Lecture Notes in
Mathematics
Edited by A. Dold and B. Eckmann
Subseries: Fondazione C.I.M.E., Firenze
Adviser:
Roberto Conti
1330
A. Ambrosetti
F. Gori
R. Lucchetti (Eds.)
Mathematical Economics
Lectures given at the 2nd 1986 Session of
the Centro Internazionale Matematico Estivo
(C.I.M.E.) held at Montecatini Terme, Italy
June 25 - July 3, 1986
Springer-Verlag
Editors
Antonio Ambrosetti Scuola Normale Superiore
Piazza dei Cavalieri 7, 5 6 1 0 0 Pisa, Italy Franco Gori
Universit& di Venezia
Dipartimento di Matematica Applicata e Informatica Dorsoduro 3825/e, 30123 Venezia, Italy
Roberto Lucchetti
Universit& di Milano, Dipartimento di Matematica Via C, Saldini 50, 20133 Milano, Italy
Mathematics Subject Classification (1980): 90A, 9 0 C , 9 0 D ISBN 3-540-50003-0 Springer-Verlag Berlin Heidelberg New York ISBN 0-38?-50003-0 Springer-Verlag New York Berlin Heidelberg
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© Springer-Verlag Berlin Heidelberg 1988 Printed in Germany
Printing and binding: Druckhaus Beltz, Hemsbach/Bergstr.
I N T R O D U C T I O N
In the last few y e a r s an ever i n c r e a s i n g interest has been shown by economists and m a t h e m a t i c i a n s in deepening' and m u l t i p l y i n g the many links already e x i s t i n g b e t w e e n their areas of research. E c o n o m i s t s are l o o k i n g for more a d v a n c e d m a t h e m a - tical t e c h n i q u e s to be a p p l i e d to the analysis of formal models of greater c o m p l e x i - ty; m a t h e m a t i c i a n s have found in problems from economics the stimulus to start n e w d i r e c t i o n s of study and to explore different trends within t h e i r theories.
The p r i n c i p a l a i m o f the CIME Session on "Mathematical Economics ~' held at V i l l a La Q u e r c e t a in M o n t e c a t i n i Terme, Italy, from June 25 to July 3 1986, has been the one of o f f e r i n g s c h o l a r s from the two fields an o p p o r t u n i t y of m e e t i n g and w o r k i n g together.
The common base of d i s c u s s i o n was p r o v i d e d by four survey courses - w h o s e texts are c o n t a i n e d in the p r e s e n t volume - which were given by I. E k e l a n d "Some V a r i a t i o n a l Methods A r i s i n g from M a t h e m a t i c a l Economics", A. M a s - C o l e l l "Differen- t i a b i l i t y T e c h n i q u e s in the Theory of General E c o n o m i c Equilibrium", J. S c h e i n k m a n "Dynamic G e n e r a l E q u i l i b r i u m Models" and S. Zamir "Topics in Non C o o p e r a t i v e Game Theory".
E v e n if E k e l a n d ' s and Zamir's lectures were more " m a t h e m a t i c a l l y oriented", w h e r e a s M a s - C o l e l l and S c h e i n k m a n put a g r e a t e r e m p h a s i s on the e c o n o m i c a l c o n - tents, in every c l a s s , t h e focus of the d i s c u s s i o n was placed over the connections n a t u r a l l y a r i s i n g b e t w e e n problems from the two sciences.
It's our f e e l i n g that the Session was very s u c c e s s f u l in r e a c h i n g its i n t e n d e d objectives, and we w i s h to express our g r a t i t u d e to the f o u r speakers, for the e x t r e m e l y high q u a l i t y of the lectures d e l i v e r e d and the s t i m u l a t i n g a t m o s p h e r e they were able to create in Montecatini, and to all the participants, who supported the m e e t i n g w i t h their interest and their lively discussions.
Our final thanks go to the CIME Scientific C o m m i t t e e for the invitation to o r g a n i z e the courses a n d to the CIME staff for its very effective job.
