The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research. A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories.

The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research. A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories.

The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research. A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories.

The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research. A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories.

A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research.

A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research.

The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research. A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories.

A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research.

The role of asymmetric information in allocation of resources, together with the associated information-revelation process, has long been a central focus of economic research. While the bulk of the literature addresses these is sues within the framework of principal-agent relationship, which essentially reduces the problem to the sole principal's (the sole Stackelberg leader's) optimization problem subject to the agents' (the Stackelberg followers') re sponses, there are recent attempts to extend analysis to other economic setups characterized by different relationships among decision-makers. A notable strand of such attempts is the core analysis of incomplete in formation. Here, there is no Stackelberg-type relationship, and more impor tantly the players can talk to each other for coordinated choice of strategies. See, e.g., Wilson (1978) for a pioneering work; Yannelis (1991) for formula tion of feasibility of a strategy as its measurability; Ichiishi and Idzik (1996) for introduction of Bayesian incentive-compatibility to this strand; Ichiishi, Idzik and Zhao (1994) for information revelation (that is, endogenous deter mination of updated information structures); Ichiishi and Radner (1997) and Ichiishi and Sertel (1998) for studies of a specific model of Chandler's firm in multidivisional form for sharper results; and Vohra (1999) for a recent work. It is a common postulate in these works that every player takes part in design of a mechanism and also in execution of the signed contract."

A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research.

A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research.

A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research.

Advances in Mathematical Economics is a publication of the Research Center for Mathematical Economics, which was founded in 1997 as an international scientific association that aims to promote research activities in mathematical economics.

Our publication was launched to realize our long-term goal of bringing together those mathematicians who are seriously interested in obtaining new challenging stimuli from economic theories and those economists who are seeking effective mathematical tools for their research.

The scope of Advances in Mathematical Economics includes, but is not limited to, the following fields: - economic theories in various fields based on rigorous mathematical reasoning; - mathematical methods (e.g., analysis, algebra, geometry, probability) motivated by economic theories; - mathematical results of potential relevance to economic theory; - historical study of mathematical economics.

Authors are asked to develop their original results as fully as possible and also to give a clear-cut expository overview of the problem under discussion. Consequently, we will also invite articles which might be considered too long for publication in journals.

A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who seek effective mathematical tools for their researchers. The editorial board of this series comprises the following prominent economists and mathematicians: Managing Editors S. Kusuoka (Univ. Tokyo), T. Maruyama (Keio Univ.); Editors R. Anderson (U.C. Berkeley), C. Castaing (Univ. Montpellier), F. H. Clarke (Univ. Lyon I), G. Debreu (U.C. Berkeley), E. Dierker (Univ. Vienna), D. Duffie (Stanford Univ.), L.C. Evans (U.C. Berkeley), T. Fujimoto (Okayama Univ.), J.-M. Grandmont (CREST-CNRS), N. Hirano (Yokohama National Univ.), L. Hurwicz (Univ. of Minnesota), T. Ichiishi (Ohio State Univ.), A. Ioffe (Israel Institute of Technology), S. Iwamoto (Kyushu Univ.), K. Kamiya (Univ. Tokyo), K. Kawamata (Keio Univ.), N. Kikuchi (Keio Univ.), H. Matano (Univ. Tokyo), K. Nishimura (Kyoto Univ.), M. K. Richter (Univ. Minnesota), Y. Takahashi (Kyoto Univ.), M. Valadier (Univ. Montpellier II), M. Yano (Keio Univ).

A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research.

A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research.

Advances in Mathematical Economics is a publication of the Research Center for Mathematical Economics, which was founded in 1997 as an international scientific association that aims to promote research activities in mathematical economics.

Our publication was launched to realize our long-term goal of bringing together those mathematicians who are seriously interested in obtaining new challenging stimuli from economic theories and those economists who are seeking effective mathematical tools for their research.

The scope of Advances in Mathematical Economics includes, but is not limited to, the following fields: - economic theories in various fields based on rigorous mathematical reasoning; - mathematical methods (e.g., analysis, algebra, geometry, probability) motivated by economic theories; - mathematical results of potential relevance to economic theory; - historical study of mathematical economics.

Authors are asked to develop their original results as fully as possible and also to give a clear-cut expository overview of the problem under discussion. Consequently, we will also invite articles which might be considered too long for publication in journals.

Advances in Mathematical Economics is a publication of the Research Center for Mathematical Economics, which was founded in 1997 as an international scientific association that aims to promote research activities in mathematical economics.

Our publication was launched to realize our long-term goal of bringing together those mathematicians who are seriously interested in obtaining new challenging stimuli from economic theories and those economists who are seeking effective mathematical tools for their research.

The scope of Advances in Mathematical Economics includes, but is not limited to, the following fields: - economic theories in various fields based on rigorous mathematical reasoning; - mathematical methods (e.g., analysis, algebra, geometry, probability) motivated by economic theories; - mathematical results of potential relevance to economic theory; - historical study of mathematical economics.

