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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

To cite articles published in the Journal of Artificial Societies and Social Simulation, reference the above information and include paragraph numbers if necessary

Received: 07-Feb-2004    Accepted: 07-Feb-2004    Published: 31-Mar-2004

* Abstract

The aim of the paper is to analyze the selection of routines within organizational structures characterized by different cognitive representations. Following a brief discussion on the role of hierarchy and the related problem of organizational practice selection in the evolutionary literature, we model the interactions between different groups within a firm trying to interfere with its coordination mechanisms in order to support their own idiosyncratic practices. Numerical simulations highlight differences in the ability to learn in different organizational set-ups with diverse patterns of knowledge distribution, also reproducing configurations analysed in the empirical literature. It is shown that networking schemes are the more profitable organizational configurations because of their dynamics of learning, although they are very sensitive to the truce problem.

Hierarchy, Interactions, Knowledge, Routines, Selection

* Introduction

Much attention has recently been devoted to the problem of knowledge creation within firms or in small communities (Brown and Duguit 2001; Grandori 1997, Grandori 2001; Garicano 2000; Amin and Cohendet 2004). In this literature, the general context of knowledge production, such as the centralized or decentralized architecture stressed by Marengo (1992), is considered as having a far from neutral effect on cognitive frameworks. Moreover, the idea that knowledge should not simply be understood as a pure cognitive process, but also as a locus where the political dimension is critical appears quite promising (Cohendet, Llerena and Marengo 1998). However, the co-evolution of these dimensions seems more difficult to tackle at the formal level, where symbolic representation may be incomplete and therefore incapable of representing this kind of dynamic (Cohen et al. 1996). Accordingly, attempts to formalise this process in the evolutionary literature, although quite promising, appear to be at their infancy because the two dynamics are always complex and therefore difficult to integrate (for some exceptions see Marengo 1995; Dosi, Levinthal and Marengo 2003). The problem is partly due to the different facets of hierarchy and to the difficulty of imposing a unified framework on the entrepreneur's vision (Adler and Borys 1996). As Witt (1998) emphasises, organizations are also social mechanisms and the communication process plays a major part in the transmission of the organizational vision. This can either emerge spontaneously or it can be the result of unintended collective learning arising from different levels of communication between a firm's members and its hierarchy. This complexity lies at the heart of the great uncertainty surrounding the process of building shared knowledge within a firm, although the entrepreneur's strategic intention remains an important factor.

At the intermediate level, groups, teams or "communities of practice", broadly, horizontal communities (communities of practice, project groups, quality groups etc.), play an important part in the creation of knowledge (Cohendet and Llerena 2003). Such groupings assume an exploratory role when co-evolution of autonomy, identity and different levels of hierarchical pressures operate on the production, dissemination and selection of organizational practices. Some empirical studies show the importance of such communities in the diffusion of organizational practices (such as quality circles, total quality management, kaizen or just in time production), their settlement as well as their replication (Becker and Lazaric 2003). It has been shown that the persistence of such organizational practices may sometimes overcome the "inefficiency arising from the agency problems of diffuse ownership [...] (because) the development of operational routines may offer more promise of economic success than prescription of incentive alignment" (Knott and MacKelvey 1999 p. 380-81). However, knowledge creation in the network configuration and communities of practices may be problematic because of the lack of appropriate intervention regulating such creativity (Miles and Snow 1992, Miles and Snow 1997, Foss 2003).

The aim of this paper is to re-examine this issue by analysing the selection of routines within an organizational structure characterized by different cognitive representations and hierarchical pressure. We put forward an applied evolutionary model capable of operationalizing internal selective forces. Indeed if selective processes have been largely explored through the driving force of the competitiveness of the external market (see notably Currie and Metcalfe 2001), hierarchical attempts to regulate knowledge creation and the emulation of organizational practices within firms have yet to be fully understood through the use of applied evolutionary models. This kind of approach could, on the one hand, give more exploratory power to empirical research in economics and business and, on the other, help us observe the impact of social regulation on the cognitive dimension practically. In what follows, we first briefly discuss the different faces hierarchy can assume and then present our model of the internal process of practice selection. Our main numerical findings are presented in the second part of this paper, leading on to the concluding remarks in the final section.

