ABSTRACT
Even if curved Bernoulli functions have not given us a better understanding of individual behavior, it could be argued that that might not be reason enough to abandon them. Perhaps they may yet help us better understand and predict aggregate phenomena in important industries and markets. An analogy from physics: myriad individual water molecules in a river move randomly in Brownian motion, yet important properties of the river are captured in the laws of hydrodynamics. Our inability to predict the movement of individual molecules does not prevent us from designing and operating pumps and turbines that depend on the highly predictable behavior of aggregates. A biological analogy: the aggregate behavior of an ant colony is described by very different principles than the individual behavior of its members (Kirman [1993]). In economics, we know that market outcomes can exhibit a degree of rationality that exceeds that of individual traders (e.g., Gode and Sunder [1993], Jamal, Maier, and Sunder [2012]).
