John Kemp (1999)
Journal of Artificial Societies and Social Simulation vol. 2, no. 3, <https://www.jasss.org/2/3/1.html>
To cite articles published in the Journal of Artificial Societies and Social Simulation, please reference the above information and include paragraph numbers if necessary
Received: 13-Jul-99 Accepted: 15-Jul-99 Published: 31-Oct-99
|Figure 1: A linear model|
With j = k = 0, Na and Nb play no part in decisions. It is obvious that J agents will always adopt A and that K agents will adopt B irrespective of Na and Nb (since aj > bj and ak < bk ) . The adoption process is such that, the difference between the numbers of adoptions (d = Na - Nb) is a simple random walk, with the shares Na / (Na +Nb) and Nb / (Na + Nb) both tending to 1/2. The adoption profile is entirely dependent upon the random entry of the two types of agents, but the long run shares are predictable. The process is ergodic (i.e. it is not path dependent) since the pattern of previous adoptions has no influence upon future adoptions. Re-running the simulation will always generate a different adoption profile, but it will be one that conforms to these same general characteristics. Thus, different simulations will be qualitatively similar.
With negative j and k, an increase in the number of adoptions of a given technology will cause the returns to diminish, and at some stage fall below the level of returns available from the alternative technology. When this occurs, agents will switch their choice of technology. As the alternative technology becomes increasingly adopted, so its returns will likewise fall and ultimately provoke re-switching. The process is now a simple random walk with reflecting barriers. Again the process is predictable and ergodic. The long run shares of A and B again tend to 1/2. The adoption profile is confined between the reflecting barriers (bj - aj)/j and (bk - ak)/k, with d the difference in adoptions never able to exceed or fall below these bounds.
With positive j and k there is a distinct and qualitative change in the dynamics of the adoption process. The process is illustrated in the computer simulation of figure 2 where the vertical axis represents the difference between the numbers of adoptions (d = Na - Nb) and the horizontal axis the total number of adoptions (N = Na + Nb). For the purposes of this simulation, the values of the parameters were set at: aj = 5 , bj =4, j = 0.1 ak =4, bk = 5, k = 0.1. Thus, with positive j and k, as the adoptions of a given technology increase, that technology becomes inexorably more attractive. If one technology, for example A, through chance happens to get sufficiently far in front, then that technology will become more attractive not only to J agents, but also to K agents despite their predisposition to select B. Thus J agents continue to select A, whereas K agents permanently switch from B to A. No further selections of B are made and the process becomes locked-in to technology A.
|Figure 2: Increasing Returns 0 < j = k|
Under increasing returns the process is a random walk with absorbing barriers given by (bj - aj)/j and (bk - ak)/k. When a technology receives sufficient adoptions so that the difference in the number of adoptions reaches an absorbing barrier, thereafter that technology is always adopted. The alternative technology becomes extinct. The final outcome is now unpredictable and non-ergodic. It is predictable that one or other of the technologies will ultimately dominate with a share of 100%, but which one that should be is completely unpredictable. Neither can it be known how many adoptions have to be made before lock-in occurs. All is dependent upon the path of previous adoptions, and that is due purely to the random, and unknowable, order in which J and K agents enter. An important implication is that the dominant technology need not necessarily be the one that would have been most efficient in the long run, given equal rates of adoption (e.g. VHS and QWERTY). Thus, in the presence of increasing returns, selection mechanisms are claimed to be inefficient. Adopted technologies are dependent upon the accidents of history, the counterfactual is of relevance, and so it becomes legitimate to ask the question "what if ?" since the situation that exists is one that need not, and in other circumstances might not have been.
|Figure 3: A general model|
UjA = aj + j.sin(Na)
UjB = bj + j.sin(Nb)
UkA = ak + k.sin(Na)
UkB = bk + k.sin(Nb)
Consider the selection process. If, |j| < (aj-bj)/2 and |k| < (bk-ak)/2, then it will always be the case that UjA > UjB and UkA < UkB . Thus, J agents will always choose A, and K agents will always choose B. This gives a selection profile similar to the case of constant returns discussed in the previous section. It is the familiar simple random walk, dependent solely upon the entry order of J and K agents. As we saw in the previous section, the process is ergodic with predictable shares tending to 1/2.
|Figure 4: Utility functions of type J consumers|
|Figure 5 (i) to (iii): Simulations Displaying Cycling|
|Figure 6: Simulations (i) to (xvii)|
|Figure 7(i) and (ii): Asymmetry|
2 Economists in particular might object to the absence of relative prices in this model. However, in many substitute and/or fashion goods there is no reason to suppose different costs of production. For example, the costs of producing different styles of trouser are unlikely to differ. Under perfect competition with constant returns to scale, this implies constant and identical prices. Clearly relative prices and incomes must form important determinants of demand, but we abstract from them here in order to isolate other issues.
