Lecture Notes in Control and Information Sciences Edited by M.Thoma and A.Wyner

157

R. P. H&m&l&inen, H. K Ehtamo (Eds.)

Dynamic Games in Economic Analysis Proceedings of the Fourth Intemational Symposium on Differential Games and Applications August 9-10, 1990, Helsinki University of Technology, Finland

Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong Barcelona Budapest

Series Editors M, Thoma • A. Wyner

Advisory Board L. D. Davisson • A. G. J. MacFarlane • H. Kwakernaak J. L Massey • Ya Z. Tsypkin • A. J. Viterbi

Editors Raimo Pertti H~m~l~inen Hard Kalevi Ehtamo

Systems Analysis Laboratory Helsinki University of Technology Otakaari 1M, 02150 Espoo Finland

ISBN 3-540-53785-6 Spdnger-Vedag Berlin Heidelberg New York ISBN 0-387-53785-6 Spdnger-Verlag NewYork Berlin Heidelberg

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© Spdnger-Vedag Bedin, Heidelberg 1991 Printed in Germany The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

Printing: Mereedes-Druck, Berlin Binding: B. Helm, Berlin 6113020-543210 Pdnted on acid-free paper.

P R E F A C E

The Fourth International Symposium on Differential Games and Applications was organized at the Systems Analysis Laboratory, Helsinki University of Technology, with the participation of tile International Federation of Automatic Control (1FAC), Mathematics of Control Committee, and the Institute of Electrical and Electronics Engineers 0EEE), Control Systems Society, on August 9 and 10, 1990.

The program of the meeting had two main tracks one concentrating on dynamic games in economics and management problems. The other track dealt with classical zero-sum differential games and computational questions as well as engineering applications. The present volume includes papers presented in the first area. The second track is covered in a related volume in this Lecture Notes Series entitled "Differential Games - Developments in Modelling and Computation".

In this proceedings the papers have been grouped into four sections according to their topic. The first five papers deal with problems in management science and economies. Next there is a section on

incentives and coordination followed by nine articles on resource management and environmental

problems and twelve articles dealing with hierarchical game models as well as computational aspects.

Chintagunta and Jain present a differential game analysis of equilibrium effort levels for a manufacturer and a retailer in a two-member marketing channel. Groot derives the feedback Stackelberg equilibrium for a cartel-versus-fringe model using the value function approach. Marcotte and Blain consider Nash and Stackelberg game problems related to the modelling of deregulated transit systems characterized by small transit firms operating a single vehicle. A feedback Nash equilibrium solution for an investment game is obtained by Yeung, and ROller and Tombak examine the timing of market entry

with multiproduct technologies by using the Nash equilibrium concept. The firms cannot observe each other's actions and therefore they irreversibly precommit themselves to a technology and a time of entry before the game starts.

The second section includes five articles dcaling with incentives and coordination. Thc objective of

Miao ct aL is m model human resource allocation and coordination in a distributed hierarchical team. Their model incorporates human limitations in decision making and coordination. Thc issues addressed

include decentralized information structure, modcl simplification, solution methodologies, and team

coordination process. P6rez studies incentives and economic efficiency of an inter-fim~ coordination arrangement. He devclopcs a modci for an iterativc brokerage system in which the optimal allocation of production levels is achieved. Houba and de Zceuw study strategic bargaining in a difference game framework by using Rubinstcin's alternating bid model. They derive perfect equilibrium proposals and

show that these proposals are not necessarily Pareto optimal in the present situation. Ruusunen et aL

consider the dynamic pricing of electricity where tile customers react to the changing tariff. The model

is tested on real data which comes from an experiment carried out in Finland. Ehtamo et al. formulate

IV

a multiple period stochastic group decision problem with nonadditive group utility function and propose

a hierarchical computational method for finding its solution.

The next section consists of nine papers devoted to resource management and environmental problems.

