Distance-based kernels for real-valued data

We consider distance-based similarity measures for real-valued vectors of interest in kernel-based machine learning algorithms. In particular, a truncated Euclidean similarity measure and a self-normalized similarity measure related to the Canberra distance. It is proved that they are positive semi-definite (p.s.d.), thus facilitating their use in kernel-based methods, like the Support Vector Machine, a very popular machine learning tool. These kernels may be better suited than standard kernels (like the RBF) in certain situations, that are described in the paper. Some rather general results concerning positivity properties are presented in detail as well as some interesting ways of proving the p.s.d. property.Peer ReviewedPostprint (author's final draft

Completing contracts ex post: How car manufacturers manage car dealers

This article illustrates how contracts are completed ex post in practice and, in so doing, indirectly suggests what the real function of contracts may be. Our evidence comes from the contracts between automobile manufacturers and their dealers in 23 dealership networks in Spain. Franchising dominates automobile distribution because of the need to decentralize pricing and control of service decisions. It motivates local managers to undertake these activities at minimum cost for the manufacturer. However, it creates incentive conflicts, both between manufacturers and dealers and among dealers themselves, concerning the level of sales and service provided. It also holds potential for expropriation of specific investments. Contracts deal with these conflicts by restricting dealers’ decision rights and granting manufacturers extensive completion, monitoring and enforcement powers. The main mechanism that may prevent abuse of these powers is the manufacturers’ reputational capital.Franchising, incomplete contracts, self-enforcement, automobile