(1) One has, of course, to be careful to avoid the confusion between different technologies and the operation ... only communicate with their neighbours. This sort ...
Revue d'économie industrielle
Variety : the coexistence of techniques Alan Kirman
Citer ce document / Cite this document : Kirman Alan. Variety : the coexistence of techniques. In: Revue d'économie industrielle, vol. 59, 1er trimestre 1992. Diversité technologique et cohérence en Europe. pp. 62-74; doi : 10.3406/rei.1992.1403 http://www.persee.fr/doc/rei_0154-3229_1992_num_59_1_1403 Document généré le 08/06/2016
Alan P. KIRMAN
VARIETY : THE COEXISTENCE OF TECHNIQUES
representative progress" learning accumulation leads explain the relative several collective by All from Standard different coexistence of shares takes to on one this are defects. periods one the firm loss technology place simplistic. seems ofaggregate firms in the of macroeconomic of are of Firstly which human in at different memory modified rival of which odds Either different to simply level the technologies the capital with athe ?technologies process superior parameters over to there Secondly increases the productivity models increasing which techniques time. simple isissome (1). one. generates essentially how reduce The the in of This idea returns. capital total ?does productivity of the explanations Industries the that coexistence capital externalities production production one monotonie. problem saving This an explain economy diminishes vision are of innovation, for can of capital can often for function the such How technical persist of allsimultaneous oscillate progresses the characterised ?firms or "technical then Iseconomy or there and of there innovation some and over could the asteadily is which some time. one has use by
I shall pursue the idea here that if the economy contains many firms and these have links with each other, then the adoption of technologies may depend on those already adopted by other firms. The sort of stochastic process involved may lead to alternating predominance of different competing technologies. This sort of phenomenon has been discussed in the literature on financial markets where different opinions may prevail as a result of stochastic interaction and transmission of opinion between individuals (see Sharfstein and Stein [1990], Day and Huang [1989], Kirman [1991], Topol [1991]). It has also been treated in sociology, where stochastic interaction models of opinion formation have been developed by Weidlich and Haag [1983]. Other authors have shown how stochastic interaction between firms may also lead to the economy being « locked into » an inferior technology (see for example Arthur [1988], David [1985], Arthur et al. [1987]).
(1) One has, of course, to be careful to avoid the confusion between different technologies and the operation of the same technology with different factor inputs. Under standard assumptions the coexistence of two firms using the same production function but with different input combinations is ruled out, since one of them could not be cost minimising. However, one might well contest the smoothness and competitive assumptions involved. 62
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I will discuss some examples of simple interaction models and their characteristics. A particular feature of these models is that they have a tendency to be selfreinforcing (see Arthur [1988] and Lesourne [1991]). As one opinion becomes prevalent on a market the probability that those currently in the minority will be recruited to it increases. As one technology is adopted by more firms there is a tendency for others to follow suit. However, a second characteristic of such models is that an opinion or technology which has been driven into a minority position may later return to dominate the market. I shall first discuss models in which the interaction between firms is stochastic, but in which no specific network of communication is assumed. Secondly, I will look at models in which firms can be thought of as the nodes of a graph and they only communicate with their neighbours. This sort of "random field" approach was first introduced into economics by Föllmer [1974] and has also been used by Durlauf [1990], Blume [1991] and Orlean [1991]. Lastly, I will briefly mention the idea of evolutionary stability which can also be used to explain the coexistence of competing technologies. RANDOM INTERACTION AND THE ADOPTION OF TECHNOLOGIES Consider a simple example in which two different technologies are available to consumers. The standard example is that of MS DOS based personal computers as opposed to the Macintosh P.C. Another obvious recent example was the competition between Betamax and VHS in the market for video recorders. In both cases it is evident that there is some advantage to adopting the technology that is prevalent. In the case of P.C. s the advantages such as the wider availability of software compatibility with other users, do not need to be spelled out. In the case of video recorders (and we will soon see the same phenomenon with the introduction of the new digital audio tape technology) the relative availability of prerecorded cassettes is a determining factor. There is thus a self-reinforcing aspect which has been emphasised by Arthur [1988]. The more clients adopt one technology the more likely are others to adopt it. Furthermore eventual predominance may be dependent on chance events which are not necessarily related to the intrinsic merits of the technology in question. Thus the process is path dependent. If one technology eventually takes over the whole market but which this is, is not determined a priori, then one can talk, as several authors do, of multiple equilibria. Similarly if the technologies terminate in fixed proportions which no longer change over time, and these proportions are not predetermined then one can also talk of multiple equilibria of the system. If we consider the original Polya urn scheme which has been used as the theoretical model for technical choice, it starts with two balls of two different colours, black and white, in an urn. A ball is then drawn at random from the urn and replaced, together with an additional ball of the same colour. What Polya showed was that if one considers the state of the system as k/N the number of white balls over the total number of balls then this converges to a limit with probability one. However, the limit value x is uniformly distributed on the interval [0, 1]. Thus the limiting properties are totally unpredictable. Indeed if one thinks of two firms using two different technologies and REVUE D'ÉCONOMIE INDUSTRIELLE — n° 59, 1er trimestre 1992
