Nathalie Lazaric and Alain Raybaut (2004)
Knowledge Creation Facing Hierarchy: the Dynamics of groups inside the Firm
Journal of Artificial Societies and Social Simulation
vol. 7, no. 2
<https://www.jasss.org/7/2/3.html>
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Received: 07-Feb-2004 Accepted: 07-Feb-2004 Published: 31-Mar-2004
ei (t) = {xi (t)}ai, i = 1, …, n, | (0.1) |
where 0 < ai ≤ 1.
(0.2) |
where
(0.3) |
(0.4) |
Figure 1. |
(0.5) |
where ei(t) refers to the effort of group i at time t.
Q(t) = B(t){E(t)}β | (1.1) |
with , and 0 < β ≤ 1. The term B(t) refers to a global learning by doing mechanism in the firm that captures the accumulation of knowledge within the same. Global learning is modelled by the combination of the activation levels of the different practices determined by knowledge creation and hierarchy pressure in each group (see below) at time t. We have:
(1.2) |
where Ψ is a positive, continuous, concave function.
π( t) = pQ(t) - C(E(t)) | (1.3) |
where p refers to the exogenous market price of the production and C(E(t)) stands for a cost function, with C > 0, C' > 0, C'' > 0 with E(t) > 0. This cost function captures the direct cost of labour and the indirect costs produced by the incentive policies implemented by management. Indeed, the role played by the motivational dimension is crucial in explaining the ability of each group to promote its practices (Lazaric and Denis 2001). Motivation relates first to salary policy and secondly to the control implemented by the hierarchy in order to increase individual and collective skills in the firm.
c(t)= Φ [ r(t)- r* (t)] | (1.4) |
(1.4) where, Φ is an increasing function of r(t)- r* (t), such that,
and
.
This function is shaped as follows:
Figure 2. |
That is to say, the owner's vision of the environment, which results in earning requirements, may induce the hierarchy to make a restrictive choice in the exploitation of idiosyncratic practices or may lead to some development and exploration of practices if the hierarchy chooses to fine tune its human resource policy.
(1.5) |
with i = 1,… n. The n parameters δi, with 0 < δi < 1, refer to the exogenous obsolescence rate of each practice. The parameters σ and (1 - σ), with 0 < σ ≤ 1, stand for the respective weights of the pressure of hierarchy and of knowledge creation in the dynamics.
Figure 3.1a. Levels of activation of practices t = 0 to 2 |
Figure 3.1b. Levels of activation of practices t=2 to 40 |
Figure 3.1c. Growth rates of activation levels of practices |
Figure 3.1d. Action of the hierarchy (a positive (negative) sign means that hierarchy promotes (brings down) the practices of group i) |
Figure 3.1e. Localized learning |
Figure 3.1f. Global learning |
Figure 3.1g. Profits |
Figure 3.2a. Levels of activation of practices t = 0 to 2 |
Figure 3.2b. Levels of activation of practices t=2 to 40 |
Figure 3.2c. Growth rates of activation levels of practices |
Figure 3.2d. Action of the hierarchy (a positive (negative) sign means that hierarchy promotes (brings down) the practices of group i) |
Figure 3.2e. Localized learning |
Figure 3.2f. Global learning |
Figure 3.2g. Profits |
Figure 3.3a. Levels of activation of practices t = 0 to 2 |
Figure 3.3b. Levels of activation of practices t=2 to 40 |
Figure 3.3c. Growth rates of activation levels of practices |
Figure 3.3d. Action of the hierarchy (a positive (negative) sign means that hierarchy promotes (brings down) the practices of group i) |
Figure 3.3e. Localized learning |
Figure 3.3f. Global learning |
Figure 3.3g. Profits |
Figure 3.4a. Levels of activation of practices t = 0 to 2 |
Figure 3.4b. Levels of activation of practices t=2 to 40 |
Figure 3.4c. Growth rates of activation levels of practices |
Figure 3.4d. Action of the hierarchy (a positive (negative) sign means that hierarchy promotes (brings down) the practices of group i) |
Figure 3.4e. Localized learning |
Figure 3.4f. Global learning |
Figure 3.4g. Profits |
2 According to Leibenstein (1987), the motivational context lies at the heart of an important part of the organizational efficiency of firms because the relation between employers and employees (which is largely incomplete) allows scope for the interpretation of instructions in line with the social relations prevailing in a particular firm. In this context, it is clear that any attempt to channel employees’ attention and energy can be rather limited and that entrepreneurial energy may have to face the passive attitude of employees who can formally accept to respond to pressures in unforeseen or unintended ways (see also Witt (1998) for a similar discussion on this point, Foss and Foss 2003).
3 The xi(t) are not percentages, but absolute levels of diffusion (activation) of each practice on an internal specific scale established by the hierarchy. Thus, we do not assume that .
4 Let us suppose that the norm r*(t), evolves according to the following motion
where, 0 ≤ ρ ≤ 1, and η(t) is a random variable with zero mean.
5 In the intermediate cases, the following Ω matrix applies:
That is to say, group 1 has zero interactions, group 2 one, group 3 two, group 4 three and group 5 four.
Table 1: Global parameters, effort parameters and prior knowledge of groups i | |||
β | θ | ρ | p |
0.75 | 2 | 0.85 | 1 |
αi | δ i | ki0 |
0.33 | 0.05 | 0.5 |
7 This means that effort parameters and prior knowledge differ among groups. We have:
Table 2a: Prior knowledge of groups i | ||||
k10 | k20 | k30 | k40 | k50 |
0.5 | 0.75 | 0.25 | 0.5 | 0.65 |
Table 2b: Effort parameters of groups i | ||||
α1 | α2 | α3 | α4 | α5 |
0.45 | 0.33 | 0.53 | 0.73 | 0.23 |
8 Which means that the parameters are the same as in 3.1.
9 ki0 are the same as in 3.7. (cf. Table 2a and 2b)
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