The Asymmetric Colonel Blotto Game

Yifan Zhu Shanghai Foreign Language School

Arithmetic Geometry and Commutative Algebra mathscidoc:1801.07001

Yau Science Award (Math), 2017.12
This paper explores the Nash equilibria of a variant of the Colonel Blotto game, which we call the Asymmetric Colonel Blotto game. In the Colonel Blotto game, two players simultaneously distribute forces across n battlefields. Within each battlefield, the player that allocates the higher level of force wins. The payo↵ of the game is the proportion of wins on the individual battlefields. In the asymmetric version, the levels of force distributed to the battlefields must be nondecreasing. In this paper, we find a family of Nash equilibria for the case with three battlefields and equal levels of force and prove the uniqueness of the marginal distributions. We also find the unique equilibrium payo↵ for all possible levels of force in the case with two battlefields, and obtain partial results for the unique equilibrium payo↵ for asymmetric levels of force in the case with three battlefields.
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  title={The Asymmetric Colonel Blotto Game},
  author={Yifan Zhu},
  booktitle={Yau Science Award (Math)},
Yifan Zhu. The Asymmetric Colonel Blotto Game. 2017. In Yau Science Award (Math).
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