Wolfgang Kerber and Nicole J. Saam (2001)
Competition as a Test of Hypotheses: Simulation of Knowledge-generating Market Processes
Journal of Artificial Societies and Social Simulation
vol. 4, no. 3,
<https://www.jasss.org/4/3/2.html>
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Received: 14-Jun-00 Accepted: 30-Mar-01 Published: 30-Jun-01
Hypothesis I: The average growth rate of the knowledge accumulation process in competition increases with the number of independently innovating firms.
Hypothesis II: The average growth rate of the knowledge accumulation process in competition decreases with the number of activities of the firms, which are simultaneously tested in the market.
Hypothesis III: The non-imitability of at least one activity will have a considerable impact on the pattern of the knowledge accumulation process and particularly decrease its average growth rate.
(1) |
Let Gt denote the average total fitness of all firms in the market at time t:
(2) |
Figure 1. Graphic representation of the formal model |
(3) |
(4) |
(5) |
Table 1: Variables and parameters of the formal model | ||
Variable | Meaning | Initialization at time t = 0 |
fijt | fitness of activity j of firm i at time t ( = the end of period t ) | 1.0 for each activity |
Fit | total fitness of firm i at time t | 1.0 for each firm |
Gt | average total fitness of all firms at time t | 1.0 |
f 'ijt | fitness of activity j of firm i at time t (after innova-tion but before imitation) | |
F'it | total fitness of firm i at time t (after innovation but before imitation) | |
F'kt* | total fitness value of the best firm k at time t (after innovation but before imitation) | |
f 'kjt* | fitness value of activity j of the fittest firm k at time t (after innovation but before imitation) | |
Parameters | Interpretation | |
λ | imitation rate ( 0 < λ < 1) | λ = 0.5 |
σ | mutation rate | σ = 0.05 |
Figure 2. Time series of one simulation run: growth of the fitness of the firms (n = 2; m = 3: mv = 3, ms = 0; full imitability) |
Figure 3. Average fitness of all firms after 100 periods in dependence on the number of firms n and number of activities m (mv = m, ms = 0; full imitability; mean values of the results of 20 simulation runs) |
Figure 4. Time series of one simulation run: growth of the fitness of the firms (n = 3; m = 3: mv = 2, ms = 1; limited imitability) |
Figure 5. Average fitness of firms in dependence on the number of firms n and number of activities m (mv = m - 1; ms = 1; limited imitability; mean values of the results of 20 simulation runs) |
Table 2: Comparison of the average fitness of firms between (1) the case of full imitability (m = 7) and (2) the case of limited imitability (mv = 6, ms = 1) for different numbers of firms (n = 2 ... 10; mean values of 20 simulation runs) | ||
n | m = 7 | m v = 6; m s = 1 |
2 | 1,6272445 | 1,20672445 |
3 | 1,9063265 | 1,37796878 |
4 | 2,064597 | 1,3458796 |
5 | 2,2569785 | 1,3794245 |
6 | 2,3468415 | 1,561882 |
7 | 2,480952 | 1,56107785 |
8 | 2,533157 | 1,588989 |
9 | 2,591838 | 1,549409 |
10 | 2,6656365 | 1,606455 |
Figure 6. Effect of Lock-ins on the average fitness of firms (selected results from 20 simulation runs; n = 6 firms, m = 7 activities: mv = 6, ms = 1) |
2 For the evolutionary epistemology approach see also Campbell (1987), and Metcalfe/Boden (1992) for its application the the development of technologies.
3 For approaches to develop such an evolutionary concept of competition (or evolutionary market process theory), in which new knowledge is generated, spread and accumulated by the generation and testing of hypotheses, see Streit/Wegner (1992), Loasby (1993), Kerber (1994), Kerber (1997), Metcalfe (1998) and Mantzavinos (2001). For a rigorous application of Popper's theory of "growth of knowledge" to the entrepreneur ("falsificationist entrepreneur") see particularly Harper (1994), Harper (1996). For the idea of an "experimentally organized economy", in which firms can be seen as "experimental learning machines", see Eliasson (1994).
