Convergence of the quantile admission process with veto power

Naomi Dvora Feldheim*, Ohad Noy Feldheim

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

The quantile admission process with veto power is a stochastic process suggested by Alon, Feldman, Mansour, Oren and Tennenholtz as a model for the evolution of an exclusive social club. Each member is represented by a real number (his opinion). On every round two new candidates, holding i.i.d. μ-distributed opinions, apply for admission. The one whose opinion is minimal is then admitted if the percentage of current members closer in their opinion to his is at least r; otherwise, neither is admitted. We show that for any μ and r, the empirical distribution of opinions in the club converges a.s. to a limit distribution. We further analyse this limit, show that it may be non-deterministic and provide conditions under which it is deterministic. The results rely on a coupling of the evolution of the empirical r-quantile of the club with a random walk in a changing environment.

Original languageAmerican English
Pages (from-to)4294-4325
Number of pages32
JournalStochastic Processes and their Applications
Volume130
Issue number7
DOIs
StatePublished - Jul 2020

Bibliographical note

Publisher Copyright:
© 2019 Elsevier B.V.

Keywords

  • Admission process
  • Evolving sets
  • Random walk in changing environment
  • Social groups

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