Authors are asked to develop their original results as fully as possible and also to give a clear-cut expository overview of the problem under discussion. Consequently, we will also invite articles which might be considered too long for publication in journals.

Advances in Mathematical Economics is a publication of the Research Center for Mathematical Economics, which was founded in 1997 as an international scientific association that aims to promote research activities in mathematical economics.

Our publication was launched to realize our long-term goal of bringing together those mathematicians who are seriously interested in obtaining new challenging stimuli from economic theories and those economists who are seeking effective mathematical tools for their research.

The scope of Advances in Mathematical Economics includes, but is not limited to, the following fields: - economic theories in various fields based on rigorous mathematical reasoning; - mathematical methods (e.g., analysis, algebra, geometry, probability) motivated by economic theories; - mathematical results of potential relevance to economic theory; - historical study of mathematical economics.

Authors are asked to develop their original results as fully as possible and also to give a clear-cut expository overview of the problem under discussion. Consequently, we will also invite articles which might be considered too long for publication in journals.

A lot of economic problems can formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who were seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking for effective mathematical tools for their researchers.

The role of asymmetric information in allocation of resources, together with the associated information-revelation process, has long been a central focus of economic research. While the bulk of the literature addresses these is sues within the framework of principal-agent relationship, which essentially reduces the problem to the sole principal's (the sole Stackelberg leader's) optimization problem subject to the agents' (the Stackelberg followers') re sponses, there are recent attempts to extend analysis to other economic setups characterized by different relationships among decision-makers. A notable strand of such attempts is the core analysis of incomplete in formation. Here, there is no Stackelberg-type relationship, and more impor tantly the players can talk to each other for coordinated choice of strategies. See, e.g., Wilson (1978) for a pioneering work; Yannelis (1991) for formula tion of feasibility of a strategy as its measurability; Ichiishi and Idzik (1996) for introduction of Bayesian incentive-compatibility to this strand; Ichiishi, Idzik and Zhao (1994) for information revelation (that is, endogenous deter mination of updated information structures); Ichiishi and Radner (1997) and Ichiishi and Sertel (1998) for studies of a specific model of Chandler's firm in multidivisional form for sharper results; and Vohra (1999) for a recent work. It is a common postulate in these works that every player takes part in design of a mechanism and also in execution of the signed contract."

The papers collected in this volume are contributions to T.I.Tech./K.E.S. Conference on Nonlinear and Convex Analysis in Economic Theory, which was held at Keio University, July 2-4, 1993. The conference was organized by Tokyo Institute of Technology (T. I. Tech.) and the Keio Economic Society (K. E. S.) , and supported by Nihon Keizai Shimbun Inc .. A lot of economic problems can be formulated as constrained optimiza tions and equilibrations of their solutions. Nonlinear-convex analysis has been supplying economists with indispensable mathematical machineries for these problems arising in economic theory. Conversely, mathematicians working in this discipline of analysis have been stimulated by various mathematical difficulties raised by economic the ories. Although our special emphasis was laid upon "nonlinearity" and "con vexity" in relation with economic theories, we also incorporated stochastic aspects of financial economics in our project taking account of the remark able rapid growth of this discipline during the last decade. The conference was designed to bring together those mathematicians who were seriously interested in getting new challenging stimuli from economic theories with those economists who were seeking for effective mathematical weapons for their researches. Thirty invited talks (six of them were plenary talks) given at the conf- ence were roughly classified under the following six headings : 1) Nonlinear Dynamical Systems and Business Fluctuations, . 2) Fixed Point Theory, 3) Convex Analysis and Optimization, 4) Eigenvalue of Positive Operators, 5) Stochastic Analysis and Financial Market, 6) General Equilibrium Analysis.

This volume is devoted to a reappraisal of the Marginal Revolution on the occasion of its 150th anniversary. The year 1871 should be remembered as one of the most important turning points in the history of economics. W.S. Jevons, C. Menger, and L. Walras published epochal works at the very beginning of the 1870s. Although these works were written independently, they shared a common mathematical structure based on classical analysis. For this reason, the emergence of the trio is called the Marginal Revolution. Indeed, 1871 is the starting point of modern economics in the proper sense. In 1971, several academic conferences were held on the occasion of the 100th anniversary of the Revolution, which exerted the stimulating influence upon the historical researches into the Revolution. Now more than fifty years have passed since then. Economic theory has experienced further substantial changes in researchers’ central interest, the way of reasonings and the styles of description during this period. In view of the new achievements acquired in recent fifty years, it seems an indispensable task for us to review and reevaluate the Marginal Revolution based upon the present status of economics. We also keep in mind that some concepts and doctrines once discarded could reappear in a later stage of history in a more or less transfigured form. The introductory chapter will be a guide for readers not only from the economics community but also from the mathematics community.

The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research. A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories.