TL;DR
The paper analyzes the Namer-Claimer game, showing that with optimal play, the game length grows on the order of log log n, revealing insights into the game's complexity.
Contribution
It establishes the asymptotic order of the game's length as log log n under optimal strategies for both players.
Findings
Game length is of order log log n with optimal play.
Optimal strategies lead to this asymptotic behavior.
Provides a mathematical analysis of the game's complexity.
Abstract
In each round of the Namer-Claimer game, Namer names a distance d, then Claimer claims a subset of [n] that does not contain two points that differ by d. Claimer wins once they have claimed sets covering [n]. I show that the length of this game is of order log log n with optimal play from each side.
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