Iterated generalized half-dominance and global game selection

We offer an equilibrium characterization of a general class of global games with strategic complementarities. The analysis highlights a form of acyclicity in the interim belief structure of global games, which allows us to formalize a selection criterion, iterated generalized half-dominance. This criterion is shown to be a unique global game selection when noise distributions satisfy a regularity condition. A similar logic also applies to the perfect foresight dynamics of Matsui and Matsuyama (1995); an iterated generalized half-dominant equilibrium is a unique globally stable state when agents are patient enough. The criterion is especially useful for games with more than two asymmetric players, and can be easily applied to local interaction games with an arbitrary network structure.