# Modeling Firm Search and Innovation Trajectory Using Swarm Intelligence
## 6 Discussion  
In the current model specification, we allow for firms to follow their own feedback (\(w_{P}\)), follow the leader (\(w_{L}\)), move to the current location of their competitors (cohesion, \(w_{C}\)), or move in the direction of where competitors are headed (alignment, \(w_{A}\)). We also define separation per the original Boids program (\(w_{S}\)). Below we discuss each of these factors and how they might be augmented for future research. Firm Feedback/Path Dependency  
We take a simple approach to modeling the firm's own feedback, using only a parameter that captures of how the firm's best performing location influences its movement through topic space. Anchoring on best performance has a parallel in the literature on NK modeling where the firm searches for the highest peak on the performance landscape. Future work could embellish this equation to capture the complexities of how the firm's own search history influences its future search behavior. For instance, the firm's prior search trajectory (rather than its best performance), represented by prior (lagged) positions in search space, could be included to model search inertia. In addition, variables that capture prior changes in performance on the performance landscape (e.g., lagged values along the gradient) could be added to incorporate more complex information on performance feedback into the model. Uncertainty, like in the bandit model, could be added by including feedback noise. We offer two simple approaches to modeling leader-following behavior. Firms can follow a global leader or a local leader, defined by a function or the firm's choosing. By modifying how to specify the leader(s), future work can fit the model to a wide range of behaviors proposed by strategy management and organizational theory literature. Competing theories on imitation, differentiation, and the general influence of a firm's peers can be tested or simulated using this framework. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Swarm Search** & **NK** & **Multiarmed Bandit** \\ \hline \multirow{4}{*}{Performance feedback:} & \multirow{4}{*}{Simple feedback based on estimated performance performance between elements} & N and K parameters define fitness landscape & Performance of different ’arms’ can have different payoffs drawn from a probability distribution & \\  & & N and  
Note that leader-following behavior does not appear to be prominent in our demonstration sample. This is not surprising given that these are the 'leading' firms in terms of patenting during out sample period. However, smaller firms and less technologically sophisticated firms may display a range of interesting behaviors. Prior literature suggests that such firms may follow cues of the leaders, which would appear as following the leader in our model. Other work suggests that firms might steer away from more technologically sophisticated leaders. Future work could use our model to shed light on these behaviors. Cohesion  
In a typical swarm model of animal behavior, cohesion represents how closely the focal actor stays to the center mass of the group. By adjusting cohesion, more concentrated (higher cohesion) or more diffuse (lower cohesion) swarming behaviors can be simulated. Applied to firm search, the current specification for cohesion represents the extent to which firms cluster in similar areas in topic space. To simulate a wide range of imitative behavior proposed in the sociology, organizational theory, or strategy literature, this equation can be adjusted by changing the set of firms in the reference group. The cohesion equation can also be extended to incorporate other information, such as multiple reference groups or performance-weighted reference groups, which can allow the research to closely map extant theories. Alignment  
In a typical swarm model of bird behavior, alignment represents how agents move towards the heading of their reference agents.