Theory of Games and Economic Behavior

The nature of the problems investigated and the techniques employed in this book necessitate a procedure which in many instances is thoroughly mathematical. The mathematical devices used are elementary in the sense that no advanced algebra, or calculus, etc., occurs. (With two, rather unimportant, exceptions: Part of the discussion of an example in 19.7. et sequ. and a remark in A.3.3. make use of some simple integrals.) Concepts originating in set theory, linear geometry and group theory play an important role, but they are invariably taken from the early chapters of those disciplines and are moreover analyzed and explained in special expository sections. Nevertheless the book is not truly elementary because the mathematical deductions are frequently intricate and the logical possibilities are extensively exploited. Thus no specific knowledge of any particular body of advanced mathematics is required. However, the reader who wants to acquaint himself more thoroughly with the subject expounded here, will have to familiarize himself with the mathematical way of reasoning definitely beyond its routine, primitive phases. The character of the procedures will be mostly that of mathematical logics, set theory and functional analysis. We have attempted to present the subject in such a form that a reader who is moderately versed in mathematics can acquire the necessary practice in the course of this study. We hope that we have not entirely failed in this endeavour. In accordance with this, the presentation is not what it would be in a strictly mathematical treatise. All definitions and deductions are considerably broader than they would be there. Besides, purely verbal discussions and analyses take up a considerable amount of space. We have in particular tried to give, whenever possible, a parallel verbal exposition for every major mathematical deduction. It is hoped that this procedure will elucidate in unmathematical language what the Search all I-Revues This Collection