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Uniqueness of optimal strategies in Captain Lotto games

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  • Nadav Amir

    (The Hebrew University of Jerusalem)

Abstract

We consider the class of two-person zero-sum allocation games known as Captain Lotto games (Hart in Int J Game Theory 45:37–61, 2016). These are Colonel Blotto type games in which the players have capacity constraints. We consider the game with non-strict constraints, and with strict constraints. We show in most cases that when optimal strategies exist, they are necessarily unique. When they don’t exist, we characterize the pointwise limit of the cumulative distribution functions of $$\varepsilon $$ ε -optimal strategies.

Suggested Citation

  • Nadav Amir, 2018. "Uniqueness of optimal strategies in Captain Lotto games," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(1), pages 55-101, March.
    • Handle: RePEc:spr:jogath:v:47:y:2018:i:1:d:10.1007_s00182-017-0578-6
    DOI: 10.1007/s00182-017-0578-6
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