* Hierarchy, knowledge and the selection of organizational practices

The problem of hierarchy has attracted the attention of many writers. Among them March and Simon (1958) have noted that the existence of a variety of aims in an organisation's members can jeopardise the quick resolution of organizational problems. The concept of heterogeneity in organizations has taken different forms in the academic literature. Simon, for example, believes that some loyalty and a certain amount of "open-mindedness" exist among an organization's members and that these allow diversity to be channelled. Thanks to these features, a degree of selection takes place, so that a certain fitness emerges between the hierarchy's will and the individuals' ability to learn (i.e. members of the firm accept the hierarchy's recommendations passively and with docility) (Simon 1991). This kind of argument has been recently further enhanced by a number of new suggestions. Adler and Borys (1996), for example, suggest that different types of bureaucracies can exist, some of which can be enabling -facilitating interaction and communication between individuals- whereas others can be coercive and therefore exert pressures that limit interactions among a firm's members.

Moreover, perception of a particular hierarchy can also vary according to the choice of organizational structure established to tackle industrial relations and different employees' attitudes to work.[1] Leibenstein (1987) illustrated the problem by making the point that a firm's members are able to exercise discretionary power in the face of hierarchical pressure. Whatever the intention underlying an action taken in a particular circumstance, inertia may prevail because a firm's members may choose to resist the dynamic in question and decide to maintain their organizational practices and their autonomy (Stinchombe 1965; Hannan and Freeman 1984; Lazaric and Denis 2001). Employees may have a different vision and keep to their own routines thus generating organizational conflicts based on the different interpretations of environmental pressures inside the firm.[2] This problem has been illustrated in a number of case studies, which emphasise the difficulty of changing organizational routines and the productive knowledge lying within firms (Postrel and Rumelt 1992) or the capacity of individuals to mobilize defensive routines in the face of organizational change (Argyris 1985). In fact, any attempt to establish new organizational practices, for example the implementation of an ISO norm, can be confronted with important difficulties that go beyond the cognitive level (for example the articulation of tasks through a quality handbook). The political level forcefully comes into play in this context and can enhance the potential for conflict despite the fact that a particular change may produce opportunities for both technicians and other employees according to their learning abilities and the modification of their social status within the firm (Lazaric and Denis 2001). Consequently, the implementation of new organizational practices often tends to be correlated with the emergence of a new effort convention to facilitate the smooth adoption of practices among employees.

The learning that takes place during the creation and implementation of routines has been described by Nelson and Winter, who emphasise the contextualised nature of knowledge, thus suggesting an examination of the political dimensions of routine behaviour. As they observe, "a firm without a viable routine is a firm without a viable truce in intra organizational conflict" (Nelson and Winter 1982 pp.122-123). To summarize, when organizational changes are about to be implemented, management should take into account the mismatch between the interests of management and employees.

Empirical research shows that tensions and conflicts become acute when an organization tries to implement new decentralisation procedures that give rise to chaotic processes (Kaminska-Labbe and Thomas 2003). In this perspective, the case of Oticon and its "Spaghetti Organization" recently emphasized in the literature is of particular interest (Morsing 1998, Ravesi and Verona 2000; Foss 2003). The story of this organization shows the advantages and the limits of networking established in order to help implement new organizational practices. This company was famous for pushing organizational practices and human resources to extremes in order to be explicitly "knowledge based [...] with a multitude of non hierarchical structures [...] The aim was to construct a spontaneously working internal network that would work with only minimal intervention on the part of Kolind [the chief executive] and the managers" (Foss 2003, 333-34). During the 1990s Oticon's "Spaghetti Organization" was considered very successful in terms of learning and innovation due particularly to the "structural ambiguity" that prevailed when knowledge integration took place (Ravesi and Verona 2000). Despite this fact, this organizational form was gradually abandoned after 1996 and replaced by a certain degree of hierarchical order. The successes of the early 1990s had been reversed and the financial difficulties that ensued were responsible for the organisational changes, which were imposed in order to avoid bankruptcy. As Foss (2003) has pointed out, conflicts arise mainly when management choices are not made clear. Motivation plunders as staff face the inconsistencies produced by this kind of organisational form due to its impact on the allocation of resources, competencies, cost coordination, complex interactions, incentive systems, etc. Foss's case study is an excellent illustration of a network's superb ability to foster interaction when knowledge is being created and of its great weakness, the inability to produce a suitable degree of consistency in the presence of political tensions.

