Understanding Complex Systems

1

• From Complex Conflicts to Stable Cooperation

Jürgen Scheffran, ACDIS Bruce Hannon,
Geography/NCSA University of Illinois
Understanding Complex Systems May 18, 2005
2
What is conflict?

• Conflict Dynamic process involving actors which
  fail to reduce their conflict potentials to
  tolerable levels
• Actors persons, groups, States, firms, etc.
• Conflict potential continued differences on
• Values/goals (interests, needs, motivations,
  risks, objectives, targets)
• Resources/means (cost, investment, time, energy,
  information, force)
• Options/actions (decision possibilities,
  technology paths, behavior modes)
• Conflict dynamics
• Conflict escalation actions lead to increasing
  conflict potential (unstable)
• Conflict resolution actions reduce conflict
  potential (stable)
• Cooperation actors achieve their goals better by
  adapting their goals, means and actions

3
The action triangle
4
The single actor feedback loop

• Feedback/learning

priorities px
Max.cost C
efficiency fx
Value V Goal V
Cost C
System X
cx unit cost
vx unit value
C Cost invested in a given period (flow
variable) for changing system state x with fx
px vx / cx action efficiency, depending on unit
cost cx, unit value vx and px percentage of
cost allocated to action path x. k cost
reactivity in logistic reaction function ?
desired decay time of value gap
5
The multi-actor feedback loop
C1 Ci Cn
C1 Ci Cn
X1 Xk Xm
V1 -V1 Vi -Vi Vn - Vn
fij
pik
cik
vik
Invested Costs
System variables
Values goals
Efficiency
Allocation preferences
6
The multi-actor dynamic system
?Vi fij Cj ?Ci - ki Ci (Ci - Ci) (Vi
- Vi ??i ?Vi) ?Xik pik Ci / cik
Satisfaction ?Ci 0 for ?Vi -(Vi - Vi)
/??i ?Vi (exponential decay) Target costs for
?Vi ?Vi Ci (?Vi - fij Cj ) /
fii
7
Conflict vs. cooperation
Cost C2
Conflicting relation
Max C2

C
Neutral relation

C2
Cooperative relation

C1
Cost C1
Max C1

Target cost Ci (?Vi fij Cj) / fii
8
The interaction matrix
?V F C ?V
C1
Ci
Cn
V1 - V1
V2 - V2
Vn - Vn
-Equilibria, stability and complexity depend on
interaction couplings fij(p) and thus can be
controlled by changing action priority
p. -Stability depends on eigenvalues of
interaction matrix F(p) -Two player stability for
fii gt 0, fij lt0 and det F f11 f22 f12 f21 gt
0 -Non-linear case fij ?Vi/ ?Cj and F is
Jacobi-Matrix
9
The two-actor model in Stella
10
The transition to chaosAnti-symmetric case as a
function of decay time tau
Parameter setting Initial V1(0) -V2(0) -0.3,
C1(0) C2(0) 30 Impacts f11 f22 -f12
-f21 0.01 k1 k2 0.02, C1 C2 60
tau0
tau0.1
tau10
11
An unstable conflict
Parameter setting Initial V1(0) -V2(0) -0.3,
C1(0) C2(0) 30 Impact f11 f22 0.009, f12
f21 -0.011 k1 k2 0.02, C1 C2 60
12
CLIMATE CHANGE

• The growing conflict between emission trends and
  targets

Emissions
Socio-economic trend
Disaster threshold?
Conflict Potential?
Viable emission targets
Time
13
Cost-regulated climate model in Stella
14
The reduced climate model
?F G ?C B F ? G ? (C C1) ?T ?
ln (C / C1) - ? (T T1)

• Greenhouse gas emissions G
• Cumulative emissions F
• CO2 concentrations C
• Global mean temperature T

C1 280 ppmv and T1 14.6 oC denote the
preindustrial levels

• ? Q2C / (coc ln 2) , ?? Q2C / (coc T2C )
• Q2C 3.7 W m-2 radiative forcing for doubling
  concentration
• coc 61.4 Wa m-2 oC-1 effective ocean heat
  capacity
• T2C ? 1.5oC, 4.5oC climate sensitivity (double
  concentration)

Source Hasselmann etal 1997, Petschel-Held etal
1999, Kriegler/Bruckner 2004
15
Role of reduction costs per emission unit

• c0 100

• c0 200

• Baseline G07.5 GtC/a, ?G00.2 GtC/a, C50b,
  c0100 b/GtC, ?0.017 (T2C3.5C). ?-0.5,
  k0.001, ?100

• c0 20

• c0 50

16
Temperature change for parameter variations
200
10
150
20
100
50
50
20
100
200
Variation of unit reduction cost c0 b/GtC
Variation of max reduction cost C b/a
0.5
0.4
0.3
0.2
0.1
0
Variation of emission trend ?G(0) GtC/a
0
Variation of climate sensitivity T2C
17
Two-region climate model
18
Two actor model with different guardrails

• Case 1 is baseline with
• Actor 1 G106 GtC/a, ?G100.1 GtC/a, R140b,
  T13 oC
• Actor 2 G201.5 GtC/a, ?G200.1 GtC/a,
  R210b, T21.5 oC

• Case 2 like case 1 with
• Actor 1 T11.5 oC
• Actor 2 T23 oC

19
FISHERY CONFLICTS

• 70 of fish stocks worldwide heavily
  overexploited
• Some of them collapsed or to be collapsed, e.g.
  NorthwestAtlantic or North Sea cod
• Low quality of management strategies
• High levels of subsidies
• Collective-action problem in common pool resource
  (Tragedy of the commons)
• Conflicts on scarce fish stocks

20
Fishery and socio-ecological interaction
Policy
r (K x) Fish productivity
? C Effective efforts
h Harvest
Technology Environment
21
Multi-actor competition in fishery
?
22
Baseline parameter set
6
0.2
23
Competitive fishery case
24
Cooperative fishery case