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The Benefits of Fractionation in Competitive Resource Allocation

Author

Listed:
  • Jonathan Lamb

    (Pardee RAND Graduate School)

  • Justin Grana

    (Microsoft Corporation and Pardee RAND Graduate School)

  • Nicholas O’Donoughue

    (RAND Corporation)

Abstract

We leverage a new algorithm for numerically solving Colonel Blotto games to gain insight into a version of the game where players have different types of resources. Specifically, the winner of a battlefield is a function of a multi-dimensional allocation vector of each player. Our main focus is on the potential benefits of fractionation, which we define as the degree to which a player can quantize its resources. When players only have one type of resource, we show that the benefits to fractionation are in general, greatest in resource poor environments and against aggregated adversaries. We then extend the model to include random dropout and show that fractionation increases robustness to failure in resource poor environments but not resource rich environments. Finally, we show that when players have different types of resources, the benefits of fractionation are no longer mitigated by an increase in the total force size. Since many real-world resource allocation problems are multi-dimensional, our results illustrate the importance of analyzing multi-resource Blotto games in tandem with the traditional specification.

Suggested Citation

  • Jonathan Lamb & Justin Grana & Nicholas O’Donoughue, 2022. "The Benefits of Fractionation in Competitive Resource Allocation," Computational Economics, Springer;Society for Computational Economics, vol. 59(2), pages 831-852, February.
    • Handle: RePEc:kap:compec:v:59:y:2022:i:2:d:10.1007_s10614-021-10108-7
    DOI: 10.1007/s10614-021-10108-7
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    References listed on IDEAS

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