Munro considers the application of differential game theory to the management of transboundary fisheries shared by two or more coastal states. He surveys the literature and points out areas in which work still remains to be done. The paper also demonstrates how analytical game models have been capable of producing new insights into the management of real world transboundary fisheries. Salehenberger and Stefani analyze optimal harvesting policies under the assumption of uncertainty about the time of extinction. Schiller considers a fishery where the population dynamics is influenced by environmental pollution impacts. The dependency of the fishery industry on the pollution is studied and different non-cooperative open-loop Nash equilibria are computed numerically. An oligopoly market for an exhaustible resource is considered by Klompstra. Both open-loop and feedback Nash equilibria arc derived in the case of a variable time horizon. Clemhout and Wan inquire in general whether environmental problems can be considered as dynamic, common-property resource games. They review past results with illustrative examples and outline topics for potentially fruitful future research. Koyama formulates a model of environmental planning as a dynamic Stackelberg game

between an environmental central agent, the leader, and the polluting firms, the followers. Malliaris and Stefani analyze the role of discount rate in partial equilibrium models of exhaustible resources. Kivijlirvi and Soismaa study competition and the opposite interests within the Finnish forest sector as a Ihree player differential game with the forest industry, forest owners and the society as players. Kaitala et al. develop a two country transboundary air pollution model and compare the cooperative and non-cooperative solutions to the resulting, dynamic acid rain game. One of their interesting conclusions is that in the present situation between Soviet Union and Finland the cooperative joint optimum can only be reached if Finland gives a transfer payment to the Soviet Union.

The last twelve papers deal with hierarchical models, computation and theory. Gmdus surveys feedback

Stackelberg equilibria in macroeconomics and derives a feedback Stackelbcrg equilibrium for a special differential game between govemment and private sector. Ito simulates a setup of competing

corporations under the control of a central govemment. Li and Wu consider a planned-economy in

which the central govemmcnt coordinates the decisions of local governments. Neck derives Nash and Stackelberg equilibrium strategies for linear-quadratic stabilization policies with two decision makers under uncertainty. Dynamic hierarchical multiple player games with coalitions are studied by

Kononenko et aL Flilm presents a continuous time adjustment process for cooperative games in characteristic form and shows that they converge towards core solutions. Bassetti and TorrieeUi present

an approach to the optimal portofolio selection by embedding the problem into a bargaining game framework. Krajewski considers two-person linear exponential-quadratic NaSh games with one-step

time delay information sharing pattern. He shows that the multistage problem can be decomposed into a series of one-stage Nash games and obtains the solution in a recursive form. Mignanego and Pied consider the derivation and existence of Nash and Stackelberg strategies for continuous time games

with decision constraints, and Radjefstudies multiple criteria differential games eovemed by differential

inclusions. The regulator problem of Caravani is formulated as the minimization of the distance

between the Nash equilibrium point and a desired point on the Pareto frontier. Conditions are given

V

under which such regulation is effective to elicit cooperation. Finally, Petrosjan investigates the time consistency properties of the optimality principles related to non-zero sum differential games by a point

to set mappings approach.

In a summary the papers show that the theory of dynamic games is becoming an increasingly important tool in economic analysis. Many resource and environmental problems are naturally formulated as dynamic games. Moreover, there is growing interest in the game analysis of dynamic incentives,

coordination and hierarchical organizations. Also energy economics is an area where dynamic solutions are used in real life problems. This volume gives a relatively wide coverage of examples from all these new developments.

Perhaps the most important result of the Symposium was the foundation of the International Society of Dynamic Games (ISDG). The founding members of the society were Tamer Basar, Pierre Bernhard, Alain Haurie, Raimo P. H~im',ilIiinen, Geert Jan Olsder, Josef Shinar, Boleslaw Tolwinski, and Klaus H. Well. The first president of the Society is professor Tamer Ba~ar, and tile Society's Headquarters are hosted by professor Raimo P. H'dm/il[iinen at the Systems Analysis Laboratory, Helsinki University of Technology. The society is open to all interested. Its main goal is to improve file exchange of

information among the researchers and take responsibility of continuing the biannual Symposium series on Dynamic Games and Applications.

