Response to "Aristocratic Equilibria"

A major point of Cole, Mailath, and Postlewaite (1992) is that the existence of nonmarket decisions leads naturally to multiple equilibria and, consequently, the possibility that ex ante identical societies might exhibit different patterns of economic growth. It was further argued that the multiplicity was not driven by technical aspects of the model but arose naturally from the economic structure of the problem. In that paper, we focused on two particular types of equilibria: wealth-isstatus and aristocratic. Unfortunately, the argument in that paper for the existence of aristocratic equilibria is incorrect, as the comment by Steven Landsburg points out. Landsburg does provide a condition (condition 1: There is a positive measure of males with zero wealth) that guarantees the existence of aristocratic equilibria. The purpose of this response is, first, to argue that the existence of aristocratic equilibria in environments not covered by condition 1 is important and, second, to demonstrate by example that aristocratic equilibria do exist in some such environments. The reason that aristocratic equilibria exist in a narrower set of environments than wealth-is-status equilibria is easy to understand. In wealth-is-status equilibria, women always accept the offer made by the wealthiest suitor, and the parents' matching (as opposed to saving) behavior has no impact on the ability of a son to match with a highendowment woman. Loosely speaking, wealth-is-status equilibria involve "myopically" optimal or Markovian behavior (behavior that depends on only the payoff relevant aspects of history). Other equilibria, in contrast, require some degree of intergenerational enforcement, since in such equilibria some women will be accepting offers to match from men other than the wealthiest suitor. Such behavior can be optimal only if deviations from the prescriptions of the social norm result in future negative consequences (e.g., a loss of