# Search on an NK Landscape with Swarm Intelligence: Limitations and Future Research Opportunities
## 3 Swarm Intelligence Algorithms
### Mathematical Development of Swarm
Such an approach could illuminate questions regarding whether incorporating information on rivals benefits the focal firm's search strategy when the extent to which payoffs to the same position vary across firms. #### 7.2.3 Incomplete Information

Swarm search typically allows the agent to absorb information from a reference group in its complete form. In other words, the agent has complete information on the location and performance of those in the reference group (i.e., \(F\) in Equation (7)). In reality, the focal firm is unlikely to know the exact performance of those in the reference group or to be able to link the position in space (e.g., position in knowledge space) to the performance of the firm. Therefore, adding noise to the signal through a random error term or devising other means of making the signal incomplete could have useful applications to the study of search under uncertainty. #### 7.2.4 Costly Movements

To our knowledge, most search papers allow for the costliest movements across the landscape. In the application of firm search for technological innovations, moving across knowledge topics or technologies is not costless. Incorporating costs could have several benefits. First, incorporating costly movement into the model can allow researchers to better compare search strategies that incur different costs. For instance, local search--searching in the neighborhood of the firm's location on the landscape--could be less costly than distant search--searching in faraway neighborhoods--as the costs of discovery of new (to the firm) knowledge likely vary based on the firm's current knowledge stock (as given by the firm'scurrent and prior positions on the landscape). Second, firms may differ in their cost of search due to their unique external factors (e.g., firm-specific access to the labor market or their own cost of capital) or internal factors (e.g., firm-specific resources and capabilities). Optimal search strategies may differ as these factors differ, and a cost function could allow the researcher to easily incorporate such elements into the model framework. Third, budget constraints could be combined with costs to simulate a resource-constrained search. ## 8 Conclusions

Recent work by [PERSON] et al. (2023) proposes using swarm-bases search to examine how competitors influence search. Although [PERSON] et al. demonstrate how to fit swarms to data, many problems related to competitive dynamics and search will be better examined with simulation. However, the literature has not considered how to best build a landscape to study firm search with swarms. We apply swarm search to the workhorse landscape model in strategy and organizational search literature--NK. While scholars have generated many valuable insights into firm decision problems using search on NK landscapes, we find that it is not well suited for swarm. We discuss these limitations and identify multiple research opportunities to improve landscapes as well as other features that could improve swarm's ability to address search problems. We hope to encourage those working with algorithms, such as scholars in computer science and related fields, to help develop tools that can be applied to firm and agent choice problems. Conceptualization, R.-R.C., C.D.M. and P.K.T. ; methodology, R.-R.C. and C.D.M. ; formal analysis, R.-R.C. ; investigation, R.-R.C., C.D.M. and P.K.T. ; resources, R.-R.C. and C.D.M. ; writing--original draft preparation, R.-R.C. and C.D.M. ; writing--review and editing, R.-R.C., C.D.M. and P.K.T. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Data Availability Statement: Data are contained within the article. The authors declare no conflict of interest. ## References

* (1) [PERSON]; [PERSON]; [PERSON] Effective search in rugged performance landscapes: A review and outlook. _J. Manag._**2019**, _45_, 285-318. [CrossRef]
* (2) [PERSON]; [PERSON] Simulation modelling and business strategy research.