Extended Proper Equilibrium
57 Pages Posted: 13 Sep 2017 Last revised: 21 Dec 2020
Date Written: December 20, 2020
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.
Keywords: equilibrium refinement, trembles, extended proper equilibrium, proper equilibrium
JEL Classification: C72
Suggested Citation: Suggested Citation