time process" apart from persistent
event-scheduler agents (if any) that a modeler
initially configures; and
no fixed rules apart from persistent agent methods
(if any) that a modeler initially configures.
The ability to model real-world systems without having to presuppose a fixed externally given "space" or "time process" permits the study of open perplexing questions in physics regarding the existence (or not) of these concepts as fundamental aspects of the physical universe.
Persistent agent methods that a researcher might want to initially configure for a modeled real-world system include methods that support self-organization and natural selection processes. These types of processes appear to be a basic driver of real-world agent interactions at all levels of agent encapsulation that humans can currently perceive. An interesting question is whether they also drive agent interactions at levels beyond current human perception, such as at a quantum level.
One Key Misconception About ACE: Agent Rationality
For ACE researchers, as for economists in general, the modeling of decision-makers 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
this macroeconomic study,
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.
See, in particular, the following learning tutorial available at this site:
Learning Algorithms: Illustrative Examples.
Learning methods covered in this tutorial include:
reactive reinforcement learning (e.g. Roth-Erev RL);
belief-based learning (e.g., fictitious play, Camerer/Ho's EWA algorithm);
anticipatory learning (e.g., Q-learning, adaptive dynamic programmming);
evolutionary learning (e.g., genetic algorithms, genetic programming);
and connectionist learning (e.g., associative memory learning, deep learning by means of artificial neural networks with multiple hidden layers).
Second Key Misconception About ACE: Agent Stochasticity
A second common misconception is the incorrect belief that the ACE modeling principles (MP1)--(MP7) rule out any consideration of stochasticity.
To the contrary, stochastic aspects can easily be represented within ACE models.
Agent data can include realizations for real-world random events, agent attributes can include beliefs based on probabilistic assessments, and agent methods can include
pseudo-random number generators (PRNGs).
A PRNG is a deterministic algorithm, initialized by a seed value, that is able to generate number sequences whose properties mimic the properties of random number sequences.
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.
An important additional point here is ACE agents are
encapsulated bundles of data, attributes, and methods.
These local agent aspects can be partially or completely hidden from other agents. Thus, agents can be unpredictable to one another even if they make no use of real-world random event realizations, probabilistic assessments, or PRNGs.
Another important point is that ACE models are required 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 the agents (i.e., the individuals, social groupings, institutions, biological entities, and/or physical entities) that actually reside within these worlds. This requirement encourages ACE modelers to think carefully about the intended empirical referents for any included stochastic shock terms.
ACE Research Objectives
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? 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 modeled 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 future behavior of dynamic systems? 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 method/tool 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.
Materials Linked to Date
Robert Axelrod and Leigh Tesfatsion (2021), "On-Line Guide for Newcomers to Agent-Based Modeling in the Social Sciences,
with Links to Demonstration Software"
Leigh Tesfatsion (2021), "Agent-Based Computational Economics: Overview and Brief History"
Working Paper No. 21004, Economics Working Paper Series, Iowa State University, Ames, IA, 2021.
Leigh Tesfatsion (2016), "Modeling Economic Systems as Locally-Constructive Sequential Games: The Places We Could Go!," Keynote Address, Duke Forest Conference, Durham, NC
Annotated pointers to ACE introductory materials
Leigh Tesfatsion (2017), Modeling Economic Systems as Locally-Constructive Sequential Games
Journal of Economic Methodology 24(4), 384-409.
Leigh Tesfatsion (2021), Elements of Dynamic Economic Modeling
Presentation and Evaluation Guidelines for Agent-Based Models
Empirical Validation and Verification of Agent-Based Models
Teaching and Self-Study Resources
Illustrative ACE Creative Modeling Exercise: Thomas Piketty (and His Critics) on Wealth Inequality