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new firms adopting the technology of one of the existing firms it is easy to see that the initial chance sequence of choices will have an important effect on the final outcome. An alternative view of this process is to think, as Cohen [1984] has suggested, of firms "spinning off" from existing ones as has been the case in the US electronics industry. If one wishes to think of an industry of many firms in the manner already described then a somewhat different result holds. In this case the proportions will again converge but the distribution of x the limit on the unit interval is Beta. Now the sort of process described here may be generalized in several ways. One of the important features to retain given the underlying economic model that we have in mind is that the probability that a firm takes up a given technique or technology should increase the more firms there are already using this technology. This reflects the externality generated by the widespread use of a technique. However the way in which the probability depends on the existing properties may have a crucial role in determining the long-run structure. This point is developed by Arthur et al. [1987]. They consider infinite urns with balls of N different colours, i.e. competition between N different techniques. Let the state of the system at time t be given by ¿-i let b =■= b\...bu and w s »■i ¿>' be the initial conditions functions and let fqt) be £ a sequence of continuous mapping the vectors Xt, from the N-l dimensional unit simplex into itself, i.e. from proportions of balls into probabilities of addings balls. Starting from an initial vector of balls the process is iterated by adding one ball at a time with the probability of its being colour i given by rft (Xt). The dynamics of the system are given at time t by ^■^^
where
(2)
u)(X,) = p\'( X,) - c¿( X) and ß ,' is a random variable defined by
P,'(*) -
1 with probability q'^ 0 with probability l " ^x) i=l,....N.
The expected motion of Xt+1 is given by 0) v '
E\X¡M\ - JÇ + [w 7-7-kW 77 + n) -*;l
Arthur et al. [1987] impose two important conditions on the process given in (1). Firstly they require that the functions fqt] converge "reasonably rapidly" to 64
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a limit q and the secondly that the deterministic counterpart of (3) i.e. the same process treated as deterministic and following the same law as the expectation of X{+i should be a gradient system. This effectively rules out cycles and obliges the system to converge to the fixed points of q. These two assumptions are not completely innocent. The rapidity of convergence of qt, in effect, means that these variation which can occur at the outset due to fluctuations in qt are quickly damped out. Thus, although this may lead to the erratic behaviour one might like to see in such models, this part of the variation quickly disappears. The second assumption on the "certainty equivalent" model, rules out strange dynamics in general and cycles in particular. All of this means that given Arthur et als' assumptions the industrial structure will after initial movement settle down to a stable configuration but since there may be many such fixed points of the system the final outcome may be unpredictable. To such a system it would be natural to add the arrival of new technologies which would then cause similar movement. The nature of the realisations of the process would then depend on the relative frequency of the arrival of new technologies and the relative speed of convergence of the process with a fixed number of technologies. If one accepts this view of the evolution of the market a reasonable prediction of the result of the introduction of the new competing technologies for audio cassettes and discs in the next year would be that after initial possibly rather wild fluctuations in market shares the latter would settle to a rather steady configuration which would persist until the next wave of innovations. Such a model would allow for reversals of market shares in the initial stages but would not permit such changes later in the process. If susch resersals do occur with no significant changes in the respective technologies another sort of stochastic model should be used. If this process does not satisfy the assumptions just specified it may not converge to any particular state. In this case the only relevant equilibrium concept will be the limit distribution of the stochastic process, i.e. the proportion of time that the process spends in each state. In the sort of process I will consider there will be a tendency for the process to spend its time in extreme states, i.e. those in which one technology dominates the other but will always eventually move to another extreme state. This sort of evolution is probably too extreme since, sooner or later, a given technology will die. This can be incorporated into the sort of model which I will now present by reducing over time the small probability which prevents the process getting absorbed. However, in the short run it does not seem unreasonable that a given technology will persist. Consider the persistence of vinyl records and the equipment for playing them. Although the market has diminished and is now reduced to one for collectors and those with a large stock of records, this still remains a profitable niche for a few firms. Thus once a technology has been adopted on a large scale there is still a tendency for it to persist as a service for those who adopted it and invested in it. There may also be a conscious desire to maintain a technology in existence to provide an alternative should others prove dangerous, for example (2).
