Control and Game-Theoretic Models of the Environment

367 Pages·1995·9.3 MB·English

by  A. Haurie, G. Zaccour (auth.), Carlo Carraro, Jerzy A. Filar (eds.)

Annals of the International Society of Dynamic Games
Volume 2
Series Editor
TamerBa~ar
Editorial Board
Leonard D. Berkovitz, Purdue University
P. Bernhard, INRIA, Sophia-Antipolis
R. P. HanUiUiinen, Helsinki University of Technology
Alain Haurie, University of Geneva
N. N. Krasovskii, Academy of Sciences, Ekaterinburg
George Leitmann, University of California, Berkeley
G. J. Olsder, Delft University of Technology
T. S. E. Raghavan, University of Illinois, Chicago
Josef Shinar, Technion-Israel Institute of Technology
B. Tolwinski, Operations Research Experts, Black Hawk, Colorado
Klaus H. Well, Stuttgart University
Annals of the International Society of Dynamic Games
Control and Game-Theoretic
Models of the Environment
CarIo Carraro
Jerzy A. Filar
Editors
Springer Science+Business Media, LLC
Carlo Carraro Jerzy A. Filar
Universita degli Studi di Venezia School of Mathematics
Dipartimento de Economica Ca Fascari University of South Australia
Venezia, Italy The Levels, SA 5095, Australia
Library of Congress Cataloging-in-Publication Data
Control and Game-Theoretic models of the environment I Carlo Carraro,
Jerzy A. Filar, editors.
p. cm. -- (Annals of the International Society of Dynamic
Games ; v.2)
Includes bibliographical references.
(hc : alk. paper )
1. Environmental policy--Mathematical models. 2. Sustainable
development--Mathematical models. 3. Game theory. 4. Control
theory. 1. Carraro, Carlo, 1957- II. Filar, Jerzy. III. Series.
GEI70.G36 1995 95-22370
363.7'OOI5118--dc20 CIP
ISBN 978-1-4612-6917-5 ISBN 978-1-4612-0841-9 (eBook)
DOI 10.1007/978-1-4612-0841-9
Printed on acid-free paper
© Springer Science+Business Media New York 1995
Originally published byBirkhiiuser Boston in 1995
Softcover reprint ofthe hardcover Ist edition 1995
Copyright is not claimed for works ofU.S. Government employees.
All rights reserved. No part of this publication may be reproduced, stored a retrieval
system, or transmitted, in any form or by any means, electronic, mechanical, photocopy-
ing, recording, or otherwise, without prior permission of the copyright owner.
Reformatted from authors' diskettes by Texniques, Inc., Brighton, MA
9 8 7 6 5 4 3 2 1
Table of Contents
Preface
Carlo Carrara and Jerzy A. Filar . .................................... vii
Introduction: The Environmental Game
O.J. Vrieze ......................................................... . xvii
Part 1: Models of Global Change and Sustainable Development
Differential Game Models of Global Environmental Management
A. Haurie and G. Zaccour ............................................. 3
Sustainability and the Greenhouse Effect:
Robustness Analysis of the Assimilation Function
Herman Cesar and Aart de Zeeuw .................................... 25
Consumption of Renewable Environmental Assets,
International Coordination and Time Preference
Andrea Beltratti ...................................................... 47
Sustainable International Agreements on Greenhouse Warming-
A Game Theory Study
Veijo Kaitala and Matti Pohjola ...................................... 67
The Environmental Costs of Greenhouse Gas Emissions
Michael Hoel and Ivar Isaksen ........................................ 89
Part 2: Environmental Taxes and Related Issues
Taxation and Environmental Innovation
Carlo Carrara and Giorgio Topa ..................................... 109
Environmental Quality, Public Finance and Sustainable Growth
Jenny E. Ligthart and Frederick van der Ploeg . ...................... 141
Environmental Pollution and Endogenous Growth:
A Comparison Between Emission Taxes and Technological Standards
Thierry Verdier ...................................................... 175
Rate-of-Return Regulation, Emission Charges
and Behavior of Monopoly
Anastasios Xepapadeas .............................................. 201
vi Table of Contents
Polluter's Capital Quality Standards and Subsidy-Tax Programs
for Environmental Externalities: A Competitive Equilibrium Analysis
Michele Moretto ..................................................... 231
Part 3: Pollution, Renewable Resources and Stability
The ESS Maximum Principle as a Tool for Modeling
and Managing Biological Systems
Thomas L. Vincent .................................................. 259
Pollution, Renewable Resources and Irreversibility
OUi Tahvonen . ...................................................... 279
The Economic Management of High Seas Fishery Resources:
Some Game Theoretic Aspects
Veijo Kaitala and Gordon Munro .................................... 299
Pollution-Induced Business Cycles: A Game Theoretical Analysis
David W.K. yeung .................................................. 319
Management of Effluent Discharges: A Dynamic Game Model
Jacek B. Krawczyk ................................................... 337
Preface
This book collects some recent works on the application of dynamic game
and control theory to the analysis of environmental problems. This collec-
tion of papers is not the outcome of a conference or of a workshop. It is
rather the result of a careful screening from among a number of contribu-
tions that we have solicited across the world. In particular, we have been
able to attract the work of some of the most prominent scholars in the field
of dynamic analyses of the environment. Engineers, mathematicians and
economists provide their views and analytical tools to better interpret the
interactions between economic and environmental phenomena, thus achiev-
ing, through this interdisciplinary effort, new and interesting results.
