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Computer exercises

MARKETS, SCIENCES, and the DYNAMICS of TECHNOLOGICAL CHANGE

Course 2004-2005, first semester.

All programs on this page are freeware and can be used and distributed without limitations.

0. Technicalities

The files that we use are available both at the Internet as will be indicated with hyperlinks, but also locally on the computers. To start up the programs in room D 306:

1. left-click on the button for “QuickBasic”

2. a screen should open in blue and you are requested to use Escape (right top of the keyboard)

3. go to “File” in the pull-down menu and open the programs as indicated below in this text.

The QBASIC.EXE and the QBASIC.HLP files can be downloaded here if you wish to use these programs elsewhere. One can run the program from within a so-called MS-DOS box.

Under the file-menu, you find the option OPEN, to open models.

We advise not to save program changes. So if the computer asks this, always click NO.

1. Background

The models you will use are similar to the models described in the article by Loet Leydesdorff and Peter van den Besselaar Competing technologies, lock-ins and lock-outs, which is part of the course materials.

The models help us to understand an evolutionary approach of competing technologies. For every function, several technological and design options may be available, and competing on the market. Whereas in ‘normal’ markets, the mechanism of diminishing returns results in the division of the markets among competitors, this can be expected to work differently in knowledge intensive markets. As Brian Arthur has argued, we may observe a mechanism of increasing returns operating, through which ‘the winner takes it all’.

The best known historical example of ‘lock-in’ has been the QWERTY keyboard of the typewriter. This design became dominant at a certain moment, and then dominated the market: all typewriters use this keyboard. Interestingly, we know that other designs are better, but these do not have a chance to diffuse. Moreover, the mechanical reasons for designing the keyboard as it is, are no longer valid given the prevailing (computer) technology. Why is this the case? In addition to the inherent quality we also have to account for the external (network) quality: if everybody has learned and used the QWERTY keyboard, the ‘externalities’ make the design attractive, and every other design unattractive.

These ‘lock-in’ processes can occur when one of the following issues has been important:

• standardization,
• learning by doing,
• economies of scale,
• increasing returns from information,
• knowledge intensive products and services,
• economies of scale,
• technological interdependencies.

Another well-known example of ‘lock-in’ is the competition between VHS and Betamax in the VCR market. The story is that the VHS won, because of the initial larger market share of VHS made it increasingly attractive for video stores to have VHS tapes for rent, and not Betamax tapes. As a consequence, customers started to buy more VHS, and this reinforced the video shops to offer even more VHS tapes. Eventually, Betamax and V-2000, although technologically superior, were completely removed from the market. In other words, technological competition can lead to a monopoly, and a technology may take the whole market despite its possible inferior characteristics compared to other (including later) competitors.

The models are designed to investigate under which conditions these phenomena occur. When are they unavoidable, and under which conditions can they perhaps be reversed.

2. The basic mode: two technologies, two types of adopters, and lock in

In the basic model, we have a situation with two technologies, and two types of adopters. As we explained in our mentioned article, the basic model is as follows:

Table 1. Return values for R- and S-type agents to adopting technology A or B, given n_A and n_B previous adopters of A and B. (The model assumes that a_R > b_R and that b_S > a_S. Both r and s are positive.)

We study this model using the simulation arthur1.bas.

(A compiled version of this model is available as arthur1.exe . This version does not allow you to change the parameters, but you can see the effects directly on the screen when you run it.)

Please open arthur1.bas

In arthur1.bas, you find the following lines of code:

Line 10 asks for input in order to specify the total number of adopters

Line 50 specifies the number of runs.

The random process is introduced in line 40.

The lines 60-90 specifies values for the parameters of the model specified in Table 1: aR, bR, aS, bS, r, s. (Note that we will use SA instead of aS because “AS” happens to be a reserved word in computer languages.)

We also assume that there is one adopter of Technology A (nA) and one of Technology B (nB) already present. (We often do that in computer programs because leaving parameters zero can easily lead to errors like divisions by zero.)

