Agent-based computational economics (ACE) is the computational study of economic processes modeled as dynamic systems of interacting agents. ACE is thus a specialization to economics of the basic artificial life (alife) paradigm. Below is a brief introduction to alife and ACE. A more extended version of this introduction is given in Tesfatsion (1997a), available online in postscript format (220KB) or pdf format (560KB). Thanks to A. De Vany, J. Duffy, D. Fogel, J. Gray, R. Noll, B. Routledge, and especially N. Vriend for helpful comments.
What is artificial life, or alife for short? And why should economists care?
As detailed in the entertaining monographs by Levy (1992) and Sigmund (1993), the roots of alife go at least as far back as the work of John von Neumann in the nineteen forties on self-replicating machines. The establishment of alife as a distinct field of inquiry, however, must be traced to the first alife conference, organized in 1987 by Chris Langton at the Los Alamos National Laboratory; see Langton (1989).
Alife is the bottom-up study of basic phenomena commonly associated with living organisms, such as self-replication, evolution, adaptation, self-organization, parasitism, competition, cooperation, and social network formation. Alife complements the traditional biological and social sciences concerned with the analytical, laboratory, and field study of living organisms by attempting to simulate or synthesize life-like behavior within computers, robots, and other man-made media. One goal is to enhance the understanding of actual and potential life processes. A second goal is to use nature as an inspiration for the development of solution algorithms for difficult optimization problems characterized by high-dimensional search domains, nonlinearities, and multiple local optima.
The systems studied by alife researchers are complex adaptive systems sharing many of the following characteristics [Holland, 1992]. Most importantly, each such system typically consists of many dispersed units acting in parallel with no global controller responsible for the behavior of all units. Rather, the actions of each unit depend upon the states and actions of a limited number of other units, and the overall direction of the system is determined by competition and coordination among the units subject to structural constraints. The complexity of the system thus tends to arise more from the interactions among the units than from any complexity inherent in the individual units per se. Moreover, the local interaction networks connecting individual units are continuously recombined and revised. In particular, niches that can be exploited by particular adaptations are continuously created, and their exploitation in turn leads to new niche creations, so that perpetual novelty exists.
Briefly put, then, alife research focuses on continually evolving systems whose global behavior arises from the local interactions of distributed co-evolving units. This is the sense in which alife research is said to be "bottom up."
The study of economies as evolving systems has been pursued by many previous researchers. For example, one has Armen Alchian's work on uncertainty and evolution in economic systems, the work of W. Brian Arthur on economies incorporating positive feedbacks, the work by Richard Day on dynamic economies characterized by complex phase transitions, the work by John Foster on an evolutionary approach to macroeconomics, Ron Heiner's work on the origins of predictable behavior, Jack Hirshleifer's work on evolutionary models in economics and law, Richard Nelson and Sidney Winter's work on an evolutionary theory of economic change, and Ulrich Witt's work on economic natural selection. These and numerous other related studies are reviewed by Witt (1993) and Nelson (1995). In addition, as detailed in Friedman (1991), a number of researchers have recently been focusing on the potential economic applicability of evolutionary game theory in which game strategies distributed over a fixed number of strategy types reproduce over time in direct proportion to their relative fitness.
Agent-based computational economics (ACE) is the computational study of economic processes modeled as dynamic systems of interacting agents. Thus, ACE is a specialization to economics of the basic alife paradigm. Exploiting the recent advent of powerful computational tools, most notably object-oriented programming languages such as C++ and Java, ACE researchers have been able to extend previous evolutionary economics work in several directions. [See Bibliographic Note 1 for citations to various ACE-related studies.]
First, much greater attention is generally focused on the endogenous determination of agent interactions. Second, a broader range of interactions is typically considered, with cooperative and predatory associations increasingly taking center stage along with price and quantity relationships. Third, agent actions and interactions are represented with a greater degree of abstraction, permitting generalizations across specific system applications. Fourth, the evolutionary process is generally expressed algorithmically in terms of operations acting directly on agent characteristics. These evolutionary selection pressures result in the continual creation of new modes of behavior and an ever-changing network of agent interactions.