August 1990,

Raimo P. Hiim~il,iinen Harri Ehtamo

LIST OF CONTRIBUTING AUTHORS

BASSETTI, A. University of Modena, Dcparlmcnt of Economics Via Giardini, 41100 Modcna

BLAIN, M. Universite de Montrdal, CRT CP 6128 suet A, Montrdal H3C 3J7

CARAVANI, P. Via Colli della Famesina 78, 00194 Rome

CHINTAGUNTA, P. Comell University, Johnson Graduate School of Management MaUot Hall, Ithaca, NY 14853

CHISTIAKOV, Y.E. USSR Academy of Sciences, Computing Center Vavilov 40, 117969 Moscow

CLEMHOUT, S. Comell University, Department of Economics Martha van Renselaer Hall, Ithaca, NY 14653

EHTAMO, H. Helsinki University of Technology, Systems Analysis Laboratory Otakaari 1 M, SF-02150 Espoo

FLAM, S,D, University of Bergen, Economics Department Jonas Reinsgt. 19, N-5014 Bergen-U

GRADUS, R. Tilburg UnivErsity, Department of Econometrics B.O. Box 90153, 5000 LE Tilburg

GROOT, F. Tilburg University, Department of Econometrics P.O. Box 90153, 5000 LE Tilburg

Italy

Canada

Italy

USA

USSR

USA

Finland

Norway

The Netherlands

The Ncthcrlands

VII

HOUBA, H. Tilburg Univcrsity, Departmcnt of Econometrics P.O. Box 90153, 5000 LE Tilburg The Netherlands

H,~M~,L,~ INEN, R.P. Helsinki University of Technology, Systems Analysis Laboratory Otakaari 1 M, SF-02150 Espoo Finland

ITO, Y. Meijo University, Dept. of Commerce and Economics Tcnpaku, Nagoya 468 Japan

JAIN, D. Northwestern University, Kellogg Graduate School of Management Leverone Hall, Evanston, IL 60208 USA

KAITALA, V. Helsinki University of Technology, Systems Analysis Laboratory Ot~aari 1 M, SF-02150 Espoo Finland

KIVIJARVI, H. Hclsinki School of Economics and Business Administration Runeberginkatu 14-16, SF-00100 Helsinki Finland

KLEINMAN, D.L. University of Connecticut, Dept. of Electrical and Systems Engineering Storrs, CT 06269-3157 USA

KLOMPSTRA, M.B. Delft University of Technology, Faculty of Tech. Math. and Informatics P.O. Box 356, 2600 AJ Delft The Netherlands

KONONENKO, A.F. USSR Academy of Sciences, Computing Center Vavilov 40, 117969 Moscow USSR

KOYAMA, N. Nagoya City University, Faculty of Economics Mizuhocho Mizuhoku, Nagoya 467 Japan

KRAJEWSKI, W. Polish Academy of sciences, Systems Rcscamh Institutc ul, Newelska 6, 01-447 Warsaw Poland

VIII

KRUTOV, B.P. USSR Academy of Sciences, Computing Center Vavilov 40, 117969 Moscow USSR

LI. B.-B. Shanghai Jiao-Tong University, Research Inst. of Systems Engineering Shanghai 200038 P.R. China

LUH, P.B. University of Connecticut, Dept. of Electrical and Systems Engineering Storm, CT 06269-3157 USA

MALLIARIS, A.G. Loyola University of Chicago, Department of Economics 820 North Michigan Avenue, Chicago, IL 60611 USA

MARCOTTE, P. University of Montreal, Center for Research in Transportation CP 6128 suce A, Montr6al, Qu6bee H3C 3J7 Canada

MIAO, X. University of Connecticut, Dept. of Electrical and Systems Engineering Storm, CF 06269-3157 USA

