## Advances in Mathematical Economics, Volume 1A 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 were seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking for effective mathematical tools for their researchers. Members of the editorial board of this series consists of 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), A. Yamaguti (Kyoto Univ./Ryukoku Univ.), M. Yano (Keio Univ.). |

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aggregate expenditures arbitrage arbitrage free Arrow-Debreu securities asset assume assumption Banach space bounded sequence brand Castaing chaotic closed in measure concave condition constraint convex cost function default defined degree of product denote dominant diagonal dynamical system elasticity endowment equilibrium prices equilibrium yield spread example exists a subsequence firm i's Gérard Debreu Given any sequence Hence heterogeneity interest rate process Keio Keio University Komlós Lemma LP problem marginal costs market power martingale Math MATHEMATICAL ECONOMICS monetary equilibrium Montpellier Nash equilibrium optimal dynamical system parameters payoff product differentiation product differentiation increases profit function Proof Proposition quasiconcavity result satisfies Section sequence fm sequence in Lk strategic complementarity strong firm subjective probabilities subperiod subsequence gn subset of Lk supermodularity Tokyo Topkis topology uniformly integrable unit costs utility function Valadier vector weak compactness weak firm weakly converges yield spread Young measures