The goal of the book is more normative than descriptive. All papers
include careful modelling of the dynamics of the main variables involved
in the game between nature and economic agents and among economic
agents themselves, as well-described in Vrieze's introductory chapter. Fur-
thermore, all papers use this careful modelling framework to provide policy
prescriptions to the public agencies authorized to regulate emission dy-
namics. Several diverse problems are addressed: from global issues, such
as the greenhouse effect or deforestation, to international ones, such as the
management of fisheries, to local ones, for example, the control of effluent
discharges. Moreover, pollution problems are not the only concern of this
book. A correct, sustainable exploitation of renewable natural resources is
also the objective of some analyses and policy recommendations (see, for
example, the papers by Yeung and Kaitala-Munro). A common theme can
be found throughout the book. There is recognition that an environmental
problem and its interrelationships with economic activity and the dynamics
of eco-systems are very complex and cannot be resolved with simple policy
tools. Instead, it is necessary to use properly designed policy-mixtures in
which several policy instruments are set at their "optimal" levels. Hence,
policymakers both at the national and international level should debate
over policy interventions which account for the interdependence between
several tools and objectives in a dynamic framework, in order to prevent
the economic and natural systems from taking unsustainable development
paths.
Notice the importance of a dynamic analysis of environmental issues.
The concern for future generations (explored in Beltratti's paper), the role
of the assimilative capacities of nature (see Cesar and de Zeeuw's paper),
viii C. Carraro and J.A. Filar
the importance of irreversibilities (as in Tahvonen's work) and of capital
stock's accumulation (cf. Xepapadeas' and Moretto's articles) are some
of the elements that make it impossible not to use a dynamic framework
when studying environmental problems. Moreover, the dynamic framework
is often coupled with a game-theoretic one. This is a consequence of the
natural context in which regulators' and polluters' decisions are recipro-
cally interdependent. However, more subtle reasons are proposed in the
book. For example, the interaction (game) among polluters may prevent
traditional emission charges from being completely effective, thus calling
for other policy tools (see, among others, Carraro-Topa's and Ligthart's
papers). In a different way, interactions among governments at the inter-
national level may offset, through the so-called leakage effects, unilateral
efforts to reduce greenhouse gas emissions, thus calling for internationally
coordinated policies (see, for example, the papers by Haurie-Zaccour and
Kaitala-Pohjola).
The book is divided into three parts. The first part is devoted to mod-
els of global change and sustainable development. It contains recent con-
tributions in the field of dynamic modelling of global warming and global
environmental management, including issues of sustainable development,
international policy coordination and optimal growth with limited renew-
able natural resources.
More precisely, in the paper "Differential Game Models of Global En-
vironmental Management," A. Haurie and G. Zaccour deal with the mod-
elling of economy-environment interactions for several countries which are
assumed to behave competitively for the control of their own economic pro-
cesses, but have to achieve jointly a common environmental management
goal. In the first part of their paper, Haurie and Zaccour treat the modelling
of issues related to process dynamics and players' interactions respectively.
They discuss the control theoretic approach for representing the economic
and pollution processes in a model of environment management, and also
give a short discussion of a possible representation of uncertainty and risk
in these models. The second part of the paper proposes a dynamic game
modelling approach which combines the N-person equilibrium model with
coupled constraints and the differential game model with active and pas-
sive players. This approach enables the authors whose strategies are such
to define a tax scheme which induces a set of equilibrium seeking players
to achieve, in the long run, a global environmental goal.
