# Modeling Firm Search and Innovation Trajectory Using Swarm Intelligence
## 2 Background  
Research on firm search traces its roots back to the early literature on the behavioral theory of the firm [7]. Unlike neoclassical economics that tends to treat decision makers as hyperrational with the ability to search over all possible solutions, the behavioral theory of the firm postulates that managers have imperfect information and are boundenly rational, thus willing to make satisfactory rather than optimal decisions [8]. Therefore, when faced with a problem, firms typically conduct a \"local search\"--searching for solutions within the neighborhood of their current knowledge. Building on these concepts, classic work in evolutionary economics suggests that the firm's search process will lead it to be \"path-dependent\" [9]--i.e., the technological topics the firm searches today will influence what technological problems it will search and solve in the future [10; 11]. (Note that we incorporate the possibility of path dependence in our model). Much of the recent search-related literature on innovation and technology strategy has focused on four questions related to firm search. First, what strategies can firms use to overcome path dependence and perform distant search effectively [12; 13; 14; 15; 16; 17; 18]? Second, how can firms effectively balance exploration of new and exploitation of current knowledge and capabilities [19; 20; 21; 22; 23; 24]? Third, what can be learned about search by studying individuals or teams [25; 26; 27; 28; 29; 30]? Fourth, how does competition share search strategies [31; 32; 33; 34; 35]? While prior research has studied all of these questions using qualitative arguments and reduced-form empirical models, simulation tools have only been applied to the first three. Scholars examining firm search and innovation trajectories have long relied on simulation models to illuminate new insights [3] For instance, scholars like Nobel Prize and Turing winner [PERSON], whose work on the decision-making processes within firms formed the early foundation of the behavioral theory of the firm, suggested that simulation models were useful tools for studying firm search and decision problems and he helped pioneer the development and application of such models in his analysis of problem-solving behavior in organizations [36]. Since then, many of the most influential papers on firm search and learning have used simulations (e.g., [PERSON] (1991)) [37]. The most popular model used to study search and organizational learning is the NK model, originally developed by biologist [PERSON] [38]. The NK model uses two parameters to create a potentially rugged fitness or performance landscape--with \(N\) capturing the number of elements in the landscape and \(K\) capturing the extent to which the elements are interdependent. The points on the landscape represent a combination of choices among the N elements and the height of the landscape at a particular point represents performance. The performance contribution of each component (\(c_{i}\)) depends on \(K\) other interdependent components. Therefore, the performance of a position on the NK landscape is determined by the sum of the component-level performance contributions for that position. This value is typically normalized by dividing it by \(N\) so that performance can be compared across landscapes with different values for \(N\). The smoothest landscape occurs when \(K=0\), where all components are independent and only one optimum is defined. As \(K\) increases, the landscape becomes more peaked and rugged, with peaks varying in height, creating multiple local optima. The landscape is most rugged when \(K=N-1\), i.e., all components are dependent on all other components. At a peak, changing the value of one component will not improve performance, instead, the values of multiple components must change for performance to improve. See [PERSON] (2018) for more technical details about NK landscapes ([PERSON], 2018).