Extended proper equilibrium

Paul Milgrom, Joshua Mollner*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We introduce extended proper equilibrium, which refines proper equilibrium (Myerson, 1978) by adding across-player restrictions on trembles. This refinement coincides with proper equilibrium in games with two players but adds new restrictions in games with three or more players. One implication of these additional restrictions is that any tremble that is costless in equilibrium is regarded by all as more likely than any costly tremble, even one by a different player. At least one extended proper equilibrium exists in every finite game. The refinement can also be characterized in terms of a symmetric, meta-version of the game in which players originate from a common pool: if these players tremble symmetrically and in the way of proper equilibrium, then the induced play in the original game is an extended proper equilibrium.

Original languageEnglish (US)
Article number105258
JournalJournal of Economic Theory
StatePublished - Jun 2021


  • Equilibrium refinement
  • Extended proper equilibrium
  • Generalized second-price auction
  • Proper equilibrium
  • Trembles

ASJC Scopus subject areas

  • Economics and Econometrics


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