Some Notes on Learning in Games with Strategic Complementarities

Fictitious play is the classical myopic learning process, and games with strategic complementarities are an important class of games including many economic applications. Knowledge about convergence properties of fictitious play in this class of games is scarce, however. Beyond dominance solvable games, global convergence has only been established for games with strategic complementarities and diminishing marginal returns (Krishna, 1992, HBSWorking Paper 92-073). This result is known to depend critically on the assumption of a tie-breaking rule. We show that restricting the analysis to nondegenerate games allows us to drop this assumption. More importantly, an ordinal version of strategic complementarities turns out to suffice. As a byproduct, we also obtain global convergence in generalized ordinal potential games with diminishing marginal returns.