Abstract
Innovation breeds new products, new processes and new organisational forms. In other words, it breeds changes to the status quo. Yet innovative change is not the sole province of the creative individual. More often than not, fundamental changes to a society or economy result from the collective behaviour of groups of interacting agents. When tacit knowledge is shared, agents can behave in a myriad of different ways. How does this heterogeneous microworld of individual behaviours generate the global macroscopic regularities of society? Much of the creative capacity of such tacit collectives is hidden within a virtual system of accumulated interactions. If we choose to isolate the agents, then these virtual parts disappear. If we choose to aggregate the agents, then the virtual parts disappear. It’s the virtual parts of an interactive society that we must discover.
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Endnotes
This contribution reviews some of the agent-based approaches discussed in Batten (2000) on a selective basis.
Krugman suggests that the first chapter of Schelling’s (1978) book is ‘surely the best essay on what economic analysis is about, on the nature of economic reasoning, that has ever been written’. (Krugman 1996a, p.16). The two chapters on ‘sorting and mixing’ provide an excellent, non-mathematical introduction to the idea of self-organisation in cities.
An equivalent way of stating this rule is that each individual is satisfied as long as at least three-eighths of his or her neighbours are of his or her class.
Because of the limited computational power available a generation ago, Schelling discovered pockets of segregation by moving coins around on top of a table decorated with suitable grid paper. As he notes: ‘Some vivid dynamics can be generated by any reader with a half hour to spare, a roll of pennies, a roll of dimes, a tabletop, a large sheet of paper and a spirit of scientific enquiry or, lacking that spirit, a fondness for games.’ (see Schelling 1978, p. 147).
This layout is one of a number of possibilities, since the order in which individuals move remains unspecified. The final outcome will also be sensitive to the initial conditions (as depicted in Fig. 15.1). As Schelling noted; repeating the experiment several times will produce slightly different configurations, but an emergent pattern of segregation will be obvious each time.
The notion of phase transitions has its roots in the physical sciences, but it’s relevance to economic evolution has been recognised recently. In the social sciences, phase transitions are difficult to grasp because the qualitative changes are hard to see. Far more transparent is the effect of temperature changes on water. As a liquid, water is a state of matter in which the molecules move in all directions, mostly without recognising each other. When we lower its temperature below freezing point, however, it changes to a crystal lattice — a new solid phase of matter. Suddenly, its properties are no longer identical in all directions. The translational symmetry characterising the liquid has been broken. This type of change is known as an equilibrium phase transition. Recent advances in systems theory, especially studies led by Hermann Haken on the one hand, and Ilya Prigogine and the Brussels School of Thermodynamacists on the other, have discovered a new class of phase transitions — one in which the lowering of temperature is replaced by the progressively intensifying application of non-equilibrium constraints. It’s non-equilibrium phase transitions that are associated with synergetics and processes of self-organisation. See, for example, Haken (1978) or Nicolis and Prigogine (1977, 1989).
Although John von Neumann and Stanislaw Ulam were the first to introduce the CA concept about fifty years ago, it’s pretty safe to say that John Conway popularised the concept through his invention of the game of ‘Life’. In Life, cells come alive [i.e. ‘turn on’], stay alive [i.e. ‘stay on’] or die [i.e. ‘turn off], depending on the states of neighbouring cells. Although Life is the best known CA, it’s perhaps the least applicable to real configurations.
In their introduction to a special issue of the journal Environment and Planning B devoted to urban systems as CA, Batty, Couclelis and Eichen (1997) make this suggestion. The reader is directed to this issue for an overview of ways in which urban dynamics can be simulated through CA.
Readable summaries of this metaphoric world of artificial life can be found in Casti (1997, chapter 4) and Ward (1999, chapter 2).
As Cohen and Stewart (1994, p. 169) have noted, ‘You can dissect axles and gears out of a car but you will never dissect out a tiny piece of motion’.
The Sante Fe Artificial Stock Market has existed in various forms since 1989. Like most artificial markets, it can be modified, tested and studied in a variety of ways. For glimpses into this new silicon world, and its methods of mimicking the marketplace and its gyrations, see Arthur (1995) or Arthur et al. (1997).
‘New’ expectational models are mostly recombinations of existing hypotheses that work better.
In a series of interesting studies — typified by De Long et al. (1990) or Farmer (1993) — it has been shown analytically that expectations can be self-fulfilling. Thus we may conclude that positive feedback loops, or Pigovian herd effects, do have a significant role in shaping the market’s co-evolutionary patterns.
In proposing his general theory of reflexivity, George Soros suggested that ‘since farfrom-equilibrium conditions arise only intermittently, economic theory is only intermittently false...’ There are long fallow periods when the movements in financial markets do not seem to follow a reflexive tune but rather resemble the random walks mandated by the efficient market theory;’ (see Soros 1994, p. 9).
GARCH = Generalized AutoRegressive Conditional Hederoscedastic behaviour.
Peter Allen has pointed out that an adaptive trading strategy is one that can give good results despite the fact that we cannot know the future, because there are different possible futures. When discernable trends become apparent, the strategy must be able to react to this. By taking such actions, however, the strategy will change what subsequently occurs in reality. This co-evolutionary behaviour implies that markets will always drive themselves to the ‘edge of predictability;’ in other words, to the edge of chaos.
For a precise definition of an adaptive linear network, see Holland (1988).
See Arthur (1995, p. 25).
Such a set of simulation experiments can be found in de la Maza and Yuret (1995).
Massively parallel ‘architecture’ means that living systems consist of many millions of parts, each one of which has its own behavioural repertoire.
See Epstein and Axtell (1996, p. 158).
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Batten, D.F. (2001). Agents, Interactions, and Co-Evolutionary Learning. In: Fischer, M.M., Fröhlich, J. (eds) Knowledge, Complexity and Innovation Systems. Advances in Spatial Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04546-6_15
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