Agent-based computational economics (ACE) is roughly characterized as the computational study of economies modelled as evolving decentralized systems of autonomous interacting agents. ACE is thus a specialization to economics of the basic artificial life (alife) paradigm. Below is a brief overview of recent work in alife/ACE. A more extended version of this alife/ACE overview (in postscript format) is given in Tesfatsion (1997). Thanks to A. De Vany, J. Duffy, D. Fogel, J. Gray, R. Noll, B. Routledge, and especially N. Vriend for helpful comments.
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 automata. 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 tends to focus on continually evolving systems whose global behavior arises from the local interactions of distributed units; this is the sense in which alife research is said to be bottom up. Although the units comprising the systems might be bit strings, molecules, or robotic insects, the abstract description of how the unit interactions result in global behavior is clearly reminiscent of a Schumpeterian economy, only filtered through an unfamiliar terminology.
The study of evolutionary economies has of course been pursued by many researchers in addition to Joseph Schumpeter. 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, and Richard Nelson and Sidney Winter's work on an evolutionary theory of economic change. 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.
Economists have recently begun to apply the alife paradigm to the computational study of evolutionary economic processes. Exploiting the recent advent of object-oriented programming languages such as C++ and Java, these "agent-based computational economics" (ACE) researchers have been able to extend previous evolutionary economics work in several directions. 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 genetic (recombination and/or mutation) 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 ACE studies evolves a new population of agents from an existing population of agents using the following four steps: (1) Evaluation, in which a fitness score is assigned to each agent in the population; (2) Selection for Reproduction, in which a subset of the existing population of agents 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 agents in the population; and (4) Mutation, in which additional variations are introduced into the population by mutating the structural characteristics of each offspring with some small probability. See Goldberg (1989) and Mitchell and Forrest (1994).
The central problem for ACE researchers is to understand the apparently spontaneous appearance of regularity in economic processes, such as the unplanned coordination of trading activities in decentralized market economies that economists associate with Adam Smith's invisible hand. The challenge is to explain how these global regularities arise from the local interactions of autonomous agents channeled through actual or potential economic institutions rather than through fictitious coordinating mechanisms such as a single representative consumer or imposed equilibrium conditions. In line with this challenge, rationality is generally viewed as a testable hypothesis, or at least as a debatable methodological assumption, rather than as an unquestioned axiom of individual behavior.
Several studies that focus on key ACE-related issues have either appeared or are in the pipeline. See, for example, Anderson et al. (1988), Arifovic (1994), Arthur (1993), Arthur et al. (1997), Bell (1997), Birchenhall (1995), Bosch and Sunder (1996), Bullard and Duffy (1994), De Vany (1996), Durlauf (1996), Epstein and Axtell (1996), Holland and Miller (1991), Kirman (1993;1997), Lane (1993), Mailath et al. (1994), Marimon et al. (1990), Marks (1992), McFadzean and Tesfatsion (1996), Miller (1989), Routledge (1994), Sargent (1993), Tesfatsion (1995;1998a,b), and Vriend (1995).
To illustrate more concretely 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; Ashlock et al., 1996; Smucker et al., 1994]. Section 3 discusses how a modified version of this framework is being used to study the endogenous formation and evolution of trade networks [Tesfatsion (1995;1998a,b); McFadzean and Tesfatsion (1996)]. Concluding comments are given in the final section.
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. [Bibliographic Note: Other game theory studies that have allowed players to avoid unwanted interactions, or more generally to affect the probability of interaction with other players through their own actions, include Fogel (1995), Guriev and Shakhova (1996), Hirshleifer and Rasmusen (1989), Kitcher (1993), Mailath et al. (1994), and Orbell and Dawes (1993). See Stanley et al. (1994, Section 2) and Ashlock et al. (1996, Section 1) for more detailed discussions of related game theory work. There is also a growing body of work on multi-agent systems with endogenous interactions in which the decision (or state) of an agent depends on the decision (or state) of certain neighboring agents, where these neighbors may change over time. See, for example, Brock and Durlauf (1995), De Vany (1996), Ionnides (1997), and Young (1993).]
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 (1996), 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.
More precisely, the dynamic structure of the TNG consists of a hierarchy of cycle loops, 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 environmental cycle during which the fitness score of each trader is calculated as the total sum of his payoffs divided by the total number of his payoffs and the current trader generation is sorted by fitness scores. At the end of the environmental cycle, a generation cycle 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 instantiated 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); and they can 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 three different levels: individual trade behavior; trade network formation; and social welfare. For example, in Tesfatsion (1995) the subtle interplay between game play and the choice and refusal of 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 (1998a,b), TNG computer experiments are reported which show how ex ante market structure is systematically correlated with trade network formation, trade behavior, and social welfare outcomes. These findings indicate that the optimality criteria conventionally used to assess the performance of matching mechanisms in static market contexts, such as Pareto efficiency and core stability, are highly incomplete indicators of performance from an evolutionary perspective.
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.