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Advances in MATHEMATICAL ECONOMICS

Managing Editors Akira Yamazaki Meisei University Tokyo, JAPAN Shigeo Kusuoka University of Tokyo Tokyo, JAPAN Editors Robert Anderson University of California, Berkeley Berkeley, U.S.A. Charles Castaing Universite Montpellier II Montpellier, FRANCE Frank H. Clarke Universite de Lyon I Villeurbanne, FRANCE Egbert Dierker University of Vienna Vienna, AUSTRIA Darrell Duffie Stanford University Stanford, U.S.A. Lawrence C. Evans University of California, Berkeley Berkeley, U.S.A. Takao Fujimoto Fukuoka University Fukuoka, JAPAN Jean-Michel Grandmont CREST-CNRS Malakoff, FRANCE Norimichi Hirano Yokohama National University Yokohama, JAPAN Leonid Hurwicz University of Minnesota MinneapoUs, U.S.A | S. Kusuoka A. Yamazaki Eds. MATHEMATICAL ECONOMICS Volume 10 Advances in MATHEMATICAL ECONOMICS Managing Editors Shigeo Kusuoka University of Tokyo Tokyo JAPAN Editors Robert Anderson University of California Berkeley Berkeley U.S.A. Charles Castaing Université Montpellier II Montpellier FRANCE Frank H. Clarke Université de Lyon I Villeurbanne FRANCE Egbert Dierker University of Vienna Vienna AUSTRIA Darrell Duffie Stanford University Stanford U.S.A. Lawrence C. Evans University of California Berkeley Berkeley U.S.A. Takao Fujimoto Fukuoka University Fukuoka JAPAN Jean-Michel Grandmont CREST-CNRS Malakoff FRANCE Akira Yamazaki Meisei University Tokyo JAPAN Norimichi Hirano Yokohama National University Yokohama JAPAN Leonid Hurwicz University of Minnesota Minneapolis U.S.A. Tatsuro Ichiishi Hitotsubashi University Tokyo JAPAN Alexander Ioffe Israel Institute of Technology Haifa ISRAEL Seiichi Iwamoto Kyushu University Fukuoka JAPAN Kazuya Kamiya University of Tokyo Tokyo JAPAN Kunio Kawamata Keio University Tokyo JAPAN Norio Kikuchi Keio University Yokohama JAPAN Toni Maruyama Keio University Tokyo JAPAN Hiroshi Matano University of Tokyo Tokyo JAPAN Kazuo Nishimura Kyoto University Kyoto JAPAN Marcel K. Richter University of Minnesota Minneapolis U.S.A. Yoichiro Takahashi Kyoto University Kyoto JAPAN Michel Valadier Université Montpellier II Montpellier FRANCE Makoto Yano Keio University Tokyo JAPAN Aims and Scope. The project is to publish Advances in Mathematical Economics once a year under the auspices of the Research Center for Mathematical Economics. It is designed to bring 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. - .