Extensive Robustness Revisited

Ehud Kalai

In "Large Robust Games" (Econometrica, forthcoming), Kalai shows that inone-simultaneous-move Baysian games with many semi-anonymous players all the equilibria are (approximately) extensively robust. This means that the equilibria survive even if the one-simultaneous-move assumption is relaxed to allow for many variations. These include sequential moves with repeated revisions of choices, information leakage, commitments, cheap talk and more. In addition to its own interest, the above result has the following implications:

1. A stronger purification result than Schmeidler's about the equilibria of Normal form games with a continuum of anonymous players,
2. Ex-post stability property of games with many players, and
3. Strong rational expectations property for market games with independent types.

The current paper shows that in the same class of games studied above oneobtains a significantly stronger, yet simpler to describe, version of the extensive robustness property.