The second paper of the first part, "Sustainability and the Greenhouse
Effect: Robustness Analysis of the Assimilation Function" by H. Cesar and
A. de Zeeuw, faces the issue of global environmental management and sus-
tainable growth by focusing on the role played in dynamic environmental
models by the assimilation function. In most existing optimal control mod-
els with an environmental stock it is generally assumed that the assimilation
Preface ix
function of nature is linear. At the same time, however, there is quite some
scientific uncertainty on the general form of this function outside a spe-
cific range of values. In their paper, Cesar and de Zeeuw consider different
(non-linear) specifications of the assimilation function in the case of the
greenhouse effect. The optimal trajectories and the steady states are anal-
ysed for the various functional forms. Slight variations in the assimilation
function can result in a dramatic change in the steady state values. Besides,
neither multiple equilibria nor the absence of non-zero production steady
states can be excluded. Hence, this paper provides useful information on
the sensitivity of dynamic environmental analyses on the specification of
the assimilation function of nature.
A similar robustness analysis is carried out in "Consumption of Re-
newable Environmental Assets, International Coordination and Time Pref-
erence" by A. Beltratti, in which a two-country linear-quadratic model of
depletion of a renewable resource is studied both in static and in dynamic
terms. The model allows for negative consumption externalities through
the action on the stock of the environmental good, which enters the util-
ity function. The main result of the paper shows that the noncooperative
solution of the dynamic model is characterised, in the steady state, by
suboptimally low levels of environmental resources and consumption, thus
providing incentives for international cooperation. The robustness of this
conclusion is then checked with respect to several parameters defining the
structure of the economy. In particular, attention is given to the rate of
intertemporal time preference, a parameter which captures the preference
for future generations' welfare of present governments. It is shown that the
sub-optimality of the non-cooperative solution increases with the rate of
time preference in a nonlinear way which depends on the other parameters
of the economy.
The issue of policy coordination is also the object of the subsequent
paper, "Sustainable International Agreements on Greenhouse Warming: A
Game Theory Study" written by V. Kaitala and M. Pohjola. It is clear,
and is well-described in O. Vrieze's introductory paper, that reducing dam-
ages caused by climatic changes requires major international efforts. Many
countries bear the view that the joint efforts should be undertaken under
international agreements. The paper by Kaitala and Pohjola presents a dy-
namic game theory model for an international environmental negotiation
problem that may arise in the context of global climate change. The basic
assumption is that countries differ in their vulnerability to global warming
and that two coalitions will possibly be formed. One coalition may include
countries that do not suffer from global warming, or where the damages are
minor, and the other coalition may be joined by countries that will suffer
as a result of global warming. The greenhouse problem is then modelled
as an economic infinite-horizon differential game. Countries negotiate an
x C. Carrara and J.A. Filar
agreement among Pareto-efficient programs by allowing for transfer pay-
ments which account for the existing international asymmetric effects of
global warming. Transfer payment programs are designed in such a way
that it is possible at any stage of the agreement to punish violations against
cooperation and to discourage the other player from selfishly polluting the
atmosphere. In this context, it is shown that the incentives for international
cooperative control of global warming will become stronger and will occur
with an increasing frequency.
The last paper of Part 1 of the book, "The Environmental Costs of
Greenhouse Gas Emissions" by M. Hoel and I. Isaksen, deals with a crucial
issue in environmental negotiations, namely the evaluation of the costs of
global warming. An efficient, comprehensive climate policy should balance
the cost of reducing emissions of each greenhouse gas against the environ-
mental costs of the emissions of the gas. However, the assessment of these
costs is generally a difficult task. In their paper, Hoel and Isaksen show
how these environmental costs may be calculated using an optimal control
dynamic model. This is first done for the traditional case in which, at any
time, one is only concerned about the state of the climate. Then, a more
general environmental cost function is considered, for which it is assumed
that the rate of climate change is more important for the environment and
the economy than the state of the climate. Besides providing a clear pre-
sentation of the methodology, the paper also shows, through a numerical
example, how the marginal costs of greenhouse gas emissions for both types
of environmental cost function can be calculated.
The second part of the volume is devoted to the analysis of the in-
teractions between technical progress, economic growth and environmental
protection. The papers included in this second part are characterised by
solid micro-foundations, and rely upon recent developments of industrial
organisation theory. In particular, the robustness of traditional environ-
mental policy prescriptions to imperfect competition is assessed in several
papers. Therefore, this part of the book provides new insight into the
optimal environmental policy-mix by showing how several tools may be ac-
tivated in order to control polluting emissions without excessively damaging
economic growth.
In the first paper, "Taxation and Environmental Innovation," C. Car-
raro and G. Topa propose an industrial organisation dynamic model to
analyse the effects of environmental taxation on firms, innovation activ-
ity. A regulator is assumed to introduce an environmental tax. Firms may
react both by changing output and by adopting anew, environmentally
friendly technology. Conditions under which innovation is a firm's opti-
mal choice are provided. The paper shows that firms innovation decisions
are not simultaneous even when firms are identical (there exists diffusion).
Moreover, firms have an incentive to delay the time of innovation, because