M1GNANEGO, F. Universit~ di Genova, Dipartimento di Matematica Via Leon Battista Alberti 4, 16132 Genova Italy

MUNRO, G.R. University of British Columbia, Department of Economics Vancouver, BC V6T 1W5 Canada

NECK, R. Wirtschaftsunivemit.'it Wien, Inst. fflr Volkwirtschaftstheorie und -Politik Augasse 2-6, A-1090 Vienna Austria

PI~REZ, M.A. Univcrsidad Catolica de Chile, Dcpart. dc Ingcnicria de Sistcmas CasiUa 6177, Santiago Chile

PETROSJAN, L.A. University of Leningrad, Department of Applied Mathematics Biblioteclmaya pl. 2, Leningrad USSR

IX

PIERI, O. Universit.~ di Sassari Via De Nicola, 07100 Sassari Italy

POHJOLA, M. ETLA - Research Institute of the Finnish Economy L0nnmtinkatu 4B, SF-00120 Helsinki Finland

RADJEF, M.S. University of Bejaia, Lab. of Modelisation and Optimisation of Systems Route de Targua-Ouzemour, B.P. 308 06000 Algeria

RUUSUNEN, J. Hclsinki University of Technology, Systems Analysis Laboratory Otakaari 1 M, SF-02150 Espoo Finland

R~,S,~NEN, M. Helsinki University of Technology, Systems Analysis Laboratory Otakaari I M, SF-02150 Espoo Finland

ROLLER, L.-tl. European Institute of Business Administration Boulevard de Constance, 77305 Fontainebleau Cedcx France

SALCHENBERGER, L. Loyola University of Chicago, Department of Management Science 10 East Pearson, Chicago, IL 60611 USA

SCHA, FER, M. Univcrsit~t der Bundeswehr, Fachb. Wirtschafts- und Organisationsw. Holstenhofweg 85, D-2000 Hamburg 70 Germany

SOISMAA, M. Helsinki School of Economics and Business Administration Runeberginkatu 14-16, SF-00100 Helsinki Finland

STEFANI, S. University of Brescia, Faculty of Economies and Business Corso Mameli 27, Brescia Italy

TAHVONEN, O. Helsinki School of Economics Runeberginkatu 14-16, SF-00100 Helsinki Finland

×

TOMBAK, M.M, European Institute of Business Administration Boulevard de Constance, 77305 Fontainebleau Cedex France

TORRICELLI, C. University of Modena, Department of Economics Via Giardini, 41100 Modena Italy

WAN, H. Jr. Comcll University, Department of Economics Martha van Renselaer Hail, Ithaca, NY 14653 USA

WU, J.-Z. Shanghai Jiao-Tong University, Research InsL of Systems Engineering Shanghai 200038 P.R. China

YEUNG, D. University of Hong Kong, Department of Economics Pokfulam Road Hong Kong

DE ZEEUW, A. Tilburg University, Department of Econometrics P.O. Box 90153, 5000 LE Tilburg The Netherlands

TABLE OF CONTENTS

MANAGEMENT SCIENCE AND ECONOMICS

A Study of Manufacturer-Retailer Marketing Strategies: A Differential Game Approach P. Chintagunta, Comell University D. Jain, Northwestern University

Tile Feedback Stackclberg Equilibrium in the Cartel-Versus-Fringe Model F. Groot, Tilburg University

A Stackclberg-Nash Model for the Design of Deregulated Transit System P. Marcotte, Colleg6 Militairc Royal de St-Jcan M. Blain, Univcrsit6 de Montreal

A Game Theoretical Approach to Public Investment Versus Private Investment D. Yeung, University of Hong Kong and University of Windsor

Entry with New Multiproduct Technologies L.-H, ROller, M.M. Tombak European Institute of Business Administration

