Epistemic Foundations of Focal Points: Common Knowledge and Posterior Beliefs

Focal points are central to equilibrium selection in coordination games. This paper provides an epistemic analysis of focal-point implementation in a standard state-space framework. Building on the Schelling-Lewis view that focal points involve salience and mutual expectations, we model focality as state-dependent and ask when it supports equilibrium play. We first formalize common-knowledge focal points and then introduce posteriorbelief focal points (µ-focal points), which replace common knowledge of salience with posterior certainty about salience. We show that commonknowledge focal points imply µ-focal points and that posterior certainty about focality is sufficient for focal-point play.