Learning in games with strategic complementarities revisited

Fictitious play is a classical learning process for games, and games with strategic complementarities are an important class including many economic applications. Knowledge about convergence properties of fictitious play in this class of games is scarce, however. Beyond games with a unique equilibrium, global convergence has only been claimed for games with diminishing returns [V. Krishna, Learning in games with strategic complementarities, HBS Working Paper 92-073, Harvard University, 1992]. This result remained unpublished, and it relies on a specific tie-breaking rule. Here we prove an extension of it by showing that the ordinal version of strategic complementarities suffices. The proof does not rely on tie-breaking rules and provides some intuition for the result.