# Modeling Firm Search and Innovation Trajectory Using Swarm Intelligence
## 5 Model Comparison  
The proposed swarm-based search model differs from the two complementary models (i.e., NK and multiarmed bandit) in multiple ways. First, the best application differs across the models. NK is ideally suited to examine complexity, which is a useful way to represent knowledge recombination or the interdependencies between elements in an organizational design problem. Researchers use multiarmed bandit models to model the exploration-exploitation problem. Neither of these models ideally fits the objective of modeling a firm's search across innovation topics. Second, the models differ in how they utilize performance feedback. In NK, the \(N\) and \(K\) parameters create a potentially rugged performance or fitness landscape that provides information to the firm as it searches. The multiarmed bandit model reveals information on payoffs as the agent makes commitments to search a particular dimension (e.g., pulls a particular lever). In our current version of the swarm search model, feedback is defined by empirically estimated performance based on observed outcomes. The firm's best performance is allowed to influence the direction of search. The NK and multiarmed bandit allow for more complex feedback; for instance, the agent searching a landscape may be allowed to view performance of other locations. Third, the models differ in how the general environment and the action of competitors (or other agents) influence search behavior. Neither NK nor bandit models are optimized for competitive dynamics. Environmental change typically comes into these models in a simple way, by exogenously shocking payoffs. The swarm search model can capture a richer set of competitive behaviors. Overall, these models appear optimized for different tasks and therefore are complementary. Table 7 summarizes the key differences in these models as applied to firm search. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Year** & \(\mathbf{W_{C}}\) & \(\mathbf{W_{A}}\) & \(\mathbf{W_{L}}\) & \(\mathbf{W_{P}}\) \\ \hline
1997 & 0.005 & 0.049 & 0.178 & 0.768 \\ \hline
1998 & 0.023 & 0.114 & 0.078 & 0.785 \\ \hline
1999 & 0.120 & 0.123 & 0.129 & 0.629 \\ \hline
2000 & 0.162 & 0.364 & 0.128 & 0.345 \\ \hline
2001 & 0.152 & 0.251 & 0.101 & 0.496 \\ \hline
2002 & 0.118 & 0.251 & 0.094 & 0.537 \\ \hline
2003 & 0.111 & 0.404 & 0.035 & 0.450 \\ \hline
2004 & 0.209 & 0.240 & 0.059 & 0.492 \\ \hline
2005 & 0.102 & 0.419 & 0.033 & 0.446 \\ \hline
2006 & 0.038 & 0.571 & 0.042 & 0.349 \\ \hline
2007 & 0.132 & 0.593 & 0.015 & 0.259 \\ \hline \hline \end{tabular} \(C\) = cohesion, A = alignment, L = following the leader, P = performance feedback.  
\end{table} 
Table 6: _Cont._ \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Swarm Search** & **NK** & **Multiarmed Bandit** & \\ \hline \multirow{3}{*}{\begin{tabular}{c} Example model \\ application: \\ \end{tabular} } & \multirow{3}{*}{\begin{tabular}{c} Search across \\ innovation topics \\ \end{tabular} } & \multicolumn{1}{c}{\begin{tabular}{c} Organizational \\ complexity; \\ \end{tabular} } & \multirow{3}{*}{\
\begin{tabular}{c} Tradeoffs between \\ exploration and \\ exploitation \\ \end{tabular} } & \multirow{3}{*}{
\begin{tabular}{c} Example model \\ application: \\ \end{tabular} } \\ \cline{1-1}  & & & \\ \hline Number of firms: & Can handle many firms & A representative firm & A representative firm & Number of firms: \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison across models on various dimensions important to firm search. To understand the differences in application, compare this paper with a study by [PERSON] (2017) [75], which uses the NK model to generate predictions regarding the performance-knowledge recombination relationship and then tests these predictions empirically using patent data in US Patent Class 360.