When Does Learning in Games Generate Convergence to Nash Equilibria? The Role of Supermodularity in an Experimental Setting

This study clarifies the conditions under which learning in games produces convergence to Nash equilibria in practice. Previous work has identified theoretical conditions under which various stylized learning processes achieve convergence. One technical condition is supermodularity, which is closely related to the more familiar concept of strategic complementarities. We experimentally investigate the role of supermodularity in achieving convergence through learning. Using a game from the literature on solutions to externalities, we systematically vary a free parameter below, close to, at and beyond the threshold of supermodularity to assess its effects on convergence. We find that supermodular and "near-supermodular" games converge significantly better than those far below the threshold. From a little below the threshold to the threshold, the improvement is statistically insignificant. Within the class of supermodular games, increasing the parameter far beyond the threshold does not significantly improve convergence. Simulation shows that while most experimental results persist in the long run, some become more pronounced.