Two remarks on Blackwell's theorem

Ehud Lehrer*, Eran Shmaya

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

In a decision problem with uncertainty a decision maker receives partial information about the actual state via an information structure. After receiving a signal, he is allowed to withdraw and gets zero profit. We say that one structure is better than another when a withdrawal option exists if it may never happen that one structure guarantees a positive profit while the other structure guarantees only zero profit. This order between information structures is characterized in terms that are different from those used by Blackwell's comparison of experiments. We also treat the case of a malevolent nature that chooses a state in an adverse manner. It turns out that Blackwell's classical characterization also holds in this case.

Original languageEnglish (US)
Pages (from-to)580-586
Number of pages7
JournalJournal of Applied Probability
Volume45
Issue number2
DOIs
StatePublished - Jun 2008

Keywords

  • Bayesian decision problem
  • Blackwell's comparison of experiments
  • Minimax
  • Withdrawal option

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty

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