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.

We investigate the effect of scale on performance in the active money management industry. We first document that fund returns, both before and after fees and expenses, decline with lagged fund size, even after accounting for various performance benchmarks. We then explore a number of potential explanations for this relationship. This association is most pronounced among funds that have to invest in small and illiquid stocks, suggesting that these adverse scale effects are related to liquidity. Controlling for its size, a fund's return does not deteriorate with the size of the family that it belongs to, indicating that scale need not be bad for performance depending on how the fund is organized. Finally, using data on whether funds are solo-managed or team-managed and the composition of fund investments, we explore the idea that scale erodes fund performance because of the interaction of liquidity and organizational diseconomies.