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Within a slightly modified version of Hotelling's model we reconsider the claim that the threat of entry induces existing firms to produce a larger number of products than they would otherwise. We show that entry deterrence, although optimal, need not be achieved through product proliferation. In some cases the incumbent monopolist resorts to an entry-deterring strategy based on location choice rather than product proliferation. We also show that in some cases the number of products chosen by the incumbent facing the threat of entry is strictly greater than the minimum number required to deter entry.

We establish a correspondence between the rationalizability of choice studied in the revealed preference literature and the notion of minimal belief revision captured by the AGM postulates. A choice frame consists of a set of alternatives , a collection E of subsets of (representing possible choice sets) and a function f : E ! 2 (representing choices made). A choice frame is rationalizable if there exists a total pre-order R on such that, for every E 2 E, f (E) coincides with the best elements of E relative to R. We re-interpret choice structures in terms of belief revision. An interpretation is obtained by adding a valuation V that assigns to every atom p the subset of at which p is true. Associated with an interpretation is an initial belief set and a partial belief revision function. A choice frame is AGM-consistent if, for every interpretation of it, the associated partial belief revision function can be extended to a full-domain belief revision function that satis…es the AGM postulates. It is shown that a …nite choice frame is AGM-consistent if and only if it is rationalizable.

Since belief revision deals with the interaction of belief and information over time, branching-time temporal logic seems a natural setting for a theory of belief change. We propose two extensions of a modal logic that, besides the next-time temporal operator, contains a belief operator and an information operator. The first logic is shown to provide an axiomatic characterization of the first six postulates of the AGM theory of belief revision, while the second, stronger, logic provides an axiomatic characterization of the full set of AGM postulates.