As we have made the model ‘symmetrical’, and the sequence of S-type and R-type adopters arriving is random, we expect that if we run the model very often, the lock-in will be in 50% of the runs in technology A, and in 50% of the runs in technology B.

Lines 120-180 model the choice process. Line 190 computes the value of the market percentages of Technology A and line 200 displays the result as a point on the screen.

Now run the program. First the program gives a ‘?’, and you have to type the number of adopters in the market. Use the first time 10000.

The horizontal axis of the picture (specified in line 30) represents the 50% market share, and the top of the screen shows the 100% for Technology A, whereas the bottom of the screen is the situation with 0% of the market for Technology A and consequently 100% market share for Technology B.

In the Arthur-model the adopters enter the market sequentially. They are represented as a graph that is drawn on the screen in pixels. Every graph shows a run of the diffusion path in terms of the market share of the two technologies. Thus, we run the program ten times. You can change the number of runs in line 50. Try it!

Experiment a bit with changing the parameters.

• Vary N, which is the number of adopters. This shows that monopoly does not occur initially, but in the longer run. With N=10000, the two technologies can sometimes remain competing in the market (of course depending on the parameter values of line 60-90). Things changes considerably with N=25000 adopters (and otherwise the the same parameter values): now you find always lock-in. 

• Is the lock-in more frequent on the side of Technology A than on that of Technology B?

• Does the lock-in occurs early in the diffusion process, or later?

• Experiment with changes in the parameters. Do not forget that the following condition were assumed by Arthur: AR > BR; AS < BS. What happens if you increase AR (to 0.9 or 1.0) and decrease BR (to 0.1 or 0)?

• Experiment also with r and s. What happened if r is increased to 0.02 or 0.03? Or decreased?

Make notes of the relations you find between the parameter values and the lock-in patterns.

3.Two technologies, two types of adopters, and uncertainty

Open arthur2.bas. In the previous model, adopters of the technologies are expected to have full information about the market shares of the two technologies, and to behave accordingly. In this model (corresponding to Table 3 in the article) we suppose that adopters do not have full knowledge about market shares. As a consequence, they only change when the market share of other technology is considerably larger than the threshold for switching (10% uncertainty in perception is introduced). Only than, the adopters can perceive the differences between the two technologies. Let us study the result of this assumption.

• Do the same experiments as with the basic model.
• Change the parameters a little. Increase the value of AR to 0.9 and 1.0 and decrease BR to 0.1 and 0. What is the effect?
• Increase r to 0.02, 0.05 and 0.1. What happens?
• Did you already try s = 0? Why don’t you get an unlock under this condition?

Make notes.

4. The reflexivity model

Open arthur3.bas.

Here we suppose that adopters only change when the benefits of the other technology are substantially (5% at least) higher than of purchasing the other. In other words, they do not react immediately. (The model corresponds to Figure 3 in the article and the text above this figure on p. 314.) What is the result? Change the parameters slightly, like in the previous sections. What is the effect? Make notes again.

5. Breaking out of the lock-in (‘lock-out’)

Let us return to the Arthur1.bas model and introduce the condition for breaking out of a lock-in.

As you will remember from the paper, lock-in occurs if, for example, an S-type agent has an advantage with buying Technology A (a_S = 0.2) despite his/her larger inclination to buy Technology B (b_S = 0.2). This is the case only if it is true that

            a_S + sn_A  > b_S + sn_B                                                    (See Table 1)

We can rewrite:

            a_S - b_S > sn_B  - sn_A      

or equivalently:

            n_B - n_A  < (a_S - b_S)/s

This condition is not true if s = 0 because the right-hand side of the equation then becomes infinite and therefore larger than the left-hand side. The ‘lock-in’ can then be reversed.

Use the model arthur1.bas and add a line 115 with the following condition:

115            IF (NA + NB) > 2000 and NA/NB > 2 THEN S = 0

 The if-statement specifies the condition that the market is sufficiently large (NA + NB > 2000) and that Technology A is locked in (NA/NB > 2). Under this condition s is set back to zero. Describe what you observe.

6. Changing the lock-in model: diffusion of competing technologies

Open now arthur1a.bas.

