architecture-rivalry-imitation-mirage

The Architecture of Rivalry and Imitation Mirages: How Activity System Interdependence Shapes Competitive Convergence and Divergence Abstract. Two mature research traditions each formalize half the interdependence system that governs competitive search. NK landscape models formalize how activity architecture shapes search on rugged fitness landscapes but assume independent search; no firm observes a rival's configuration. Competitive dynamics research studies observation, imitation, and rivalry but lacks a formal model of the internal architecture determining whether copied activities create synergies or dissynergies. We integrate both traditions by introducing the {K} interdependence system, a typology identifying four coupled types of interdependence (Scope, Epistasis, Popularity, and Sociality) within a Logit-NK simulation that is a form of stochastic actor-oriented model (SAOM). Monte Carlo experiments crossing activity system architectures with competition regimes demonstrate that the architecture of activity interdependence determines whether imitation produces convergence or divergence, a structural reversal that resolves contradictions between the resource-based view's prediction that imitation erodes heterogeneity and recent evidence that it can increase it. The simulation further reveals that competition mechanisms function as risk management devices under environmental shocks, and that architecturally determined "imitation mirages" systematically confound observed imitation returns. Because each coupling enters as a distinct, manipulable parameter, the simulation enables counterfactual decomposition of imitation and rivalry, mechanisms that are empirically confounded but theoretically opposed. The {K} framework's Sociality coupling further provides a micro-foundation for the mutual forbearance mechanism central to multimarket competition theory, endogenizing rivalry through activity-level overlap rather than exogenous market co-presence. Keywords: competitive dynamics, NK landscapes, activity systems, imitation, simulation