A Generalized Macaulay Theorem and Generalized Face Rings

We prove that the $f$-vector of members in a certain class of meet semi-lattices satisfies Macaulay inequalities. We construct a large family of meet semi-lattices belonging to this class, which includes all posets of multicomplexes, as well as meet semi-lattices with the "diamond property", discussed by Wegner, as spacial cases. Specializing the proof to that later family, one obtains the Kruskal-Katona inequalities and their proof as in Wegner's. For geometric meet semi lattices we construct an analogue of the exterior face ring, generalizing the classic construction for simplicial complexes. For a more general class, which include also multicomplexes, we construct an analogue of the Stanley-Reisner ring. These two constructions provide algebraic counterparts (and thus also algebraic proofs) of Kruskal-Katona's and Macaulay's inequalities for these classes, respectively.Comment: Final version: 13 pages, 2 figures. Improved presentation, more detailed proofs, same results. To appear in JCT

Recent Developments in Empirical IO: Dynamic Demand and Dynamic Games

Empirically studying dynamic competition in oligopoly markets requires dealing with large states spaces and tackling difficult computational problems, while handling heterogeneity and multiple equilibria. In this paper, we discuss some of the ways recent work in Industrial Organization has dealt with these challenges. We illustrate problems and proposed solutions using as examples recent work on dynamic demand for differentiated products and on dynamic games of oligopoly competition. Our discussion of dynamic demand focuses on models for storable and durable goods and surveys how researchers have used the \Industrial Organization; Oligopoly competition; Dynamic demand; Dynamic games; Estimation; Counterfactual experiments; Multiple equilibria; Inclusive values; Unobserved heterogeneity.

MEASURING MARKET POWER USING DISCRETE CHOICE MODELS OF DEMAND: AN APPLICATION TO THE READY-TO-EAT CEREAL INDUSTRY

Market power, consumer demand, cereal industry, Demand and Price Analysis,