# Search on an NK Landscape with Swarm Intelligence: Limitations and Future Research Opportunities
## 3 Swarm Intelligence Algorithms
### Mathematical Development of Swarm
from search is thereby eliminated, which constrains the swarm model's ability to address interesting search problems. Second, in our application of the NK landscape, we assume that all firms face the same performance landscape, which may not be realistic. Returns to a position on the landscape could be a function of other firm factors, such as unique resources and capabilities, not captured in the simulation model. This poses no problem for most researchers who apply NK to model one agent's search but could make multiagent search unrealistic if agents are heterogeneous. Note that such a problem is not specific to NK landscapes but is true for any payoff structure that does not vary across agents. Nevertheless, to make the best use of swarm, a more flexible performance landscape structure is needed. Overall, the benefits of the NK landscape for individual search limit its ability to appropriately capture a landscape suitable for multiagent search where agents influence each other's search trajectories through multiple variables. ## 7 Directions for Future Research

In this section, we discuss how future research can address gaps in swarm modeling as applied to firm search. ### The Need for a Flexible Landscape

The stylized 3-D representation of the NK landscape, as seen in Figure 3, depicts landscapes of different ruggedness, and this stylized view provides powerful insights into the challenges of search. To reap the benefits of swarm models in their application to firm search, researchers need a way to create multidimensional landscapes that can capture the same essence of 'varying ruggedness' but can be searched by multiple agents in a continuous way. Those in computer science or related fields that work on search algorithms can contribute to the strategy and management science literature by developing methods of creating such landscapes. Some scholars have begun to examine this problem [55]. ### Landscape and Search Process Extensions

Researchers interested in firm/agent search could benefit from the development of several extensions to performance landscapes and search processes. Below, we call for several extensions that, when combined with swarm, could allow the model to better illuminate the challenges of developing search strategies in the real world. #### 7.2.1 Endogenous Landscapes

From our understanding, the prior literature using search simulations has only considered exogenously given payoffs or performance landscapes. In such work, users generate a landscape based on some parameters and then analyze the search on the landscape. The agent's position on the landscape does not affect the payoff, which of course makes sense for many of the research questions in which single agent search has been applied. In the analysis of multiagent search, it can make sense for agent positions to alter the payoffs. Consider simulating a firm search across innovation topics, according to [PERSON] et al. (2023). One might expect that the more firms that develop products using the same knowledge, the lower the returns on using such knowledge. From the perspective of the performance landscape, the height of the hill (payoff) falls as more agents take a position on the hill. Endogenizing the landscape in this way can allow researchers to examine more nuanced strategies that better reflect the reality of market competition. #### 7.2.2 Agent-Specific Landscapes

As discussed in the limitations section above, it is unrealistic to believe that firms with varying endowments of resources and capabilities will perform in the same way by taking the same position on the landscape. To incorporate heterogeneity in the search-performance relationship without directly modeling the heterogeneity, future work could model each agent (firm) on their own landscape. Information about other agents and their payoffs in their own landscapes could be incorporated into the focal agent's search in its own landscape.