(2) This was the case with the different technologies for nuclear reactors. REVUE D'ÉCONOMIE INDUSTRIELLE — n° 59, 1« trimestre 1992
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To establish some of the basic ideas consider a population of N individuals k of whom have adopted technology 1 and N-k of whom use technology 2. We could also consider a model with a larger but finite number of technologies and also one in which a certain proportion of the population has not yet adopted either technology. At each period individuals meet each other and when two individuals who have adopted different technologies meet, the first is converted to the second's with probability p = [1 - the distribution ¿i will be of the form shown in figure 1.
e = 0.005 6 = 0.01
N=1000
Figure 1 and the process will spend most of its time near — k = 0 or — k = 1 and will N N periodically switch back and forth (4). If there were several say m technologies, the process would spend most of its time at the vertices of the m-1 dimensional unit simplex. This sort of behaviour, which is also familiar from the literature on learning from repeated games see Young and Foster [1991] and contagion in financial markets see Kirman [1991], Topol [1991] and Sharfstein and Stein [1990] has very different dynamics from that of the "lock-in" models of Arthur [1988] and David [1985] and which is appropriate to the study of a particular process of technological innovation is largely an empirical question. The analogy with the repeated games literature is interesting. In the latter there are bilateral meetings in which each player plays against a randomly drawn opponent and at each point in time. A player is characterised by the strategy he adopts. The proportions of players playing different strategies is modified according to the success achieved by each strategy in the population as a whole. In the case of technologies it is perhaps better to think of each player as playing against a group of competitors and strategies being modified in the light of their success. If the groups were interconnected, one would again observe the sort of epidemic phenomena mentioned earlier. Here we are somewhat changing perspective in that the probability of changing technology will depend on the relative profitability of that technology. Only if there are strong externalities do we come back to the simple relation between profitability and level of adoption.
(4) It has been proved by Föllmer (see Kirman [1992]) that if N becomes large the limit distribution of k/N is a continuous symmetric Beta distribution with density f (x) = const xal (l-x)""1REVUE D'ÉCONOMIE INDUSTRIELLE — n° 59, 1er trimestre 1992
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We then come to a further question. If there are important external economies in the adopting of technology an individual before taking a decision should look at two things. Which technology he evaluates as best from a technical point of view and then what he judges majority opinion to be. A double stochastic process of this sort is given in Kirman [1991]. The proportion of individuals kt/N judging a certain technology to be best is determined by the stochastic process given by (4). Then each individual i receives a signal (with some noise) qu as to what the majority view is. That is (9)
**-£
+ £*
'-I..».*
where the eit ~ N (0,a2) and independent for all i.. Here there are two possibilities. The simplest assumption is that the firm, having observed its signal, chooses that technology which it perceives to be that viewed as best by the majority. If everybody does this and everybody is known to do this there will be a Nash equilibrium. In the case of financial markets in which prices evolve according to people's expectations and those expectations are formed in the light of contacts with others, this is a plausible assumption. However, in the case of the adoption of technologies this is less clear. If new firms are arriving and being added to the population of existing firms, it is reasonable to think of them as adopting the majority technology. However, in this case we are back in the context of the Arthur et al. [1987] model and the process will "settle down" to a fixed configuration after a period of time. If, on the other hand, we consider the population as of a fixed size then either we must think of existing firms as dying and being replaced by new ones or we must think of firms as converting from one technology to another. Thus there are three basic models : 1) The growing industry with eventual "lock in" either to a particular, possibly inferior, technology (5) or to a particular market division (see Hanson [1985]). Here the essential motivations for wishing to follow the majority are either some sort of network externality or a learning effect which in turn generates an externality (see Arthur [1988, 1989]). 2) The evolving but essentially constant size industry in which firms are being replaced by new ones who make an adoption decision on entry. In principle here, of course, the choice decision of the entrants should take into account the, presumably bad, choice of those leaving the market. In this case, provided the process does not get absorbed, i.e. providing with positive probability some old or new firm switches to each of the existing technologies, the process will switch around, passing through all states and given the underlying assumptions, will spend most of its time in extreme positions. This means that one technology will dominate for a period but that there will be reversion to dominance by another.