A n t o n i o A m b r o s e t t i F r a n c o Gori Roberto Lucchetti
C.I.M.E. Session on "Mathematical Economics" List of Participants
E. ALVONI, Istituto di Matematica Gen. e Finanz., UniversitY, Piazza Scaravilli 2, 40126 Bologna, Italy
A. AMBROSETTI, Scuola Normale Superiore, Piazza del Cavalieri 7, 56100 Pisa, Italy
E. BALDER, Mathematical Institute, University of Utrecht, Budapestlaan 6, 3584 CD Utrecht~ The Netherlands
A. BATTINELLI, Istituto di Matematica Applicata alle Scienze Economiche e Sociali, Unlversit~, Via Montebello 7, 50123 Firenze, Italy
F. BIRARDI, Via Bertani 26, 50139 Firenze, Italy P. CANNARSA, Via O. Tommasini 34, 00].62 Roma, Italy
A. CARBONE, Dipartimento di Matematica, Universit& delia Calabria, 87036 Arcavacata di Rende, Cosenza, Italy
E. CAVAZZUTI, Dipartimento di Matematica, UniversitY, Via G. Campi 213/B, 41100 Modena, Italy
G. CIMATTI, Dipartimento di Matematica,Universit~, Via Buonarroti 2, 56100 Pisa,Italy G. COSTA, Istituto di Economia e Finanza, Facolt~ di Scienze Politiche,
Via Serafini 3, 56100 Pisa, Italy R.-A. DANA, 9 Square Port-Royal, Paris 13e, France
L. DE BIASE, Istituto Matematico, Universit&, Via C. Saldini 50, 20133 Milano, Italy G. DECIMA, Dipartimento di Matematica Appl. e Inf., UniversitY, Ca' Dolfini,
30123 Venezia, Italy
S. DELAGUICHE, 19 avenue d'Eylau, 75116 Paris, France F. DELBONO, Linacre College, Oxford OX1 3JA, U.K.
V. DENICOLO', Dipartimento di Scienze Economiche, Piazza Scaravilli 2, 40126 Bologna, Italy
D. DI GIOACCHINO, Via Campo Ligure 30, 00168 Roma, Italy
B. D'ONOFRIO, Dipartimento di Matematiea, UniversitA dell'Aquila, Via Roma 33, 67100 L'Aquila, Italy
E. EINY, Institute of Mathematics, Hebrew University, Jerusalem 91904, Israel I. EKELAND, CEREMADE, Universit6 de Paris-Dauphine,
Place du Mar6chal De Lattre de Tassigny, 75775 Paris 16, France P. FABBRI, Via P. Palagi 36, 40138 Bologna, Italy
L. FERRARA, Via Roccaraso 44, 00135 Roma, Italy
M. GALEOTTI, Istituto di Matematica, FacoltA di Arehitettura, Piazza Brunelleschi 6, 50100 Firenze, Italy
M. GILLI, Via dei Benedettini 4, 20146 Milano, Italy
F. GORI, Unlverslt~ di Venezia, Dipartimento di Matematica Applicata e Informatica, Dorsoduro 38251e, 30123 Venezia, Italy
G. GOZZI, Via Carducci 5, 46100 Mantova, Italy
V. GUIDI, Dipartimento di Scienze Economiche, UniversitY, Via Curtatone I, 50123 Firenze, Italy
J. HERNANDEZ, Universidad Autonoma, Dep. de Matematica, 28036 Madrid, Spain D. HOMANN, IMW, Universitat Bielefeld, Postfach, 4800 Bielefeld i, West Germany E. LEHRER, Hebrew University, Institute of Mathematics, Givat Ram,
91904 Jerusalem, Israel
R. LEONCINI, c/o Cassola, Via del Proconsolo 5, 50122 Firenze, Italy R. LUCCHETTI, Universit~ di Milano, Dipartimento di Matematica,
Via C° Saldini 50, 20~33 Milano, Italy L. MALAGUTI, Via G. Benassi 5, 41012 Carpi (MO), Italy
A. MAS-COLELL, Mathematical Sciences Research Institute, i000 Centennial Drive, Berkeley, CA 94720, USA
