[Available theorems establishing the existence of general equilibrium in models incorporating imperfectly competitive firms rely on the assumption that reaction curves are continuous functions (or convex-valued, upper hemi-continuous correspondences). However, this property has not been derived from conditions on the fundamental data of tastes, technology, and maximizing behavior. We show here that continuity may fail even in extremely simple cases, with the result that equilibrium price and/or quantity choices fail to exist. The non-pathological nature of the examples we present suggests the need for a fundamental re-examination of the way our partial and general equilibrium models of monopolistic competition fit together.]

Consider a Bayesian collective decision problem in which the preferences of agents are private information. We provide a general demonstration that the utility costs associated with incentive constraints become negligible when the decision problem is linked with a large number of independent copies of itself. This is established by defining a mechanism in which agents must budget their representations of preferences so that the frequency of preferences across problems mirrors the underlying distribution of preferences, and then arguing that agents' incentives are to satisfy their budget by being as truthful as possible. We also show that all equilibria of the linking mechanisms converge to the target utility levels. The mechanisms do not require transferable utility or interpersonal comparisons of utility, and are immune to manipulations by coalitions.