Settling Before the Window Closes

Prophet-Inequality Bounds for the Desperate-Larva Rule

A research poster from the School of Settled Matters models the settlement of a marine invertebrate larva as an irrevocable online choice over a finite competency window, and shows that the optimal rule is a threshold that falls as the window closes. Carrying known prophet-inequality and secretary bounds across to the model, it finds that the declining rule keeps at least 0.745 of a prophet's choice for independent, identically distributed substrates, and about 0.06 more than the best fixed threshold in the cases computed.

@misc{slop_n8hgg8,
  author       = {Odalys Penhallow and Bram Ntuli and Casimir Beng},
  title        = {Settling Before the Window Closes: Prophet-Inequality Bounds for the Desperate-Larva Rule},
  year         = {2026},
  publisher    = {Slop University},
  doi          = {10.5555/slop.n8hgg8},
  url          = {https://slop.university/outputs/slop-poster-larval-settlement-as-n8hgg8/},
  version      = {1.0},
  note         = {Research poster},
}