Game theory has had a deep impact on the theory of industrial organization, in a similar (but less controversial) way as the rational expectations revolution in macroeconomics. The reason it has been embraced by a majority of researchers in the field is that it imposes some discipline on theoretical thinking. It forces economists to clearly specify the strategic variables, their timing, and the information structure faced by firms. As is often the case in economics, the researcher learns as much from constructing the model (the extensive form) as from

Drew Fudenberg, and Jean Tirole, “The Fat-Cat Effect, the Puppy-Dog Ploy, and the Lean and Hungry Look”, in Industrial Organization, Oliver E. Williamson (ed.), Edward Elgar Publishing, 1990, pp. 450–455.

We argue that some, but not all, superstitions can persist when learning is rational and players are patient, and illustrate our argument with an example inspired by the Code of Hammurabi. The code specified an “appeal by surviving in the river” as a way of deciding whether an accusation was true. According to our theory, a mechanism that uses superstitions two or more steps off the equilibrium path, such as “appeal by surviving in the river,” is more likely to persist than a superstition where the false beliefs are only one step off the equilibrium path.

We model the joint distribution of choice probabilities and decision times in binary decisions as the solution to a problem of optimal sequential sampling, where the agent is uncertain of the utility of each action and pays a constant cost per unit time for gathering information. We show that choices are more likely to be correct when the agent chooses to decide quickly, provided the agent’s prior beliefs are correct. This better matches the observed correlation between decision time and choice probability than does the classical drift-diffusion model (DDM), where the agent knows the utility difference between the choices.