# Search on an NK Landscape with Swarm Intelligence: Limitations and Future Research Opportunities
## 1 Introduction  
Firm managers are often faced with complex problems that require searching across many, potentially interdependent elements in order to make a choice with significant financial consequences [1]. Examples include developing new products, designing organizational processes, or assembling resources. To examine these problems, strategic management and organizational science scholars often employ simulations of search strategies [2]. To evaluate strategy performance, scholars typically apply the search strategy to a performance or fitness landscape. The leading tool for this, the NK model, has been highly influential in the strategy and management science literature and has been applied to a variety of search problems [3]. Using NK, the researcher can create a performance landscape consisting of \(N\) components with \(K\) interdependencies. As \(K\) increases, the landscape becomes more rugged, with more peaks and valleys [4]. Recently, scholars interested in how competitors influence firm search have turned to swarm intelligence models [5]. Unlike previous firm search models that focused only on the firm's own performance feedback, swarm models allow for the various behaviors of other firms to influence the focal firm's search strategy. For instance, [PERSON], [PERSON], and [PERSON] (2023) develop a swarm intelligence model that provides a flexible way to incorporate a range of competitive influences, and they demonstrate how to use patent filings and patent citation data to fit the model parameters and assess search performance [5]. However, to investigate many problems, scholars will want to develop simulations to enable them to abstract from the constraints of real-world data. Swarm simulations appear to have manypromising applications for firm search and choice problems, but to utilize simulations effectively, the researcher needs to devise a performance landscape in order to evaluate the effectiveness of different search strategies. The best way to form a search landscape for swarm remains unclear. A natural place to start is to simulate swarm search on the current leading landscape tool--NK. In this paper, we assess whether NK provides a suitable performance landscape to conduct realistic swarm-based simulations of firm behavior. Note that our focus is not on evaluating the effectiveness of our swarm algorithm on the NK landscape, as one might evaluate the effectiveness of different optimization models to solve a particular problem; rather, we want to know if the swarm-NK combination allows one to study firm search phenomena in a realistic and insightful manner. We apply the Boids-based algorithm of [PERSON] et al. (2015) to various NK landscapes. We find that because search on an NK landscape is limited to movements along the hypercube rather than continuous movements in real space, we cannot harness the full power of our swarm model. In fact, we can only have one variable influence search at a time, thus collapsing our multivariate model into a simple univariate model. Therefore, using NK to generate the performance landscape constrains our swarm model from incorporating a full range of information from the environment. A different way to generate the performance landscape is needed to harness the full potential of our swarm model. Through our investigation, we also uncover a variety of potential technical needs that could allow strategy and organizational scholars to apply swarm models in a richer way. Our main contribution is identifying necessary features (such as more appropriate landscape attributes) to improve swarm search. We hope that by identifying these gaps, researchers, including those in computer science and adjacent fields, can contribute to the development of swarm search and its application to firm search and decision-choice problems. We briefly summarize the potential research directions below. Future Research Directions
* A payoff landscape or function that allows for continuous movement so that the full value of swarm in modeling agent (firm or human) behavior can be realized.