4 For a more elaborated presentation see Kerber (1994,236ff); Kerber (1997).
5 This can be called the knowledge base of the firm (Dosi 1988, 1126). Therefore a firm can be seen as a bundle of resources enabling the carrying out of those activities. For resource-based and competence theories of the firm see Foss/Knudsen (1996).
6 For the original concept in biology see Mayr (1982); for its application on competition see e.g. Metcalfe (1989); Metcalfe (1998, 24ff.) and Vanberg/Kerber (1994, 193ff.).
7 See particularly Nelson/Winter's evolutionary growth models, which are based upon the variation and selection of routines, as e.g. technologies (Nelson/Winter 1982).
8 See also Röpke (1977, 1990), Fehl (1983), Dosi (1988), Saviotti (1991) and Metcalfe (1998).
9 In this paper we only deal with the problem of firm concentration and mergers. Another possibility how the number of independent sources of innovation can be reduced are R & D cooperations between firms, because the cooperating firms do not decide independently from each other about their R & D projects and mostly give up parallel research. From the perspective of competition policy R & D cooperations are seen as cartel-like restrictions of competition, leading to the question, whether they can be exempted from the general prohibition of cartels (see e.g. Art. 81 EC Treaty). Therefore our analysis is also relevant for the assessment of R & D cooperations in competition policy.
10 For the economic discussion on firm concentration see e.g. Schmalensee 1989, Scherer/Ross 1990, and Schmidt 1999.
11 There are differences between the merger policies in the U.S., the EU and Germany, which cannot be discussed here (see Schmidt 1999and particularly for the EU Kerber 2000a).
12 In U.S. antitrust policy the effects of mergers on innovative activities have been investigated in some specific cases (see e.g. Widnell 1996), but not from the perspective of evolutionary economics.
13 See also the discussion with regard to the Schumpeter hypotheses about the correlation between firm size / concentration on one hand and innovation activities on the other (e.g. Scherer/Ross 1990, 172ff.).
14 See Kerber (1997, 54) and Mantzavinos (2001, 194ff.). From a methodological point of view this problem is connected with the Duhem-Quine thesis that it is impossible to falsify a single hypothesis because it is always tested in conjunction with other (auxiliary) hypotheses; see in detail Harper (1996, 266ff.).
15 One possibility to overcome this problem is the divisionalization of firms with the introduction of independent profit centers. In section 2.11 - 2.20 we will come back to the implications of the Hayekian informational feedback from the market for the organizational structure of the firm.
16 See e.g. also the evolutionary models of Nelson/Winter (1982) and Bush/Mosteller (1955).
17 See Gilbert/Troitzsch (1999).
18 The assumption that the ranking of the total fitness of the firms is identical with the ranking of their profits implies that the selection of the market works appropriately, i.e. there are no systematic distortions by technological external effects, market power, rent seeking revenues etc. This is doubtless a critical assumption, which has to be held in mind for further scrutiny.
19 Many thanks to Michael Möhring and Klaus G. Troitzsch who have supported us.
20 Please note that the non-imitable activity is the same for all firms. This is not a necessary assumption, because it also might be possible that - due to different competences of the firms - some firms might be able to imitate certain activities and other are not.
21 The average growth rate of knowledge accumulation per period, g, can be calculated by:
(6) |
22 A table with the numeric results in regard to the average fitness of the firms after 100 periods in dependence on the number of firms and on the number of activities can be found in the appendix.
23 Small deviations from the linear trend follow from the standard error of the simulation (deviation of the mean value of several simulations from the true mean value). The standard error decreases with the square root of the number of simulations.
24 A closer inspection of Tables 3 and 4 shows that the reduction of growth is largest for smaller m and smaller for higher m whereas different numbers of firms seem to have a lower impact on the extent of the slowing-down of the knowledge accumulation process through the non-imitability of one activity.
25 The observation that the results do not fit so smoothly to a clear correlation as in our basic model, i.e. that larger fluctuations emerge (compare the third column in Table 2), is also due to the higher variability of the simulation results in the case of non-imitability. We presume that the running of more than 20 simulation runs would lead to more stabile results. Small deviations from the linear trend follow from the standard error of the simulation (deviation of the mean value of several simulations from the true mean value). The standard error decreases with the square root of the number of simulations.