In what follows, we put forward a model capable of reproducing a network's properties as discussed above. The model depicts different groups trying to promote their own idiosyncratic routines and activated practices. The process of knowledge creation is constrained by the pressures imposed by a hierarchy, which introduces coordination mechanisms in an attempt to improve efficiency through the selection of particular practices.

Let us consider a firm organized around n interacting different groups ( i). Each group is endowed with its own idiosyncratic organizational practice. Given that different forms of knowledge are present within a firm, we assume that the routine selection process refers only to activated knowledge and, more specifically, to routines in operation, in other words, the organizational practices activated by the firm's members (see Lazaric and Mangolte 1999 and Lazaric 2000, on those specific aspects). We therefore limit the notion of routines to actual performance and do not consider knowledge that remains inert. A range of different methodologies can be used in order to analyse such routines or organizational practices (see Cohen et al. 1996, Lazaric 2000). On the one hand, they can be examined through the use of historical and ethno-methodological studies that attempt, in a qualitative manner, to understand the way routines change and are disrupted (Lazaric and Denis 2001, Edmondson et al. 2001). On the other hand, organizational practices can also be scrutinized from a quantitative perspective. While this approach does not reconstruct the historical and political context within which organizational practices operate, it provides us with a set of tools that can be used to compare different organizational set-ups. Laboratory experiments have also been conducted to shed light on the ways in which practices emerge at both individual and collective levels (Garapin and Hollard 1999, Betsch et al. 1998). Moreover, the question of routine selection has been tackled through the use of econometric studies (Greenan 2003, Caroli et al. 2001, Massini et al. 2002). In particular, Massini et al. focus on the adoption of new organizational practices like project-based work and decentralisation aimed at fostering and sharing knowledge. This kind of strategy, which allows Western innovative firms to adopt Japanese managerial practices, has been captured by Massini et al. through quantitative indicators showing relative adoption levels. We also make use of this kind of method in this paper and denote by xi(t) the level of activation of the organizational practices of group i at time t [3].

We assume that the level of effort of each group, ei(t), depends positively on the level of activation of its organizational practice, xi(t). Thus we have:

ei (t) = {xi (t)}ai, i = 1, …, n, (0.1)

where 0 < ai ≤ 1.

Since these practices are distributed, the task of the hierarchy is to achieve a minimal level of compatibility between them. The hierarchy tries to regulate the efforts exercised by different groups by promoting an average effort norm. Thus, the pressure of hierarchy for each group i, Hi(t) is given by the following relation:



Define by the knowledge component in each group. It is assumed that localized knowledge creation is stochastic and modelled in each group by a Poisson process with an arrival rate, λi = μi + ξ i, i = 1, …, n.

The first element μi, encapsulates the role played by the initial, or prior knowledge, ki0 > 0, i = 1, …, n, of each group in the process of knowledge creation. These levels, which refer to both tacit and articulated knowledge, are supposed to be randomly distributed among groups at time t = 0 and are time invariant. Thus we have for i = 1, …, n :


The second element ξ i, refers to the role played by interactions between groups in the process of localized knowledge creation. Interactions are modelled as a directed graph with nodes (denoted by i = 1, …, n) representing groups and links representing the cognitive interactions between the groups where two nodes are joined. Each interaction between two groups is assumed to be given by a single real number, lij ≥ 0, in order to link i to j, with lii = 0. Thus, the structure of interactions between the groups in the firm is completely specified by the non negative n × n matrix, Ω , which is supposed to be time invariant.

Let us define the number of interactions of group i, i = 1, …, n , by , and the total number of interactions by . For i = 1, …, n we have:


Hence, the cumulative distribution of knowledge creation in group i, i.e. the probability that knowledge in group i is created before t, is depicted by

Figure 1.

The flow probability of knowledge creation in group i, that is the probability that knowledge creation occurs now, is therefore, λi = μi + ξ i, i = 1, …, n. Hence, the knowledge component for group i, , finally comes down to:


where ei(t) refers to the effort of group i at time t.

Production in the firm, Q(t), is the outcome of the total level of effort E(t)resulting from the different groups. Accordingly we have:

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:


where Ψ is a positive, continuous, concave function.

Total profits are given by the profit 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.

Finally, we introduce a global level of control, c(t), which represents the choices made by the ownership structure of the firm. Accordingly, we suppose that owners only pay attention to the performance of the firm by comparing actual profitability, r(t), to some exogenous target, r*(t).[4] Thus, the level of control implemented at time t, c(t), is given by:

c(t)= Φ [ r(t)- r* (t)] (1.4)

(1.4) where, Φ is an increasing function of r(t)- r* (t), such that,



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.