Take a precise look at the table 1 above. In Arthur’s model, the network effects are attributed to the types of adopter, and not to the technology. For R-agents, the effect of the number of users of technology A and technology B depends on the same parameter ‘r’. For S-agents, the effect of the number of users of technology A and technology B depends on the same parameter ‘s’. However, would it not be better to attribute this effect to the diffusion parameters of the respective technologies rather than to the network externalities among the different type of adopters? This would result in a different model, as represented in table 2 (that is, Table 4 in the article). In this case ‘r’ and ‘s’ are diffusion parameters of the respective technologies A and B.

Table 2. Return values for Technologies A and B being adopted, given n_A and n_B previous adopters of A and B. (The model assumes that a_R > b_R and that b_S > a_S. Both r and s are positive.)

This now is modeled in Arthur1a.bas. Using the standard parameter settings, the model of course behaves identically as Arthur1.bas, the standard model. However, this may change if we do not use parameter values in which we assume that r = s.

Do some simulations for various parameter values. Does the change of the model make any difference if you compare it with the first model? In what sense? Make notes.

1  REM the standard model, but r and s linked to the respective

2  REM technologies and not to the adopter types

10 INPUT N                               

20 SCREEN 11: WINDOW (-2, 0)-(N, 100): CLS

22 LINE (-2, 50)-(N, 50)

23 RANDOMIZE TIMER

25 FOR J = 1 TO 25

40     AR = .8: BR = .2

41     SA = .2: BS = .8

42     NA = 1: NB = 1

43     s = .02: r = .02

50     FOR I = 1 TO N

70     CHOICE = RND

90     IF CHOICE > .5 GOTO 125

100    RETURNA = AR + r * NA: RETURNB = BR + s * NB

120    GOTO 130

125    RETURNA = SA + r * NA: RETURNB = BS + s * NB

130    IF RETURNA > RETURNB THEN NA = NA + 1 ELSE NB = NB + 1

140    X = NA + NB: Y = 100 * NA / X

150    PSET (X, Y)

160 NEXT I

170 NEXT J

180 END

 You can apply the reasoning about diffusion also to the models arthur2 and arthur3.bas, respectively.

7. The original Arthur model with a spatial representation on the screen

The results of the Arthur model can be displayed in different ways. Try this version of the original Arthur model, available as arthur1g.bas. Explain what you see.

Exercise: Try to adjust the program in such a way that the behaviour of the actors becomes purely random.

A further extension of this model is given in Loet Leydesdorff’s paper entitled ‘Technology and Culture: The Dissemination and the Potential 'Lock-in' of New Technologies,’ Journal of Artificial Societies and Social Simulation, Vol. 4, Issue 3, (2001) Paper 5, at < http://jasss.soc.surrey.ac.uk/4/3/5.html >.

8. Conclusions

Arthur’s (1988) model (arthur1.bas) aimed at illustrating the ‘lock-in effects’ that had been noted in evolutionary economics. Evolutionary economists have criticized neo-classical economists for not taking into account the uncertainty of the actors generated (1) by the lack of incomplete information about the market and (2) because of their partial rationality. We have modeled these two effects above in arthur2.bas and arthur3.bas, respectively, and we have observed that under these conditions the ‘lock-in’ effect tends to disappear.

In the paper we derived a condition that would dissolve the ‘lock-in’. This is modeled above by inserting a line in arthur1.bas –under the condition of prevailing ‘lock-in’ – which brings the network-parameter s to zero. We can then observe the return to equilibrium. Note that a focus on reducing the network externality of a technology is different from a focus on improving the technology intrinsically. As was shown in the paper, this would in general not lead to an inversion of the ‘lock-in’. (Did you try it?)

Then we noted also that the assumption that the purchasing behaviour of adopters (with increasing return) would generate the ‘lock-in’ can be debated from the perspective of technology dynamics. Isn’t it the dynamics of the diffusion of the technology? We experimented with this assumption using model arthur1b.bas. Which differences did you note using this somewhat different model?

Finally, model artur1g.bas provided us with a spatial representation of the ‘lock-in’ effect. Further reading exploring this model was suggested.

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