Homotopy types of box complexes

In [MZ04] Matousek and Ziegler compared various topological lower bounds for the chromatic number. They proved that Lovasz's original bound [L78] can be restated as \chr G \geq \ind (\B(G)) +2. Sarkaria's bound [S90] can be formulated as \chr G \geq \ind (\B_0(G)) +1. It is known that these lower bounds are close to each other, namely the difference between them is at most 1. In this paper we study these lower bounds, and the homotopy types of box complexes. Some of the results was announced in [MZ04].Comment: 11 page

Screening Contracts in the Presence of Positive Network Effects

Based on the critical assumption of strategic complementarity, this paper builds a general model to describe and solve the screening problem faced by the monopolist seller of a network good. By applying monotone comparative static tools, we demonstrate that the joint presence of asymmetric information and positive network effects leads to a strict downward distortion for all consumers in the quantities provided. We also show that the equilibrium allocation is an increasing function of the intensity of network effects, and that a discriminating monopoly may supply large quantities for all consumers than a competitive industry.network effects, strategic complementarities, contracting with externalities, second-degree discrimination, monotone comparative statics

Estimating the Lock-in Effects of Switching Costs from Firm-Level Data

This paper proposes a simple method for estimating the lock-in effects of switching costs from firm-level data. We compare the behavior of already contracted consumers to the behavior of new consumers as the latter can serve as contrafactual to the former. In panel regressions on firms' incoming and quitting consumers, we look at the differential response to price changes and identify the lock-in effect of switching costs from the difference between the two. We illustrate our method by analyzing the Hungarian personal loan market and find strong lock-in effects.switching costs, lock-in, panel data

Debreceni Ember Pál könyvtára

Ez a tanulmány a kora újkori szerző virtuális könyvtárát vizsgálja, annak lehetséges összeállását, és statisztikai adatait közli

Box complexes, neighborhood complexes, and the chromatic number

Lovasz's striking proof of Kneser's conjecture from 1978 using the Borsuk--Ulam theorem provides a lower bound on the chromatic number of a graph. We introduce the shore subdivision of simplicial complexes and use it to show an upper bound to this topological lower bound and to construct a strong Z_2-deformation retraction from the box complex (in the version introduced by Matousek and Ziegler) to the Lovasz complex. In the process, we analyze and clarify the combinatorics of the complexes involved and link their structure via several ``intermediate'' complexes.Comment: 8 pages, 1 figur