For example, the basic genetic algorithm used in many early ACE studies evolves a new population of agent behavioral rules from an existing population of agent behavioral rules using the following four steps: (1) Evaluation, in which a fitness score is assigned to each rule in the population; (2) Selection for Reproduction, in which a subset of the existing population of rules is selected for reproduction, with selection biased in favor of fitness; (3) Recombination, in which "offspring" (new ideas) are generated by combining the genetic material (structural characteristics) of pairs of "parents" chosen from among the most fit rules in the population; and (4) Mutation, in which additional variations are introduced into the population of rules by mutating the structural characteristics of each offspring with some small probability. See Goldberg (1989) and Mitchell and Forrest (1994) for a general discussion of genetic algorithm design and use and Sargent (1993) for a discussion of the possible uses of genetic algorithms within economics. As detailed in Tesfatsion (2002a), ACE researchers are now also exploring many alternative ways to represent evolutionary economic processes.
One principal concern of ACE researchers is to understand why certain global regularities have been observed to evolve and persist in decentralized market economies despite the absence of top-down planning and control: for example, trade networks, socially accepted monies, and market protocols. The challenge is to demonstrate constructively how these global regularities might arise from the bottom up, through the repeated local interactions of autonomous agents acting in their own self-interest. Another principal concern is to use ACE frameworks normatively, as computational laboratories within which alternative socioeconomic structures can be studied and tested with regard to their effects on individual behavior and social welfare. This normative concern complements a descriptive concern with actually observed global regularities by seeking deeper possible explanations not only for why certain global regularities have been observed to evolve but also why others have not.
To illustrate the potential usefulness of the ACE approach, as well as the hurdles that remain to be cleared, the following two sections briefly outline some ongoing ACE work that appears to be particularly relevant for the modelling of decentralized market economies. Section 2 describes recent attempts to combine evolutionary game theory with preferential partner selection [Stanley et al. (1994); Smucker et al. (1994); Ashlock et al. (1996); Hauk (2001)]. Section 3 discusses how a modified version of this framework is being used to study the endogenous formation and evolution of trade networks [Tesfatsion (1997b;1998;2001;2002b); McFadzean and Tesfatsion (1997,1999), McFadzean et al. (2001)]. Concluding comments are given in the final section.
Following the seminal work of Axelrod (1984, 1987, 1997), the iterated prisoner's dilemma (IPD) game has been extensively used by economists and other researchers to explore the potential emergence of mutually cooperative behavior among non-altruistic agents. As detailed in Kirman (1997) and Lindgren and Nordahl (1994), these studies have typically assumed that individual players have no control over whom they play. Rather, game partners are generally determined by an extraneous matching mechanism such as a roulette wheel, a neighborhood grid, or a round-robin tournament . The general conclusion reached by these studies has been that mutually cooperative behavior tends to emerge if the number of game iterations is either unknown or infinite, the frequency of mutually cooperative play in initial game iterations is sufficiently large, and the perceived probability of future interactions with any given current partner is sufficiently high.
In actuality, however, socio-economic interactions are often characterized by the preferential choice and refusal of partners. The question then arises whether the emergence and long-run viability of cooperative behavior in the IPD game would be enhanced if players were more realistically allowed to choose and refuse their potential game partners.
This question is taken up in Stanley et al. (1994). The traditional IPD game is extended to an IPD/CR game in which players choose and refuse partners on the basis of continually updated expected payoffs. [For related work on endogenous partner selection, see Bibliographic Note 2.]
The introduction of partner choice and refusal fundamentally modifies the ways in which players interact in the IPD game and the characteristics that result in high payoff scores. Choice allows players to increase their chances of encountering other cooperative players, refusal gives players a way to protect themselves from defections without having to defect themselves, and ostracism of defectors occurs endogenously as an increasing number of players individually refuse the defectors' game offers. On the other hand, choice and refusal also permit opportunistic players to home in quickly on exploitable players and form parasitic relationships.
The analytical and simulation findings reported for the IPD/CR game in Stanley et al. (1994), and in the subsequent studies by Smucker et al. (1994), Ashlock et al. (1996), and Hauk (2001), indicate that the overall emergence of cooperation is accelerated in evolutionary IPD games by the introduction of choice and refusal. Nevertheless, the underlying player interaction patterns induced by choice and refusal can be complex and time varying, even when expressed play behavior is largely cooperative. Consequently, it has proven to be extremely difficult to get an analytical handle on the mapping from parameter configurations to evolutionary IPD/CR outcomes.
A reasonable next step, then, is to focus on more concrete problem settings which impose natural constraints on the range of feasible player interactions. In the next section it is explained how a modified version of the IPD/CR game is being used to examine the endogenous formation and evolution of trade networks among resource-constrained traders. [See Bibliographic Note 3 for other work focusing on the endogenous formation of socioeconomic networks.]
