Moving Off NK Models' Local Peak: Introducing Structured Interaction Landscape Networks

Abstract

The innovation of modeling firm search behavior using NK fitness landscapes is twenty years old, but despite the potential of this method its adoption remains sparse. This is likely be due to three reasons. First, many questions of current interest are not amenable to the classic NK model formulation, especially those involving the structure of interactions within firms. Second, rugged landscapes for larger N values are impossible to conceptualize. Third, generating landscapes of significant scale can be computationally intensive. We introduce and extend two innovations, the NM parametric formulation of fitness landscapes and the LON mapping of landscapes, that resolve these issues. The maximal order of interaction specification~(NM) greatly simplifies the landscape computational requirements as well as provides a straightforward, transparent and consistent method of defining interaction structure within a landscape with varying degrees of interaction~(K). We extend the NM specification by introducing the Structured Interaction NM~(SINM) specification. The local optima network~(LON) mapping of a landscape provides insights into landscape structure through a meaningful visualization of the entire landscape, as well as searchability metrics that allow for relevant comparisons between landscapes. By combining these innovations, we can directly structure the interactions in a landscape and then describe how this structure affects the landscape's searchability characteristics. We demonstrate that these searchability characteristics are different for structured and random landscapes, and furthermore that these characteristics actually represent differences in ease of search with a simple iterated search algorithm. We close by considering applications for the application of agent based models with strategic management.