Avoiding Complexity Catastrophe in Coevolutionary Pockets: Strategies for Rugged Landscapes
Authors: McKelvey Bill 
Published: October 2008

Can firms and coevolutionary groups suffer from too much interdependent complexity? Is complexity theory an alternative explanation to competitive selection for the emergent order apparent in coevolutionary industry groups? The biologist Stewart Kauffman suggests a theory of complexity catastrophe offering universal principles explaining phenomena normally attributed to Darwinian natural selection theory. Kauffman's complexity theory seems to apply equally well to firms in coevolutionary pockets. Based on complexity theory, four kinds of complexity are identified. Kauffman's “NK[C] model” is positioned “at the edge of chaos” between complexity driven by “Newtonian” simple rules and rule-driven deterministic chaos. Kauffman's insight, which is the basis of the findings in this paper, is that complexity is both a consequence and a cause. Multicoevolutionary complexity in firms is defined by moving natural selection processes inside firms and down to a “parts” level of analysis, in this instance Porter's value chain level, to focus on microstate activities by agents. The assumptions of stochastically idiosyncratic microstates and coevolution in firms are analyzed. Competitive advantage, as a dependent variable, is defined in terms of Nash equilibrium fitness levels. This allows a translation of Kauffman's theory to firms, paying particular attention to (1) how value chain landscapes might be modeled, (2) assumptions underlying Kauffman's models making them amenable to firms, and (3) a delineation of seven of Kauffman's computational experiments. As part of the translation, possible parallels between the application of complexity catastrophe theory to coevolutionary pockets and studies by institutional theorists and social network analysts are discussed. The models derive from spin-glass microstate models resulting in Boolean games. Kauffman's Boolean statistical mechanics is introduced in developing the logic underlying the somewhat simplified NK[C] model. The model allows the use of computational experiments to better understand how the dependent variable—value chain fitness—is affected by changes in the number of internal interdependencies K, the number of coevolutionary links with opponents C, the size of the coevolutionary pocket S, and the number of simultaneous adaptive changes, among other things. Various computational experiments are presented that suggest strategic organizing approaches most likely to foster competitive advantage. High or low Nash equilibrium fitness levels are shown to result from internal and external coevolutionary densities as a function of links among value chain competencies within a firm and between a firm and an opponent. Complexity phenomena appear to suggest a number of expected (and thus validating) and surprising strategies with respect to complex organizational interdependencies. For example, moderate complexity fares best and external coevolutionary complexity sets an upper bound to advantages likely to be gained from internal complexity. Various complexity “lessons” are discussed. Models such as the NK[C] could offer insights into strategic organizing.