(5) The commonly cited examples are the use of FORTRAN, the use of the QWERTY typewriter keyboard or its equivalents in different countries, or the use of light water nuclear reactors in the U.S. 68
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3) The industry in which the same firms remain, but in which the choice by firms of technologies may change. If nothing about the technologies changes over time, it is difficult to envisage this "valse hesitation" as continuing. However if one takes into consideration the fact that technologies are subject to continuous modification then this becomes quite plausible. One can think of the case of the PCs and the change in the IBM MS DOS environment with the introduction of "Windows" and the mouse for example. Here I have been putting emphasis on the uses of some technology in the sense that they are buyers of equipment incorporating that technology. However one can also envisage examples in which firms adopt a particular way of doing things such as car or aeroplane assembly which does not imply any purchase by them of particular equipment. In the case of the purchase of a particular technology, the presence of increasing returns in the manufacture of the associated equipment will reinforce the tendency of the market shares to be captured for long periods in extreme situations. Another variant of the contagion process is to think of producers as trying to imitate the (patented) technology developed by their opponents and succeeding with a certain probability. They cannot, of course, produce the identical technology because of the patent. Once again such a process would lead to what Topol [1991] has called "mimetic contagion" : waves of a certain type of technology. That this is empirically plausible is shown by Mansfield, Schwartz and Wagner [1981], who find that in a survey of 48 industries, 60 percent of all patents were imitated within 4 years. Dasgupta [1986] looks at a game theoretical model of such a process and shows that the Nash equilibrium will have one firm introducing a technology and others imitate. All of this shows that whether a system of the to a fixed structure or not depends crucially individuals involved is fixed, the probabilities choices, and from the economic point of view there is exit and entry.
"urn" type eventually settles down on whether or not the numbers of with which they affect each others' whether in the fixed number setting
Till now I have argued in a very general context, akin to that used in repeated game tournaments (see Axelrod [1984] and Young and Foster [1991]) or to that in many agent bargaining problems (see Roth and Sotomayor [1990]) or in the search literature (see Diamond [1989]). In all these cases the idea is that agents meet each other at random. Thus one could think of agents sampling other agents for their characteristics. P.C. users would somehow, by inquiring of a few individuals, form their opinion about the technology to adopt. However, in general there is some structure in terms of communication in the economy. Thus agents will not be influenced by all other agents equally. Nearest neighbours will have more influence than those further away. "Nearer" here has to be interpreted with caution. It can mean in terms of spatial location (Gabszewicz and Thisse [1986]), in terms of similarity (see Gilles and al. [1989]) or may be due to some communication structure in which nearness way be determined by industrial interdependence or may simply be viewed as random (see Kirman, Oddou and Weber [1986]). REVUE D'ÉCONOMIE INDUSTRIELLE — n° 59, 1" trimestre 1992
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The basic idea is that through the communication structure, messages should be transmitted which would affect the behaviour of neighbours and at the next stop there would be further transmission. There are two basic possibilities for modelling. Firstly, the underlying network could be considered as fixed and determined trnt that the transmission of messages through it is random. The actual structure of the network may be the result of the prior decisions of the players as to where to place themselves (see Blume [1991]). This would correspond to the Ising structure, a model first introduced into economics by Föllmer [1974], and if one thinks of the individual firms as nodes in a lattice-like graph could lead to clusters of firms coloured in a certain way, i.e. having adopted a certain technology. A typical model would be that of Blume [1991], who considers a countable infinity of sites, each of which is occupied by one player who is directly connected to a finite set of neighbours. Each firm can then be thought of as adopting a technology and then receiving a pay-off, depending on the technologies adopted by his neighbours. If the set of sites is Ô and of technologies W, then a configuration will be : S -*■ W and the pay off to s of choosing W whom his neighbours choose according to can be written Gs (w^V,,)) where Vs is the neighbourhood of s, i.e. all sites with distance less than k from s. A stochastic revision process such as
hence P.("M>(V,)) -
£«pßG,(w,(V,))-G,(v,
