Introductions of invasive species:
Failure of the weaker link
Kimberly M. Burnett
Prevention of invasions as a public good
• Prevention in 1 place is prevention in another
• Doing inspections, regulations, monitoring, quarantines, etc.
→ less likely species will invade
→ less likely to invade other regions (esp. if shared borders,
lots of trade between places)
• Examples:
– West Nile in HI
– Yellow star thistle
– Zebra mussels
Prevention of YST
AR?
MS?
2005 map – http://plants.usda.gov
Prevention of Zebra Mussels
GA?
FL?
2003 Map – USGS
Special kind of public good
• “The exclusion and control of invasive species is a
weakest link public good” (Perrings et al. 2002)
• Hirshleifer (1983,1985) –introduced weakest link
public goods (levy example)
• Weakest link implies the following aggregation
technology:
P  min p
i
i
Prevention as weaker link
• Own prevention helps, even if others do less
• Prevention beyond lowest level provides benefit, but
progressively less as exceed min
• Public good aggregation given by geometric mean 1
n
n
(Cornes 1993):
P  ( p )
i 1
• If 2 regions,
P( p1 , p2) 
i
p1 p2
• What this means is regions have incentive to know what
other will provide, since better off if don’t provide more.
May or may not know.
Prevention based on cost
Costs can represent technological, institutional, political, environmental, etc.
differences, e.g., heterogeneous environments (diversity, islands vs.
continents, etc.)
Easier to invade, “high cost”
Harder to invade, “low cost”
Objectives
1. Use “weaker link” public good model to
describe prevention of invasive species
2. Compare equilibrium prevention levels to
efficient levels
3. Investigate how the structure of information
between regions (regarding cost of prevention)
changes this
Model
2 region, static, utility maximization
U ( p i , p j )  P  ci p i ,
2
i
P( p1 , p2) 
2 cost types:
i j
p1 (c1) p2 (c2)
cH with probability θ
cL with probability (1-θ)
Solve & compare:
• PO levels of prevention (Social planner)
• Complete information equilibrium (NEq)
• Incomplete information equilibrium (BNE)
Results: Underprovision of prevention
PO prevention > NEq (complete info) prevention
PO prevention > BNE (incomplete info) prevention
→
In equilibrium, prevention of
invasive species will be underprovided
compared to the efficient level
How does NEq compare to BNE?
Complete vs. incomplete information
Cost structure Probability Complete
Incomplete
HH
θ
Pc(cH,cH) <,=,>
Pi(cH,cH)
HL
θ(1-θ)
Pc(cH,cL) <,=,>
Pi(cH,cL)
LH
(1-θ)θ
Pc(cL,cH) <,=,>
Pi(cL,cH)
Pc(cL,cL) <,=,>
Pi(cL,cL)
LL
2
(1 - θ)
2
Deviation function
• Need to look at expected difference between complete and
incomplete information:
D( , c H , c L ) 
 2 [ PCOMPLETE (c H , c H )  P INCOMPLETE (c H , c H )]
 2 (1 -  )[ PCOMPLETE (c H , c L )  P INCOMPLETE (c H , c L )]
 (1 -  )2 [ P COMPLETE (c L , c L )  P INCOMPLETE (c L , c L )]
Ex ante analysis
• Value of this function is positive given any θ, cH, cL
→ More prevention expected to be provided under
complete information
• Costs comparative statics:
D
0
 cH
D
0
 cL
Absolute cost values or difference?
D
0.02
0.015
0.01
0.005
0.02
0.04
0.06
0.08
0.1
cH
cL
Ex post analysis
• Numerical analysis
• After types are realized, how do provision levels
compare?
• Result: anything can happen
• Under some specifications of θ, incomplete
information more efficient
Lessons
• Prevention of invasive species will be
underprovided in equilibrium compared to the
efficient level
• Ex ante, incompleteness of information leads to
inefficiently low levels of prevention
• Ex post, possible that incomplete information
more efficient
Implications and extensions
• Complete information more efficient – make costs
transparent (improved reporting, communication). We see
this happening (GISP, NISC, NBII, ISSG…)
• Costs closer together – higher efficiency – Pareto-improving
transfers from low cost to high cost countries?
• As a first step, focused on how weaker link technology
affects equilibrium prevention
• More complete model would include type of prevention
activity, income/preferences, probability of invasion.
Thanks to
USDA/ERS
(43-3AEM-3-80083)
&
University of Hawaii
Arts and Sciences Advisory Council
for financial support