The Benefits of Fractionation in Competitive Resource Allocation

Findings on Mosaic Warfare from a Colonel Blotto Game

“…This result suggests that it is generally wise for the monolithic player to allocate platforms preferentially to battlefields where both of their resources are used and for the Mosaic player to allocate platforms to battlefields that require only one capability. A more detailed discussion and mathematical proof of this result can be found in Grana, Lamb, and O'Donoughue, 2020. This heterogeneity of battlefields breaks the dependence of prior results on force size, because the ability of the monolithic force to efficiently allocate its resources is no longer improved with larger force sizes. This is effectively a handicap on the monolithic force, which must concentrate on battlefields that require all of the capabilities or else risk wasting some capabilities on battlefields that do not value them, while the Mosaic force is capable of allocating capabilities only to battlefields where they will have a positive impact.…”

“…Additionally, the Mosaic force's expected utility advantage decreases as the total number of resources increases. The technical mechanism behind these results is discussed in Grana, Lamb, and O'Donoughue, 2020. From a high-level perspective, as the overall force becomes large compared with the number of resources per monolithic platform (which can be thought of as clumps of resources), the disadvantages of that clumping are mitigated for the monolithic force.…”

“…That is, we examine whether it is better to have several different capabilities aggregated onto one platform or several platforms that each have one capability. A detailed discussion of heterogeneous Blotto games, including the formulation that we employed in this study, is provided in Grana, Lamb, and O'Donoughue, 2020. The solutions to our games employ a mixed strategy. In game theory, a mixed strategy is one in which players strategically randomize their specific actions to remain unpredictable.…”

Acquiring a Mosaic Force: Issues, Options, and Trade-Offs

“…A complete survey of the Mosaic warfighting concept is beyond the scope of this report but can be found in other sources (Clark, Patt, and Schramm, 2020;Deptula et al, 2019;Grana, Lamb, and O'Donoughue, 2020;O'Donoughue, McBirney, and Persons, 2021). For the purposes of this research, we accept without question the via-bility and virtues of Mosaic Warfare from a technological and operational perspective so that we may focus on its acquisition-related implications.…”