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• To impose or exploit complexity is to take an action that increases an aspect of the complexity of the environment in a way that makes it more difficult for an adversary to make decisions or to operate, essentially shaping conditions to favor Blue. Thus, to conduct a complexity attack is to take an action that exploits characteristics of complex adaptive systems (CAS) in a way that will have a deliberate negative effect on the adversary.
• Applying a CAS lens to warfare is useful to understand how a planner might leverage complexity to U.S. advantage.
• Four general categories of U.S. actions benefit from the CAS's nature of adversary decision processes. These are degrading the operational picture, impairing adversary response, spanning organizational boundaries, and exploiting nonlinearities.
• The difference between complexity exploitation and more-traditional actions are that a complexity-based response reshapes an adversary's decision calculus, while more-traditional options simply lower the probability associated with a given transition from one decision step to the next.
• U.S. actions on the adversary's decision points in a military vignette can be represented by CAS characteristics that are represented in a Markov chain.
• Understanding the underlying transition matrix structure (or associated directed graph) tells us some fundamental things about complexity (e.g., the creation of feedback loops).
• Developing a model with defined probabilities, while challenging, may provide additional insights for warfighting.

The United States should aim to minimize the element of complexity for itself while maximizing it for its adversary in great-power competition and warfare. Multidomain actions are viewed as imposing complexity on the adversary's decision process. There is a current lack of understanding about how to impose complexity to maximize operational effects. Science and technology investments are not presently aligned to quantify complexity, measure its operational effects, or determine how to impose it and thus shape adversary behavior.

The research outlined in this report includes a literature review to ground the complexity characterization in warfare. Historical case studies of warfare and competition and workshops verify and validate the characterization. The complexity lens, developed by RAND Corporation researchers, can be applied to warfighting by leveraging emerging multidomain operations (MDO) concept of operations (CONOP) from recent wargames and surveying historical case studies. The authors also provide four concrete example vignettes to examine.

The U.S. Air Force should apply a complexity lens to review ongoing and future efforts to best leverage complexity to U.S. decision advantage. Efforts that can leverage complex adaptive systems thinking include the science and technology research agenda, MDOs planning, and MDO effectiveness evaluation. Pacific Air Forces and U.S. Air Forces in Europe should integrate complexity lens thinking into existing tabletop and command post exercises to help evaluate multidomain courses of action during operational planning.

• Chapter One

  Complexity Imposition: The Hypothesis

• Chapter Two

  Complex Adaptive Systems

• Chapter Three

  Application of the Complex Adaptive System Lens to a Mission Vignette

• Chapter Four

  Conclusions and Recommendations