3 It should be noted that the variety displayed within figures 5 and 6 has NOT been contrived by making a small selection from a large number of simulations. The variety is inherent, for only three or four simulations have been discarded from the total performed.
4 However, see Benhabib and Day (1981) for an approach that produces deterministic endogenous fluctuations which are chaotic and shown to arise because of the presence of some cyclicity in preferences.
5 For example, Pashigian, Bowen and Gould (1995) claim that reductions in style changes by automobile manufactures have led to a decrease in the amplitude of the seasonal fluctuation in automobile prices.
6 As already pointed out in Paragraph 3.6, the particular utility function adopted is not meant to be realistic nor to encapsulate consumers' attitudes to any particular commodity, and it is not suggested that it is, even theoretically, applicable to all commodities. To discover the true utility function for a commodity is clearly impossible. All that is being said is that, if preferences are not linear and do not monotonically vary with consumption, then unpredictable and apparently spontaneous change is possible. Any other of, or a composite of, the circular functions could equally serve to illustrate this proposition.
ARTHUR, W. B. (1988) Competing Technologies: An Overview, in Dosi, G., Freeman, C., Nelson, R., Silverberg, G. and Soete, L. eds. (1988) Technical Change and Economic Theory, London, Pinter.
ARTHUR, W. B. (1989) Competing Technologies, Increasing Returns, and Lock-in by Historical Events, Economic Journal, Vol. 99, pp. 116-131, reprinted in Arthur (1994a).
ARTHUR, W. B. (1990) Positive Feedbacks in the Economy, Scientific American February, pp. 92-99.
ARTHUR, W. B. (1994a) Increasing Returns and Path Dependence in the Economy, Ann Arbor, University of Michigan Press.
ARTHUR, W. B. (1994b) Inductive Reasoning and Bounded Rationality, American Economic Association, Papers and Proceedings, Vol.84, pp.406-411.
ARTHUR, W. B. , Durlauf, S. N. and Lane, D. A. eds. (1997) The Economy as an Evolving Complex System II, Proc. Vol. V, Santa Fe Institute Studies in the Sciences of Complexity, Redwood City, CA: Addison-Wesley.
BANDURA, A. (1986) Social Foundations of Thought and Social Action: A Social Cognitive Theory, Englewood Cliffs, N.J., Prentice Hall.
BENHABIB, J. and Day, R. H. (1981) Rational Choice and Erratic Behaviour, Review of Economic Studies, Vol. XLVIII, pp.459-471.
BIKHCHANDANI, S., Hirshleifer, D. and Welch, I. (1992) A Theory of Fads, Fashion, Custom and Cultural Change as Informational Cascades, Journal of Political Economy, Vol. 100, pp.992-1026.
COWAN, R. (1990a), Nuclear Power Reactors: A Study in Technological Lock-in, Journal of Economic History, Vol.L No.3 Sept., pp.541-567.
COWAN, R. (1990b) Tortoises and Hares: Choice Among Technologies of Unknown Merit, Economic Journal, 101 July, pp.801-14.
COWAN, R. and Gunby, P. (1996) Sprayed to Death: Path Dependence, Lock-in and Pest Control Strategies, Economic Journal, Vol. 106, pp.521-542.
DAVID, P. A. (1975) Clio and the Economics of QWERTY, American Economic Review, Papers and Proceedings, Vol. 75, pp. 332-7.
DAVID, P. A. and Bunn, J. A. (1988) The Economics of Gateway Technologies and Network Externalities, , Information Economics and Policy, 3, pp.165-202.
DEBREU, G. (1959) Theory of Value: An Axiomatic Analysis of Economic Equilibrium, New Haven, Yale University Press.
FESTINGER, L. (1954) A Theory of Social Comparison Processes, Human Relations, Vol. 7, pp. 117-140.
FREEMAN, C and Soete, L (1997) The Economics of Industrial Innovation, 3rd. edn., London, Pinter.
GALBRAITH, J. K. (1952) American Capitalism, Boston, Houghton Mifflin.
GALBRAITH, J. K. (1967) The New Industrial State, London, Hamish Hamilton.
GOULD, S. J. (1992) Bully for Brontosaurus, London, Penguin.
GRANOVETTER, M. and Soong, R. (1986) Threshold Models of Interpersonal Effects in Consumer Demand, Journal of Economic Behaviour and Organization, 7, pp. 83-99.