The Trade Network Game (TNG) developed in Tesfatsion (1997b) consists of successive generations of resource-constrained traders who choose and refuse trade partners on the basis of continually updated expected payoffs, engage in risky trades modelled as two person games, and evolve their trade strategies over time. A C++ implementation for the TNG has been developed by McFadzean and Tesfatsion (1997,1999) and made available as freeware. This implementation is supported by a general class framework for evolutionary simulations, SimBioSys, developed by McFadzean (1995), also available as freeware. TNG/SimBioSys has been incorporated into a computational laboratory developed by McFadzean, Stewart, and Tesfatsion (2001). This computational laboratory, referred to as the TNG Lab, permits the visualization of trade network evolution through real-time network animations as well as real-time chart and data table displays. [See Bibliographic Note 4 for information about the online availability of an automatic installation program for the TNG Lab as well as pointers to TNG research articles, TNG/SimBioSys source code, and other ACE-related software.]
The dynamic structure of the TNG consists of sequence of generations, as follows. Each trader in the initial trader generation has a random trade strategy and assigns a prior expected payoff to each of his potential trade partners. The traders then engage in a trade cycle loop consisting of a fixed number of trade cycles. In each trade cycle the traders undertake three activities: the determination of trade partners, given current expected payoffs; the carrying out of potentially risky trades; and the updating of expected payoffs based on any new payoffs received during trade partner determination and trading. At the end of the trade cycle loop the traders enter into an environment step during which the fitness score of each trader is calculated as a function of the payoffs he has attained to date and the current trader generation is sorted by fitness scores. At the end of the environment step an evolution step commences during which evolutionary selection pressures are applied to the current trader generation to obtain a new trader generation with evolved trade strategies. This new trader generation then enters into a new trade cycle loop, and the process repeats.
The TNG facilitates the general study of trade from a bottom up perspective in two key ways. First, the TNG traders are implemented as autonomous endogenously-interacting software agents (tradebots) with internal behavioral functions and with internally stored information that includes addresses for other tradebots. The tradebots can therefore display anticipatory behavior (expectation formation). They can also communicate with each other at event-triggered times, a feature not present in standard economic models. Second, the modular design of the TNG permits experimentation with alternative specifications for market structure, trade partner matching, trading, expectation formation, and trade behavior evolution. All of these specifications can potentially be grounded in tradebot-initiated actions.
The TNG is currently being used to study the evolutionary implications of alternative market structures at four different levels: individual agent characteristics; network formations; expressed agent behaviors; and individual and social welfare outcomes. For example, in Tesfatsion (1997b) the subtle interplay between game play and the choice and refusal of game partners in the TNG is illustrated by means of an analytically solved 5-tradebot TNG for which the parameter space is shown to partition into economically interpretable regions corresponding to distinct trade network formations. In Tesfatsion (1998,2001,2002b) and Pingle and Tesfatsion (2003), TNG computer experiments are undertaken for an ACE labor market framework to investigate the relationship between market structure and worker-employer network formation, and between network formation and the worksite behaviors, welfare outcomes, market power outcomes, and persistent "excess earnings heterogeneity" that these network formations support.
The hallmark of the ACE approach to the study of economic processes is a bottom up perspective, in the sense that global behavior is grounded in local agent interactions. The agent-based trade network game (TNG) briefly outlined in the previous section illustrates how the ACE approach might be specialized to the study of the formation and evolution of trade networks.
As currently implemented, however, the TNG only partially achieves the goal of a bottom up perspective. The TNG tradebots are surely more autonomous than agents in traditional economic models. For example, in order to determine their trade partners, the tradebots send messages back and forth to each other at event-triggered times. Nevertheless, they are still controlled by a main program that synchronizes the commencement of their trading activities and the evolution of their trade behavior. The advantage of imposing this synchronized dynamic structure is that it permits some analytical results to be obtained concerning the configuration, stability, uniqueness, and social optimality of the trade networks that emerge. The disadvantage is that these networks may not be robust to realistic relaxations of the imposed synchronizations.
As the TNG illustrates, then, the challenges to economists posed by the ACE approach are great and the payoffs are yet to be fully determined. Using the ACE approach, however, economists can at last begin to test seriously the self-organizing capabilities of decentralized market economies.