Cycles in revealed preference data are often interpreted as fundamental units of choice-theoretic inconsistency. We fully characterize the manner in which the structure of a choice environment can lead to non-trivial dependence relations between cyclic choice patterns in data. We show that for any finite data set, while there may not be a unique maximal independent collection of choice cycles that explain the entirety of the inconsistency, the size of any such collection of cycles is well-defined. We utilize this to provide a means of controlling for the influence of experimental structure in the construction of inconsistency indices for choice data.
We investigate the manner in which the power of the weak axiom of revealed preference is affected by the completeness of the choice environment. We fully characterize those domains on which the weak axiom coincides with strong rationalizability for arbitrary choice correspondences. We also provide a related result that characterizes those domains on which the strong rationalizability of a choice correspondence is equivalent to (i) the satisfaction of the weak axiom, and (ii) the strong rationalizability of its restrictions to suitable collections of small sets. Our proof technique involves a generalization of many of the differential concepts of classical demand theory to the abstract choice model. We conclude with an application to the problem of aggregating incomplete preferences.
We analyze mergers and entry in a differentiated products oligopoly model of price competition. We prove that any merger among incumbents is unprofitable if it spurs entry sufficient in magnitude to preserve consumer surplus. Thus, mergers occur in equilibrium only if barriers limit entry. Numerical simulations indicate that with profit-neutral mergers the best-case for consumers entry mitigates under 30 percent of the adverse price effects and, in most cases, under 50 percent of the consumer surplus loss. The results suggest a limited and conditional role for entry analysis in merger review.