GRAVELLE, H and Rees, R. (1992) Microeconomics, 2nd. Edn., London, Longmans.
HARGREAVES HEAP , S. Hollis, M. Lyons, B. Sugden, R and Weale, A (1992) The Theory of Rational Choice A Critical Guide, Oxford, Blackwell.
HODGSON, G. M, (1993) Economics and Evolution Bringing Life back into Economics, Cambridge, Polity Press
JANSSEN, M and Jager, W. (1999) An Integrated Approach to Simulating Behavioural Processes: A Case Study in Lock-in of Consumption Patterns, Journal of Artificial Societies and Social Simulation, Vol. 2, No. 2.
KEMP, J. (1997) New Methods and Understanding in Economic Dynamics? An Introductory Guide to Chaos and Economics, Economic Issues, Vol. 2 part 1, pp.1-26.
KEMP, J. and Wilson, T. (1999) Monetary Regime Transformation: the scramble to gold in the late nineteenth century, Review of Political Economy, Vol. 11, No. 2 pp. 125-149.
KIEL, L.D. and Elliott, E. (1996) Chaos Theory in the Social Sciences Foundations and Applications, Ann Arbor, University of Michigan Press.
KIRMAN, P (1993) Ants, Rationality and Recruitment, Quarterly Journal of Economics, Feb., pp. 138-156.
KRUGMAN, P. (1996) The Self-Organizing Economy, Oxford, Blackwell
LANCASTER, K. J. (1966) A New Approach to Consumer Theory, Journal of Political Economy Vol. 74, pp.132-157
LANCASTER, K. J. (1971) Consumer Demand: A New Approach, New York, Columbia University Press.
LEIBENSTEIN, H. (1950) Bandwagon Snob and Veblen Effects in the Theory of Consumer Demand, Quarterly Journal of Economics, Vol. 64, pp. 183-207.
LEIBENSTEIN, H. (1976) Beyond Economic Man: Anew foundation for microeconomics, Cambridge Mass. Harvard University Press.
LIEBOWITZ, S. J. and Margolis, S. E. (1990) The Fable of the Keys, Journal of Law and Economics, Vol. XXXIII, pp. 1-25.
LIEBOWITZ, S. J. and Margolis, S. E. (1994) Network Externality and Uncommon Tragedy, Journal of Economic Perspectives, Vol. 8 No.2 Spring, pp.133-50
MASLOW, A. H. (1954) Motivation and Personality, New York, Harper and Row.
MOSCOVICI, S. and Faucheux, C. (1972) Social Influence, Conformity Bias, and the Study of Active Memories,. In Berkowitz, L. (ed), Advances in Experimental Social Psychology,Vol. 6, pp. 149-202., London, Academic Press.
NELSON, R. R. (1995) Recent Evolutionary Theorizing About Economic Change, XXXIII, pp.48-90, Journal of Economic Literature.
NICHOLSON, W. (1998) Microeconomic Theory, 7th edn. New York, Harcourt Brace.
NOWAK, A. and Latané, B. (1994) Simulating the Emergence of Social Order from Individual Behaviour, in Gilbert, N and Doran, J. Simulating Societies: the Computer Simulation of Social Phenomena, London, UCL Press.
ORMEROD, P. (1995) The Death of Economics, London, Faber and Faber.
ORMEROD, P. (1998) Butterfly Economics, London, Faber and Faber.
PASHIGIAN, B. P. Bowen, B. and Gould, E. (1995) Fashion, Styling and the Within-season Decline in Automobile Prices, Journal of Law and Economics, Vol. XXXVIII Oct., pp.281-309.
POLLAK, R. A. (1977) Price Dependent Preferences, American Economic Review, .67 pp.64-75.
POLLAK, R. A. (1978) Endogenous Tastes in Demand and Welfare Analysis, American Economic Review, Papers and Proceedings, Vol. 68, pp.374-379.
SCHARFSTEIN, D. S. and Stein, J. C. (1990) Herd Behaviour and Investment, American Economic Review, Vol. 80, pp.465-479.
SHILLER, R. J., (1989), Market Volatility, Cambridge, Massachussetts Institute of Technology Press.
STIGLER, G. J. and Becker, G. S. (1977), De Gustibus Non Est Disputandum, American Economic Review, Vol. 67, pp.76-90.
VARIAN, H. R. (1992) Microeconomic Analysis, 3rd.Edn., New York, W.W.Norton.
WALDROP, M. M. (1992) Complexity The Emerging Science at the Edge of Order and Chaos, New York, Simon and Schuster.
Return to Contents of this issue
© Copyright Journal of Artificial Societies and Social Simulation, 1999