O modelo NK de Kauffman - uma introdução

"An important contribution of Kauffman's work is the finding that the topography of the fitness landscape is determined by the degree of interdependence of the fitness contribution of the various attributes (genes) of an organism. In the literature on population genetics, such interaction effects are termed epistatic effects. If organizational fitness is highly interactive, that is the value of a particular feature of the organization depends on a variety of other features of the organization, then the fitness landscape will tend to be quite rugged. (Moi ici: Fundamental este ponto.

Não há uma receita única!!!) In such a setting, even if only one element is changed, the fitness contribution of those attributes that did not change might still be affected.
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Despite the importance of such interactive effects on fitness, much of the population genetics literature, as well as the organizations' literature, has tended to treat facets of the organism (organization) as if their fitness contribution is independent of other attributes of the organism (organization). Kauffman (1993) has developed a simple but powerful analytic structure to represent epistatic interactions, which he terms the NK model. An entity, an organization for our purposes here, is characterized as consisting of N attributes where each attribute can take on A possible values. Thus, the fitness space consists of A (elevado a) N possible types of organizations. The degree to which the fitness of the organization depends on interaction effects among the attributes is specified by the variable K. In particular, the contribution of a given attribute of the organization to the organization's overall fitness is assumed to be influenced by K other attributes. Therefore, if K equals zero, then the contribution of each element of the organization (such as strategy, personal system, structure, etc.) is independent of all other attributes. At the other extreme, if K equals N − 1, then the fitness contribution of any one attribute depends on the value of all other attributes of the organization. As a result, adjacent locations in the fitness space need not have similar fitness values. In this sense, the value K determines the intensity of interaction effects and, in turn, how rugged or correlated is the fitness space.
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Consider the problem of identifying a coherent set of policies, that is a set of behaviours for which there are positive complementarities. This is a problem of finding an attractive peak in a rugged fitness landscape. If organizational capabilities are an outcome of such a search process, what general statements can we make about such a process?
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Intelligent, non-exhaustive, search processes are sensitive to the topography of the problem space being explored. This may be the actual topography or, as in many efforts at calculative rationality, a representation of the actual topography.
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At one level, this sensitivity to the topography is a statement of minimal intelligence of the search process. Clearly, if a search process is to reflect any intelligence, it should be sensitive to the fitness value of alternative locations in the space of possible solutions. In particular, the engineering challenge is to design an algorithm that is effective at finding extreme points in such a space.
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However, search processes tend to be sensitive to the topography of the solution space in a stronger sense as well. The particular extreme value that is identified by a given algorithm is typically sensitive to the initial proposed solution at which search started. Furthermore, the extreme value that is identified will be (or quite close to) a local peak in the solution space.


Consider the outcome of a process of local search on a rugged landscape. In particular, suppose that search takes the form of examining alternatives in the immediate neighborhood of the current proposed solution and that search ceases when a local optimum is obtained. Finally, imagine carrying out a large number of such search efforts at randomly chosen starting locations in the space of possible solutions. Except by chance, the initial ‘solutions’ for each of the search efforts will differ. However, after a few iterations of local search, the number of distinct solutions will decline radically. This reduction in the number of identified ‘solutions’ reflects the fact that while the solutions were initially distributed randomly in the landscape, many initial starting points share the same local optimum. Kauffman (1993) terms the set of locations in the landscape for which local search results in a common local optimum as belonging to a common ‘basin of attraction’.
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The number of local optima that are reached increases as the landscape becomes more ‘rugged’. In particular, consider the landscape that results when K = 0. As noted earlier, when K = 0 there is a single maximum in the space of alternative solutions. If a policy array is located at any point other than the optimum, there is a location in the immediate neighborhood, involving a change in a single attribute that enhances performance. Since K = 0, changing this attribute improves the performance independent of the other N−1 attributes. Therefore, a process of local search results in a ‘walk’ to the optimum from all starting positions.


For K > 0, the landscape has multiple local optima. More generally, as K increases the landscape becomes less correlated and the number of local optima increases. (Moi ici: Estão a ver as consequências? Pode-se competir de muito mais maneiras do que simplesmente pelo preço/custo!!!) As a result, search efforts may become ‘trapped’ at a suboptimal local peak. (Moi ici: E não só, não é tudo falta de visão para descobrir o pico máximo, é também o leque de opções deixado aberto pelo espaço de MInkowski. è possível visionar picos mais atraentes mas reconhecer que não se tem ADN empresarial para lá chegar e triunfar de forma sustentada) This property is clearly an implication of the limited nature of local search. The ‘ruggedness’ of the landscape has an impact on organizational form to the extent that there are peaks and valleys beyond the ‘vision’ of the search algorithm. Thus, greater vision attenuates the effect of a given level of K. However, as long as the search effort is not exhaustive, the qualitative properties of search leading to, possibly inferior, local peaks remains. Furthermore, the number of such peaks increases with K for a given range, or vision, of neighborhood search.
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This analysis of local search in complex landscapes has important implications for contingency theory arguments regarding variation in organizational forms in a population. Contingency theory is typically expressed as an argument for a correspondence between facets of organizations and features of the environment in which organizations function. In this discussion of movement on rugged fitness landscapes, all organizations face the same environment. What differs is their initial composition. As a result of these different starting points, organizations are led to adopt distinct organizational forms. Local search in a multi-peak landscape results in organizational adaptation being path-or history-dependent. (Moi ici: Cá está o espaço de Minkowski) As a result, the observed distribution of organizational forms in a population may reflect heterogeneity in the population of organizations at earlier points in time rather than variation in niches in the environment, as suggested by ecological analyses, or a set of distinct external conditions, as generally suggested by contingency theories."
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Isto faz-me pensar numa outra consequência... a exploração que uma empresa faz na paisagem enrugada em busca da optimização do seu desempenho pode levar aquilo a que se chamam estratégias puras... (estratégias puras e híbridas - o dilema: parte I e parte II, ou seja, não há almoços grátis) estratégias puras geram maiores retornos mas têm um problema...
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Empresas que seguem estratégias puras são menos robustas a enfrentar alterações importantes no meio abiótico!!! Quanto mais interdependência, quanto mais sinérgico for o mosaico, maior o compromisso com determinada visão do futuro do meio abiótico... e se este muda... menor a flexibilidade da empresa, Minkowski outra vez, para recuar para uma posição anterior e recomeçar a busca numa paisagem alterada.

Empresa (ponto vermelho) aperfeiçoa-se para trepar de 1 para 2 e de 2 para 3. Quando começa a pensar em chegar a uma etapa 4...
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Oooppsss!
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Uma alteração imprevista do meio abiótico baralha os planos da empresa que aterrou na etapa 4.
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E quem garante que a alteração no meio abiótico não terá réplicas que fragilizarão ainda mais a posição competitiva da empresa?
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Em Portugal a reacção típica nestas circunstâncias é pedir ajuda ao governo... ou seja, adiar o inevitável... como as escolas privadas hoje em dia. Recordarei sempre o exemplo da Pirelli.
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Trecho retirado de capítulo 13 "Organizational Capabilities in Complex" de Daniel Levinthal que faz parte do livro “The Nature and Dynamics of Organizational Capabilities”, editado por Giovanni Dosi, Richard R. Nelson, Sidney G. Winter.