26 But this limited imitation effect can help to explain, why Hypothesis II is nearly reversed in the case of the non-imitability of one activity. In the case of very few activities (small m), the relative weight of one non-imitable activity is much higher than in the case of a larger number of activities (large m).
27 This hints to a fundamental problem of our modified simulation model with limited imitability. Since we vary m, but always have only one non-imitable activity the relation between the imitable and the non-imitable activities changes if we increase m. Consequently, we get systematic distortions which might be responsible for our failure to confirm Hypothesis II also in the case of non-imitability. We accept this as an important objection to our modified model, but it primarily concerns our results in regard to Hypothesis II.
28 Especially, the numeric results of the last figure should be interpreted carefully as there was only one in 20 runs of this type.
29 One possibility is that one firm with on average superior fitness values is not the best firm, because it has a particularly low fitness value in regard to the non-imitable activity. This is also a kind of lock-in situation, because this firm cannot catch up with its non-imitable activity by imitation. In this case the competing firms cannot learn from the superior imitable activities of this firm, because it is not the leading firm.
30 Another problem is that through our calculation of the average fitness of the industry as an unweighted arithmetical mean of the total fitness values of the firms, we implicitly assume that all firms have the same market share. This need not be the case, if the performance of the firms differ. A similar objection is that successful firms are more easily able to invest more in R&D, implying e.g. a higher probability of successful innovations. This leads back to the objection (2).
31 For a broad survey of possibilities, how entrepreneurs can test their hypotheses see Harper (1996, 206ff.).
32 Our findings in Table 3 also show that the marginal increase of additional firms to the average growth rate of the fitness of the industry decreases, although we expect that it remains always larger than zero.
33 But keep in mind that the empirical studies about the alleged efficiency effects of mergers show that in most cases the expectations have not been fulfilled (Mueller 1996).
34 See Dye (1990), Vihanto (1992), Oates (1999), Kerber (1998); Kerber (2000b), Van den Bergh (2000).
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Table 3: Numeric results of the basic model (full imitability): average fitness of firms (n: number of firms; m: number of activities: mv = m; ms = 0) | |||||
n | m | ||||
2 | 4 | 6 | 8 | 10 | |
2 | 2,201272 | 1,84427 | 1,7044185 | 1,523272 | 1,497191 |
3 | 2,70812 | 2,205084 | 1,944649 | 1,848566 | 1,7695765 |
4 | 3,06579 | 2,4199 | 2,204144 | 1,6128365 | 1,9376865 |
5 | 3,291577 | 2,628876 | 2,3285205 | 2,157238 | 2,067783 |
6 | 3,5144595 | 2,8242085 | 2,4581245 | 2,2405285 | 2,1447285 |
7 | 3,51664 | 2,947427 | 2,60209 | 2,380793 | 2,2034705 |
8 | 3,928052 | 2,977871 | 2,628626 | 2,437706 | 2,3113575 |
9 | 3,998169 | 3,1447815 | 2,750766 | 2,4933575 | 2,341004 |
10 | 4,144693 | 3,157192 | 2,796321 | 2,539427 | 2,394632 |
Table 4: Numeric results of the extended model (limited imitability): average fitness of firms (n: number of firms, m: number of activities: mv = m - 1; ms = 1) | |||||
n | m 2 | 4 | 6 | 8 | 10 |
2 | 1,1389252 | 1,24326725 | 1,1924827 | 1,2369558 | 1,2702847 |
3 | 1,13677633 | 1,39129893 | 1,3500062 | 1,40118125 | 1,3897935 |
4 | 1,3029016 | 1,36568655 | 1,471161 | 1,3895475 | 1,496388 |
5 | 1,39153015 | 1,41691735 | 1,4002998 | 1,4600145 | 1,460914 |
6 | 1,4771355 | 1,541617 | 1,54079275 | 1,591404 | 1,463035 |
7 | 1,26548185 | 1,5023995 | 1,50662655 | 1,671637 | 1,549602 |
8 | 1,4229425 | 1,48901625 | 1,615524 | 1,5678895 | 1,584062 |
9 | 1,4821965 | 1,5593335 | 1,683825 | 1,6697865 | 1,642705 |
10 | 1,5259288 | 1,6074115 | 1,6292645 | 1,7360235 | 1,725264 |
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