This is a study of the axiomatic method and its recent applications to game theory and resource allocation. It begins with a user's guide. This guide first describes the components of an axiomatic study, discusses the logical and conceptual independence of the axioms in a characterization, exposes mistakes that are often made in the formulation of axioms, and emphasizes the importance of seeing each axiomatic study from the perspective of the axiomatic program. It closes with a schematic presentation of this program. The second part of this study discusses the scope of the axiomatic method and briefly presents a number of models where its use have been particularly successful. It presents alternatives to the axiomatic method and answers criticisms often addressed at the axiomatic method. It delimits the scope of the method and illustrates its relevance to the study of resource allocation and the study of strategic interaction. Finally, it provides extensive illustrations of the considerable recent success that the method has met in the study of a number of new models.
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