Download F(x) = h

International (fisheries)
agreements and game theory
• Why is international fisheries
management important?
• What are the major international
agreements governing the exploitation
of marine fisheries?
• An example of failure
• How can game theory help in explaining
and predicting the behaviour of
countries?
International agreements:
characteristics
• Countries negotiate on exploitation of
common environmental & natural
resources
• Negotiations slow, countries or groups of
countries may later find it optimal to
deviate from the agreements
• Disagreements on the size of
environmental and natural resources
• Lead even to military conflicts
List of International Environmental Agreements
• London Convention on the Protection of Wild Fauna in
Africa (1900; never ratified)
• International Convention for the Regulation of Whaling
(1946)
• Convention for the Prevention of Pollution of the Sea by
Oil (1954)
• Antarctic Treaty (1959)
• Treaty Banning Nuclear Weapon Tests in the
Atmosphere, in Outer Space and Under Water (1963)
• Treaty on Principles Governing the Activities of States in
the Exploration and Use of Outer Space (1967)
List of IEAs Continuing
• Convention on International Trade in Endangered
Species (CITES) (1973)
• International Tropical Timber Agreement (1983;
renegotiated in 1994)
• Vienna Convention for the Protection of the Ozone Layer
(1985)
• Framework Convention on Climate Change (1992)
• Convention on Biological Diversity (1992)
• International Conference on Population and
Development (1994)
• International Convention to Combat Desertification
(1994)
Overexploitation of fish stocks
• historical records from 1600’s
• resources are scarce, negative
externalities
• harvesting technologies have developed in
the 1960’s
• important food source and industry for
many countries
• Consequences: international conflicts,
decreased economic value of fisheries
Law of the sea convention 1982
• Established the Exclusive Economic Zones (EEZ)
for the coastal states (200 nautical miles from the
coastline)
• 90 % of the marine fish stocks are found inside the
EEZs
• Fisheries disputes remained
• 1992 UN Conference on Environment and
Development, Rio 1992
Transboundary Fish Stocks
EEZ 1
C1
SH
STR
C2
EEZ 2
SH = Shared fish stocks
STR = Straddling (and highly migratory) fish stocks
EEZ = Exclusive Economic Zone
UN Conference on Straddling and
Highly Migratory Fish Stocks 1993-95
• Attempt to establish property rights for the
remaining 10 % of marine fisheries
• Suggests cooperation through regional
fisheries organisations
• What are the optimal structures of these
organisations?
Example: the Norwegian springspawning herring
• One of the most valuable fish stocks in the
world
• Stock was depleted in 1970’s due to
intensive harvesting
• Migratory pattern changed
• Fishing moratorium was declared for
almost 20 years
Spawning stock biomass (kg)
14
x 10
9
Norwegian spring-spawning herring
12
10
8
6
Collapse!
4
2
0
1950
1955
1960
1965
1970
1975
Time
1980
1985
1990
1995
2000
Fisheries economics and game
theory
• Rational countries maximise their net
present value from harvesting for given
strategies of other countries
• Equilibrium where unilateral deviation not
optimal
• Cooperation vs. non-cooperation
Nash solutions to the fishery
games
• Non-cooperative, Clark 1980: Every fishing
nation harvests at maximum effort until it is no
longer profitable. At this equilibrium the stock
is below the optimum of the most efficient
country - “tragedy of the commons”
• Cooperative, Kaitala & Pohjola 1988: The
surplus benefits from cooperation are equally
divided between the fishing nations. Thus the
countries in a three-player game receive their
threat point payoff + a third from the benefits
generated by cooperation
Coalitional games
• If countries can form coalitions with each
other the solution of the game may be
changed
• The bargaining strength is then also
defined by the coalitions
• Stability of coalitions
• Coalitional free-riding vs. individual freeriding
Bioeconomic modelling: from
open access to full
cooperation
Agenda
• Bioeconomic = biological models +
economic models
• National vs International fisheries
management
• International: non-cooperation vs.
cooperation
Bioeconomic modelling
• National level: Fishermen exploit a common fish
stock, say herring.
• Biological model predicts the development of the
stock without any economic activities  natural
equilibrium
• For economic analysis production function is
needed, how the resource is harvested h = Ex
• Further, we need prices to build objective functions
for the agents interested in harvesting the stock 
economic equilibrium
• International level: Countries exploit a common fish
stock
International cooperation:
how to share benefits
• Assume an agreement is reached for the two countries.
• Then the question remains how they should allocate
cooperative benefits
• A further question arises whether they find the
agreement satisfactory on this path.
• In practice countries negotiate on TACs (Total Allowable
Catch)
• After receiving the national TAC they still need to
implement national management (open access, TAC,
ITQ (Individual Transferable Quotas), ITE (Individual
Transferable Effort)
Game theory and fisheries
• Countries exploit common fish stocks
• Strategic incentives to subsidise the national
fleet and create overcapacity  biological and
economic inefficiency
• Game theory helps to explain the reasons and
find ways to reach sustainable agreements
Schäfer-Gordon model
Gordon (Journal of Political Economy 1954),
Schäfer (1957), Scott (JPE 1955)
Biology
• Logistic growth F(x)
• Biomass x
Logistic function
x
F ( x )  Rx (1  )
K
• R: intrinsic growth rate
• x: fish stock
• K: carrying capacity of the ecosystem
Production
• Harvest function:
h  qEx
• E: Fishing effort
• q: Catchability
Sustainability
• F(x) = h
• Steady state
Steady state fish stock
x
Rx (1  )  qEx
K
R (1 
x
)  qE
K
qE
 x  K (1 
)
R
Steady state harvest
• Insert steady state stock into production
function :
x  K (1 
qE
)
R
h  qEx
qE
h  qEK (1 
)
R
Economics
Assumptions:
• Fish price per kg constant
• Unit cost of effort c constant (constant
marginal cost). Note marginal revenue not
constant.
Optimum
• Maximise economic yield by choosing E.
max
FOC:
qE
  ph  cE  pqEK (1  )  cE
R

2qE
 pqK (1 
)c  0
E
R
 E* 
R
cR
R
c


(1 
)
2
2q 2 pq K 2q
pqK
Comparative statics
• dE/dR > 0
• dE/dK > 0
• dE/dc < 0
• dE/dp > 0
• dE/dq ?
Open access
• Unregulated fishing. E.g. no international
fisheries agreement.
• Fishers (countries) enter into the fishery
until profits (rent) is equal to zero.
Open access effort
ph  cE  0
qE
pqEK (1 
)  cE  0
R
qE
pqK (1 
)c 0
R
E
OA
R
Rc
R
c
 
 (1 
)
q pq 2 K q
pqK