Incomplete information games, local interaction games and random matching games are all special cases of a general class of interaction games (Morris (1997)). In this paper, we use this equivalence to present a unified treatment of arguments generating uniqueness in games with strategic complementarities by introducing heterogeneity in these different settings. We also report on the relation between local and global heterogeneity, on the role of strategic multipliers and on purification in the three types of interaction game.