# Modeling Firm Search and Innovation Trajectory Using Swarm Intelligence
## 2 Background
The NK performance landscape can be used to represent a variety of complex organizational problems that have a performance landscape that the simulated managers can \"search.\" The more rugged the landscape (higher K), the more challenging the search process and the greater chance that simple sequential search strategies will result in low performance ([PERSON], 2018). For instance, a simple search strategy in which the manager changes one component at a time is unlikely to effectively identify a global optimum in a rugged landscape. Prior research has applied NK to a number of business problems in which the firm must search for a solution among many interdependent elements. For instance, researchers have used NK to examine adaptation to a changing external environment ([PERSON] and [PERSON], 2018, 2019), the influence of organizational design on search ([PERSON] and [PERSON], 2018, 2019), coordination within a multi-business firm ([PERSON], 2019), and innovative search within ecosystems ([PERSON], 2019). Although the NK model has proven to be a powerful tool, it has several limitations when applied to the study of a firm's search for innovations. First, the NK model focuses on search on the performance landscape without incorporating any other influences. Therefore, the model has a firm-centric focus. Second, the ability to incorporate information from the environment is limited. For instance, [PERSON] (1997) incorporated environmental change into the NK model through a reorientation of the entire landscape. There does not appear to be an easy way to incorporate multiple sets of competitor actions or complex external dynamics into the model. Another useful (but less used) formulation to study firm search behavior is the multiarmed bandit model. The literature on economics, strategy, and computer science uses the multiarmed bandit model to represent exploration-exploitation problems. The model allows for the study of how managers allocate resources or make search decisions under payoff uncertainty ([PERSON] and [PERSON], 2018). For example, [PERSON] and [PERSON] (2012) used the multiarmed bandit model to examine exploration and exploitation in response to environment change. Like the NK model, it is difficult to incorporate non-firm centric information in a rich way. In [PERSON] and [PERSON]'s study, they only incorporated environmental information as a stochastic shock to the payoff values. Overall, NK and Bandit models do not appear to be easily extended to incorporate the search behaviors of other actors, thereby prompting the need for a different approach. Swarm intelligence offers another approach to dynamic search problems. Inspired by the natural world ([PERSON], 2018), swarm intelligence systems use a population of independent agents that can be made to interact with their environment and with each other ([PERSON], 2018, 2019). Swarm intelligence has found a wide set of applications in the physical and social sciences. One of the most fruitful areas of application has been the study of optimization problems ([PERSON], 2018, 2019). Particle swarm optimization (PSO) moves 'particles' around a search space to discover the best position (global optimum) ([PERSON], 2018). In the standard PSO, particles are guided by simple formulas that define their velocities and update their positions in the search space. PSO algorithms have been improved and extended to increase their speed, accuracy, and ability to tackle more difficult optimization problems ([PERSON], 2018, 2019; [PERSON], 2019). See [PERSON], [PERSON], and [PERSON] (2018) for a survey of the PSO literature ([PERSON], 2018). Prior literature in business and economics has used swarm intelligence, particularly PSO, to solve business-related optimization problems. For instance, in the field of financial economics, particle swarm has been used for portfolio optimization ([PERSON], 2018), efficient frontier estimation ([PERSON], 2018), interest rate modeling ([PERSON], 2018), and earnings forecasting ([PERSON], 2018).