This study clarifies the conditions under which learning in games produces convergence to Nash equilibria in practice. We experimentally investigate the role of supermodularity, which is closely related to the more familiar concept of strategic complementarities, in achieving convergence through learning. Using a game from the literature on solutions to externalities, we find that supermodular and "near-supermodular" games converge significantly better than those far below the threshold of supermodularity. From a little below the threshold to the threshold, the improvement is statistically insignificant. Increasing the parameter far beyond the threshold does not significantly improve convergence.
Chen, Yan and Robert Gazzale.
2004."When Does Learning in Games Generate Convergence to Nash Equilibria? The Role of Supermodularity in an Experimental Setting."American Economic Review,
94(5): 1505-1535.DOI: 10.1257/0002828043052349