F. MIGNANEGO, Dipartimento di Matematica, UniversitY, Via L.B. Alberti 4, 16132 Genova, Italy
S. MODICA, Via M. Rutelli 38, 90143 Palermo, Italy
D. MONDERER, Department of Mathematics, Everyman's University, Ramat Aviv, Tel Aviv 61392, Israel
L. MONTRUCCHIO, Dipartimento di Matematica, Politecnico, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
J. MORGAN, Dipartimento di Matematica e Applicazioni, UniversitY, Via Mezzocannone 8, 80134 Napoli, Italy
A. MORI, Via S. Martino 284, 55049 Viareggio, Italy
I. NADA, Tel Aviv University, Faculty of Management, University Campus, Ramat Aviv, Tel Aviv 69978, Israel
F. NARDINI, Dipartimento Matematico, UniversitY, Piazza di Porta S. Donato 5, 40127 Bologna, Italy
K. OLSEN, European University Institute, Badia Fiesolana, Via dei Roccettini 9, 50016 San Domenico di Fiesole, Firenze, Italy
N. PACCHIAROTTI, Dipartimento di Matematica, UniversitY, Via G. Campi 213/B, 41100 Modena, Italy
P.-M. PACINI, Istituto Universitario Europeo, Badia Fiesolana, Via Roccettini 9, 50016 San Domenico di Fiesole, Firenze, Italy
F. PATRONE, Dipartimento di Matematica, Universit&, Strada Nuova 65, 27100 Pavia, Italy
E. PETAZZONI, Via Ognibene 2, 40135 Bologna, Italy
G. PIERI, Dipartimento di Matematica, Universit&, Via L.B. Alberti 4, 16132 Genova, Italy
Vl
C. van der PLOEG, Department of Mathematics, University of Sussex, Falmer, Brighton BNI 9QE, East Sussex, England
N, RICCIARDI, CEREMADE, Universit6 de Paris-Dauphine,
Place du Mar~chal De Lattre de Tassigny, 75775 Paris 16, France G. ROSSINI, Dipartimento di Scienze Economiche, Strada Maggiore a5,
40125 Bologna, Italy
M. SABATINI, Dipartimento di Matematica pura ed applicata, UniversitA, Via Roma 33, 67110 L'Aquila, Italy
M. SCARSINI, Istituto di Matematica Finanziaria, Via Kennedy 6, 43100 Parma, Italy J. SCHEINKMAN, The University of Chicago, Department of Economics,
1126 East 59th Street, Chicago, Ill. 60697, USA
A. SICONOLFI, Dipartimento di Matematica, Universit~ della Calabria, 87096 Arcavacata di Rende, Cosenza, Italy
P. SUDHOLTER, Institut fur Mathematische Wirtschartsforschung, Universit~tstrasse, D-4800 Bielefeld i, West Germany
B. TERRENI, Dipartimento di Matematica, Universft~, Via F. Buonarroti 2, 56100 Pisa, Italy
A. TORRE, Dipartimento di Matematica, UniversitY, Strada Nuova 65, 27100 Pavia, Italy
A. VILLANACCI, Via Pasquini 2, 50127 Firenze, Italy
S. ZAMIR, The Hebrew University of Jerusalem, Department of Statistics, Mount Scopus, Jerusalem 91905
T A B L E O F C O N T E N T S I. E K E L A N D , S o m e V a r i a t i o n a l M e t h o d s A r i s i n g f r o m M a t h e m a t i c a l E c o n o m i c s ... I A. M A S - C O L E L L , F o u r L e c t u r e s o n t h e D i f f e r e n t i a b l e A p p r o a c h to G e n e r a l E q u i l i b r i u m T h e o r y . . . 19 J. S C H E I N K M A N , D y n a m i c G e n e r a l E q u i l i b r i u m M o d e l s . . . 4 4 S. ZAMIR, T o p i c s i n N o n C o o p e r a £ i v e G a m e T h e o r y . . . ~ . . . 72