It is now possible to characterize the evolution of the structure of the activated practices in the firm. This process is captured by the dynamics of the levels of activation of the different organizational practices xi (t)and modelled by a kind of replicator system of n differential equations with non-symmetric and non-local interactions. Indeed, these models are often used to study evolutionary dynamics among mutually interacting populations or agents (cf. e.g. Kauffman 1993, Sato and Crutchfield 2002). As is well known, population dynamics with hierarchical structures of this kind are closely related with Lotka-Volterra equations (Metcalfe 2003). Recently, Yokozawa and Hara (1999) and Sakaguchi (2003) developed replicator models with non-symmetric and non-linear population dynamics. Based on these assumptions, it is shown that both dynamically and evolutionarily stable solutions exist in a hierarchical structure. We adopt this perspective in this paper.

Accordingly, we suppose that dynamics are driven, for a given level of global control c(t), by the interplay between knowledge creation in each group and the pressure of hierarchy Hi(t) defined above. From this standpoint, we consider the following system of differential equations:


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.

In the remainder of the paper we conduct numerical simulations of this system to mimic some stylised examples of organizational dynamics discussed above.

When σ = 1 the model depicts the dynamics of the extreme classical hierarchy. The properties and robustness of this form have largely been studied in the managerial literature. As is well known, Crozier shed light both on inertia and on the political coalitions exemplifying this organizational set-up.

When σ = 0 the model becomes the network, which attracted a lot of attention during the last decade due to its ability to promote new organizational practices. According to Miles and Snow (1992, 1997) this organizational form conveys a high degree of learning by offering new opportunities of interactions and innovation patterns.

Apart from these two polar cases, a variety of intermediary configurations that are more empirically relevant today can be dealt by setting 0 < σ < 1. Consequently, we shall limit our investigation to the co-evolution of the political and cognitive dimensions in these configurations, where potential conflicts are a key element for stability and performance.

* Forces and limits of networking and hierarchical set-ups: some numerical illustrations

We distinguish between four intermediary organizational set-ups, based on the nature of the co-evolution of the political and cognitive dimensions: Restricting the number of groups to five in order to obtain tractable results on the interplay between cognitive and hierarchical dimensions in the intermediary cases, the following results obtain.[5]

Coherence of learning with strong hierarchical pressure

In this example σ = 0.85, which means that the impact of hierarchical pressure on the dynamics is quite important. Hierarchical forces and their consequent alignment of the cognitive and political dimensions drive the first organizational set-up.[6] Our main findings refer to the activation and selection of practices (Fig 3.1 a, b, c), the actions of the hierarchy (Fig. 3.1 d), local and global learning (Fig 3.1 d and Fig .3.1 f) and finally the profitability of this configuration. The following results obtain:

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

In this kind of organizational design, coordination mechanisms are sufficiently powerful to create an efficient selective process of the routines in operation. Coherent actions by the hierarchy induce the selection of two practices, which, following a degree of co-evolution at different stages, appear to be dominant. If the global learning mechanism appears to be rather efficient, profitability seems however to be quite inferior to the one obtained in different, more horizontal designs. This tends to show that hierarchical pressures are indeed very costly to monitor and may face unintended effects in terms of profitability.

A conflicting situation with strong hierarchical pressure

In this case, σ = 0.85. The weight of the hierarchy's pressure is more significant. In addition, this organizational set-up is characterised by a misalignment of prior knowledge and the efforts of each group, in other words, between the cognitive and the political dimension. We see discrepancies in the effort parameters, &alphai , of groups on the one hand, and their prior knowledge, ki0, on the other, as a source of potential conflicts.[7] Indeed groups here display different kinds of emulative behaviours, which can be more or less controlled by the hierarchy. Diversity of efforts among groups, for instance, may provoke some tensions potentially giving rise to conflicts in the firm that require costly adjustments in order to re-establish a certain degree of consistency within the firm. It is thus not surprising, compared to the previous case, that profits decrease and that a co-evolution of practices is observed.

