Table Of ContenterutceL Notes ni
Control dna
noitamrofnI Sciences
detidE yb amohT.M dna A.Wyner
157
.R .P ,neni&l&m&H
.H K Ehtamo (Eds.)
Dynamic Games
ni Economic Analysis
Proceedings of the Intemational Fourth Symposium
no Differential Games dna Applications
August 9-10, ,0991 University Helsinki of Technology,
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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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PREFACE
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
a retailer and 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.
ehT dnoces section includes five articles dcaling with incentives dna coordination. Thc objective of
Miao ct aL is allocation m model resource human dna coordination in distributed a hierarchical team.
human incorporates model Their limitations in making decision dna coordination. Thc issues desserdda
edulcni decentralized information structure, modcl simplification, solution methodologies, dna team
noitanidrooc incentives studies P6rez process. dna economic efficiency of an inter-fim~ coordination
.tnemegnarra devclopcs He a modci for na iterativc system brokerage in which the optimal allocation
of production levels is Houba achieved. dna Zceuw de study bargaining strategic in difference a 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
si 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 thep ollution 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 ni
which the central govemmcnt coordinates the decisions of local governments. Neck derives Nash dna
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 multiplec riteria 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
consistepnrcoyp erties 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.T his 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. ,neniiIli,'mi~H 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. nenii,li~miiH Harri Ehtamo
LIST OF CONTRIBUTING AUTHORS
BASSETTI, A.
ytisrevinU of Modena, of Dcparlmcnt Economics
Via ,inidraiG 41100 Modcna ylatI
BLAIN, M.
Universite de Montrdal, CRT
CP 6128 suet A, Montrdal H3C 3J7 Canada
CARAVANI, P.
Via Colli della Famesina 78, 00194 Rome Italy
CHINTAGUNTA, P.
Comell University, Johnson Graduate School of Management
MaUot Hall, Ithaca, NY 14853 USA
CHISTIAKOV, Y.E.
USSR Academy of Sciences, Computing Center
Vavilov 40, 117969 Moscow USSR
CLEMHOUT, S.
Comell University, Department of Economics
Martha van Renselaer Hall, Ithaca, NY 14653 USA
EHTAMO, H.
Helsinki University of Technology, Systems Analysis Laboratory
Otakaari 1 M, SF-02150 Espoo dnalniF
FLAM, S,D,
University of Bergen, Economics Department
Jonas Reinsgt. ,91 N-5014 Bergen-U Norway
GRADUS, R.
Tilburg UnivErsity, Department of Econometrics
B.O. Box 90153, 5000 LE Tilburg The Netherlands
GROOT, F.
Tilburg University, Department of Econometrics
P.O. Box 90153, 5000 LE Tilburg The sdnalrchtcN
VII
HOUBA, H.
grubliT ,ytisrcvinU of Departmcnt scirtemonocE
.O.P Box 90153, 5000 LE grubliT The Netherlands
~,L,~M~,H 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
sciences,
hsiloP Academy of smetsyS Institutc Rcscamh
,lu 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 5W1 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
~.tisrevinU di Sassari
aiV De Nicola, 07100 Sassari Italy
M. POHJOLA,
ALTE - Research Institute of the Finnish Economy
L0nnmtinkatu 4B, SF-00120 Helsinki Finland
,FEJDAR M.S.
ytisrevinU of Bejaia, Lab. of Modelisation and Optimisation of Systems
Route de Targua-Ouzemour, B.P. 308 06000 Algeria
J. RUUSUNEN,
iknislcH University of Technology, Systems Analysis Laboratory
iraakatO 1 M, SF-02150 Espoo Finland
,NEN~,S,~R .M
iknisleH University of Technology, Systems Analysis Laboratory
iraakatO I M, SF-02150 Espoo Finland
ROLLER, L.-tl.
Institute naeporuE of Business Administration
draveluoB de Constance, 77305 Fontainebleau Cedcx France
L. SALCHENBERGER,
University Loyola of Chicago, Department of Management Science
01 East Pearson, Chicago, IL 60611 USA
,AHCS FER, M.
t~tisrcvinU der Bundeswehr, Fachb. Wirtschafts- und Organisationsw.
gewfohnetsloH 85, D-2000 Hamburg 70 Germany
M. SOISMAA,
iknisleH School of Economics dna Business Administration
utaknigrebenuR 14-16, SF-00100 Helsinki Finland
S. STEFANI,
ytisrevinU of Brescia, Faculty of Economies dna Business
Corso Mameli 27, Brescia Italy
TAHVONEN, .O
iknisleH School of Economics
utaknigrebenuR 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