11

21

29

39

INCENTIVES AND COORDINATION

Distributed Ilierarcldcai Team Resource Allocation X. Miao, P.B. Luh, D.L. Klcinman University of Connecticut

Incentive Stratt~ies in an Inter-Firm Coordination Arrangement M.A. P~rez, Universidad Catolica de Chile and AT&T Bell Laboratories

Strategic Bargaining and Difference Games H. Houba, Tilburg University A. de Zceuw, Tilburg University and Free University

Game-Theoretic Modelling in the Dynamic Pricing of Electricity J. Ruusunen, R.P. H~im:iltiincn, M. R~incn Helsinki University of Technology

48

58

68

78

Xl l

On Intertemporal Cooperation - A Dynamic Stochastic Problem with Nonadditive Group Utility Function H. Ehtamo, J, Ruusunen, R.P. H~n~ilSncn Helsinki University of Technology

88

RESOURCE MANAGEMENT AND ENVIRONMENT

Differential Games and the Optimal Management of Transboundary Fisheries G.R. Munro, University of British Columbia

Economic Planning and Uncertainty in Renewable Resources L. Salchenbcrger, Loyola University of Chicago S. Stefani, University of Brescia

Pollution Vs. Nature - Differential Game Models M. Sch~ffer, Universi~t der Bundeswehr, Hamburg

A Nonzero-Sum Game with Variable Final Time M.B. Klompstra, Delft University of Technology

Euvironment Problem as a Common-Property Resource Game S. Clemhout, H. Wan, Jr. Comell University

Tile Environmental-Economic Planning Model with tile Dynamic Slackelberg Game N. Koyama, Nagoya City University, Japan

IIeterogeneous Discount Rates: A Generalization of Hotclling's Rule A.G. MaUiads, Loyola University of Chicago S. Stef;mi, University of Brescia

Investment, Harvest, and Taxation Strategies of the Forest Sector: A Differential Game Approach with a Computational Decision-Aid H. Kivijarvi, M.Soismaa Helsinki School of Economics

Transboundary Air Pollution between Finland and tile USSR: A Dynamic Acid Rain Game V. Kaitala, Helsinki University of Technology M. Pohjola, Research Institute of the Finnish Economy O. Tahvonen, Hclsinki School of Economics

95

102

112

122

132

155

163

170

183

XIII

HIERARCHICAL MODELS AND COMPUTATION

Tile Derivation of Feedback Slaekelberg Equilibria in Dynamic Economic Games R. Gradus, Tilburg University

193

Dynamic Game Strategies for Coi'porate Demand Models in National Economy Y. Ito, Meijo University, Nagoya

204

Hierarchical Dynamic Planned-Economy Models with Central Government Coordination of One-Step Delay Information B.-B. Li, J.-Z. Wu Shanghai/iao-Tong University

213

Non-Cooperative Equilibrium Solutions for a Stochastic Dynamic Game of Economic Stabilization Policies R, Neck, Winschaftsuniversittit Wien

221

Dynamic Hierarchical N-Person Games Theory wlth Coalitions A.F. Kononenko, B.P. Kmtov, Y.E. Chistiakov Computing Center of the USSR Academy of Sciences, Moscow

231

Approaching Core Solutions by Means of Continuous Bargaining S.D. Fl~m, University of Bergen

239

Optimal Portfolio Selection as a Bargaining Game A. Bassetti, C. Torricclli University of Modena

249

A Note on the Dynamic Risk Sensitive Nash Games W. Krajewski, Systems Research lnstititute, Polish Acad. Sci

260

Equilibrium Points in Constrained Minimization and Games F. Mignanego, Univcrsith di Genova G. Pied, Universi~ di Sassari

269

A Cooperative Game Governed by a Differential Inclusion M.S. Radjef, University of Bejaia

276

Regulation of Linear Quadratic Games p. Caravani, University of Aquila

283

The Time Consistency of the Optimality Principles in Non-Zero Sum Differential Games L.A. Petrosjan, University of Leningrad

299