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

A "peaceful" networking configuration with low hierarchical pressure

IIn this case σ= 0.15, which means that the impact of hierarchical pressure is low and that the dynamics are driven by the knowledge component. This organizational design is characterized by a high degree of cognitive interactions and by an alignment of the cognitive and the political dimension.[8] We obtain the following:

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

In this kind of organisation, where the hierarchical power is low, the creativity of groups is confirmed. This leads to high profitability and results in a significant learning process. Nevertheless, due to a lack of hierarchical pressures, this learning dynamic implies difficulties in the selection of organizational practices. In actual fact, three organizational practices are co-evolving in the firm. The richness of learning and knowledge in this context is counterbalanced by sluggish selective mechanisms, which can create difficulties in terms of short-term efficiency. In this specific configuration, the political and cognitive dimensions run smoothly and therefore inhibit the activation of potential conflicts.

A conflicting networking situation with low hierarchical pressure

IIn this intermediate case, where σ = 0.15, we consider different prior knowledge and effort parameters αi.[9] In this way we introduce potential conflicts and misalignment in the cognitive and political dimensions of the framework discussed above, which are characterized by a high degree of cognitive interactions and low hierarchical pressure. In the absence of a truce, the following results obtain:

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

In this design, groups have a sufficient degree of autonomy to promote their own organizational practices. Accordingly, two organizational practices are selected. However, it appears that the political and cognitive variables are not running smoothly. In other words, there exists some discrepancy between the effort implemented by these groups and their cognitive ability. This case, interpreted as a conflict situation, has many similarities with the Oticon "Spaghetti Organization" as it operated in the 1990s. Moreover, it appears that conflict gives rise to significant coordination costs, since profits are insufficient and the global learning mechanism is quite limited, as compared to the intermediate hierarchical and networking set-ups described above. This rather interesting result tends to prove that conflicts in organizations are very costly, not only because they inhibit the implementation of satisfactory routines, but also because latent conflicts may prevent routines in operation from running smoothly (Nelson and Winter 1982). The absence of truce observed by Nelson and Winter at the analytical level and the potential inefficiency and profitability of this organizational configuration seems to be confirmed by this case.

* Conclusion

This paper set out to explore the selection of routines within firms in different organizational settings. Numerical simulations have highlighted variations in the ability to learn in different organizational set-ups with diverse knowledge distributions. In hierarchical configurations, the ability to control organizational design and to select organizational practices is confirmed. This case, which is however also associated with low profits, has the advantages of coherence and of a satisfactory global learning function. In the networking configuration, coherence is more difficult to obtain and selective mechanisms are characterized by their slowness. Despite this fact, this design turns out to be highly profitable when the political and cognitive dimensions are running smoothly (and is indeed more profitable than the previous configuration). However, when the political and cognitive dimensions are dissonant and when conflicts persist, profits appear to be quite low (i.e. inferior to the hierarchical configuration and to the "peaceful networking configuration"). These findings echo the Oticon case study recently reported in the literature (see for example Foss 2003).

Networking designs are more profitable organizational configurations because of their learning dynamic but that they are also very sensitive to the truce problem. When conflicts are present the profitability of this design becomes surprisingly low, thus compromising the configuration's chances of survival in the long term. Secondly, this result tends to support the evolutionary view of the firm and the problem of latent conflicts introduced by Cyert and March (1963), later also taken up and redeveloped by Nelson and Winter and further enhanced by Foss (2003), which show the limits of non-hierarchical organizational set-ups.

At an analytical level, our results illustrate the delicate character of leadership in the presence of distributed knowledge. The problem of knowledge selection at a collective level is difficult because co-ordination is never neutral at a political level. Authority is key (Foss and Foss 2003) in giving a sense to the selective process and the motivation of employees. While our results share a part of the theoretical vision of hierarchy developed by Foss and Foss (2003), the conclusions are complementary despite the fact that our purpose is not to investigate the power and limits of authority but the ability of hierarchy to impose levels of control on knowledge production. A key issue for a future research agenda is an examination of the interaction between external constraints arising from the environment and the internal atmosphere in more depth in order to balance hierarchical attitudes in the selective mechanisms and fluctuating degrees of control within the firm.

* Notes

1 This point was put forward a long time ago by Barnard (1938), who suggested that formal hierarchy could be limited in its ability to govern if it failed to gain the acceptance and support of an organisation’s informal hierarchy.

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


αi δ i ki0




In this configuration without conflict, all prior knowledge and effort parameters are identical in the different groups.

7 This means that effort parameters and prior knowledge differ among groups. We have:

Table 2a: Prior knowledge of groups i

k10k20k30 k40k50

Table 2b: Effort parameters of groups i


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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