Maximal-Element Rationalizability

We examine the maximal-element rationalizability of choice functions with arbitrary domains. While rationality formulated in terms of the choice of greatest elements according to a rationalizing relation has been analyzed relatively thoroughly in the earlier literature, this is not the case for maximal-element rationalizability, except when it coincides with greatest-element rationalizability because of properties imposed on the rationalizing relation. We develop necessary and sufficient conditions for maximal-element rationalizability by itself, and for maximal-element rationalizability in conjunction with additional properties of a rationalizing relation such as reflexivity, completeness, P-acyclicity, quasi-transitivity, consistency and transitivity. Financial support through grants from the Social Sciences and Humanities Research Council of Canada, the Fonds pour la Formation de Chercheurs et l'Aide à la Recherche of Québec, and a Grant-in-Aid for Scientific Research for Priority Areas from the Ministry of Education, Culture, Sports, Science and Technology of Japan is gratefully acknowledged. Thanks are also due to the editor and the two referees for the opportunity to improve the exposition of this paper.     

Sourcing Decisions with Competitive Suppliers and Imperfect Information

Manufacturers often must choose between outsourcing and producing internally. This choice is complex and influenced by a variety of factors, including the costs and capabilities of the potential suppliers. In addition, if the manufacturer outsources, he must design the sourcing process. We study the manufacturer's outsourcing decision, with a focus on the impact of the sourcing process on that decision. We consider a setting in which the manufacturer has imperfect information regarding the suppliers' costs and capabilities, and we assume that the manufacturer uses a two‐stage sourcing process. The first stage is the qualification stage, in which the manufacturer seeks to reduce the uncertainty regarding the suppliers' capabilities. The second stage is the supplier selection stage, in which the manufacturer selects among the qualified suppliers on the basis of price. We first characterize the optimal design of the two‐stage process, and then consider the outsourcing decision. We demonstrate several trade‐offs. Vertical integration enables the manufacturer to reduce uncertainty and extract all of the profits of production. However, outsourcing enables the manufacturer to take advantage of the (potentially) lower costs and higher capabilities of the suppliers, particularly if competition between suppliers can be encouraged. We find that the manufacturer is more likely to vertically integrate when the warranty cost and the cost of exerting effort during qualification are large, and when there is significant uncertainty regarding the suppliers' capabilities. The manufacturer is more likely to outsource when the suppliers' costs (capabilities) are low (high), and when the number of suppliers is large.