A Global Game with Heterogenous Priors

TL;DR

This paper investigates how heterogeneity in agents' prior beliefs affects equilibrium outcomes in a global game, revealing conditions under which unique or multiple equilibria emerge, and highlighting the stabilizing role of public signals.

Contribution

It extends the global game framework by relaxing the common prior assumption, deriving conditions for equilibrium multiplicity or uniqueness with heterogeneous priors, and analyzing the impact of public signals.

Findings

Unique equilibria occur with substantial public disagreement.

Equilibrium multiplicity depends on private signal precision and prior heterogeneity.

Public signals of high quality can ensure equilibrium uniqueness.

Abstract

This paper relaxes the common prior assumption in the public and private information game of Morris and Shin (2000, 2004). For the generalized game, where the agent's prior expectations are heterogenous, it derives a sharp condition for the emergence of unique/multiple equilibria. This condition indicates that unique equilibria are played if player's public disagreement is substantial. If disagreement is small, equilibrium multiplicity depends on the relative precisions of private signals and subjective priors. Extensions to environments with public signals of exogenous and endogenous quality show that prior heterogeneity, unlike heterogeneity in private information, provides a robust anchor for unique equilibria. Finally, irrespective of whether priors are common or not, we show that public signals can ensure equilibrium uniqueness, rather than multiplicity, if they are sufficiently precise.