Tolerance and herd behavior: Sophistication of ideas under payoff complementarity

In this paper, I first show that there may be inefficient herd behavior even with a continuous choice set and a continuous loss function if there is payoff complementarity. Then, I show that the probability of inefficient herd behavior is asymptotically zero and the choice sequence converges to the optimal one almost surely if people have even a small amount of tolerance that they are willing to accept one another as a partner in joint work. This result is closely related to the argument in J. S. Mill's On Liberty, where he states that tolerance for others' ideas is essential for sophistication of ideas.