Problem. Prove that under the optimal strategy (for minimizing mean cost) the mean cost \( \mathbb{E} Y_n \) converges to some limit constant, and determine that constant.
This incomplete 2008 draft by Aldous-Angel-Berestycki provides numerical bounds and a conjectured expression for the limit in terms of a PDE on the infinite simplex, but we do not have a rigorous proof that the limit exists.
History. Mentioned to many people since 2008 but not posted here until 2018.
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