Modeling Conflict and Cooperation Among Multiple Agents

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Modeling Conflict and Cooperation Among
Multiple Agents

• Jürgen Scheffran, ACDIS, UIUC
• Ken Webb, Primordion, Ottawa, Canada
• Understanding Complex Systems Conference
• May 16, 2007

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Conflict, cooperation and coalition formation in
socio-economic networks

• Socio-economic networks are based on decisions,
  actions and perceptions of actors who - in the
  context of their values, goals and action
  resources - pursue strategies and policies that
  interact with their natural and social
  environment.
• How does the interconnection among the actors
  evolve such that stable social structures and
  institutions emerge?
• What is the link between the complexity and the
  stability of socio-economic networks?
• Which mathematical approaches are adequate to
  analyse coalition formation and phase transitions
  between societal micro level' and macro level'?
• Which strategies and policies are compatible to
  avoid instabilities and conflicts that weaken the
  efficiency of the social system?
• Which mechanisms can be implemented to achieve
  (self-)control of complex socio-eonomic networks?
• Social learning in natural environments
  Evolution of cooperation in resource conflicts
  (energy, climate, fishery)

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Structure of an actor
Capital, Power Cost Ci
Values Vi, Goals Vi
Priority pi
Actions ai(x,Ci,pi)
State of the environment x
4
Interaction between two actors
f21C21
C2
V1
Environment x
a1
f11C11
a2
f22C22
p1
p2
V2
C1
f12C12
Target condition V1 f1(C) f11 C1 f12
C2V1 V2 f2(C) f22 C2 f21 C1V2
V F C V
Stability (for fiigt0, fijlt0) Df11f22 f12 f21
gt 0 Conflict for D lt 0
Adaptation dynamics
Equilibrium Ci (Vi - fij Cj) / fii

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Power-value interaction and coalition-formation am
ong three actors
f13C13
f21C21
f31C31
f12C12
Mediation
Negotiation
C
V
p
x
Coalition Formation
f23C23
f32C32
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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
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The multi-actor dynamic system
?Vi fij Cj ?Ci - ki Ci (Ci - Ci) (Vi
- Vi ??i ?Vi) ?Xik pik Ci / cik
Vi Value of actor i Ci Costs of actor i Xik
Variables k affected by i
fij Value-cost efficiencies (interaction
coefficients) ki Reaction strength ?i Decay
time
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The interaction matrix and its complexity
V F C V
C1
Ci
Cn
V1 - V1
V2 - V2
Vn - Vn
Indicator for connectionist complexity of matrix
F
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Conflict vs. cooperation
Unstable dynamics
Cost C2

• Disturbance

Regulation Governance
Conflicting relation
Max C2

C
Neutral relation

C2
Cooperative relation

C1
Cost C1
Max C1

Taget cost Ci (?Vi fij Cj) / fii
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The two-actor model in Stella
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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
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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
Value 1
Costs 1
tau0
Value 2
Costs 2
Costs 1
Value 1
tau10
Costs 2
Value 2
Time
Time
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Security bifurcations
Critical decay time ?
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Lyapunov exponents of the conflict model
Decay time (?)
Decay time (?)
Reactivity (k)
Reactivity (k)
Decay time (?)
Decay time (?)

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Simulation of a multi-actor world
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Offense-defense interaction between multiple
actors
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Offense-defense arms race between 5 countries
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The coalition formation process

• Major questions
• What are the driving forces in evolving complex
  social structures?
• How can the transition from non-cooperation to
  cooperation be modelled? How do coalitions form?
• Under which conditions are coalitions
  stable/unstable?
• Examples
• Voting in UN Security Council or European
  Community
• Formation of international organizations
• Nation-breakup and nation-building (e.g.
  Southeast Europe)
• Concentration process to larger firms
• Coalition formation in emission reduction or
  sustainable resource management (sustainability
  transition)
• Power concentration players use power resources
  to change priorities and probabilities of other
  players to join coalitions until critical mass of
  coalition is reached (e.g. voting threshold)

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Multiple actors and coalitions
Coalition formation
Resource allocation
Unit value
Value distribution
Efficiency fij
C1 Ci Cn
C1 CI CN
X1 Xk Xm
V1 Vi Vn
V1 VI VN
piI
pIk
vIk
pIi
cIk
aIk
Feedback
Resources Costs
Action
Coalition power
Coalition values
System
Unit cost
Individual values
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Interaction of players and coalitions

• Two kinds of actors
• Single players (i 1, ..., n) with power
  resources Ci
• Coalitions (I 1, ..., N) with power resources
• C I f I (C1, ..., Cn)
• Decisions on three levels
• Power allocation piI of player i to coalition I
• Power allocation pIk of coalition to actions k I
• Value distribution pIi of coalition I to player
  i
• Agent value Vi fi (Ci , C-i , pi I, pIk,
  pIi)
• Coalition value V I f I (Ci , C-i , pi I, pIk,
  pIi)

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Values and adaptation in coalition formation
Adaptive evolutionary game
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Two players, coalitions and actions
Feedback
p1
1-p1
1-pi
piI
pi
p2
1-p2
Action
Distribution
Allocation
Players
Power
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Two players, coalitions and actions
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Two players, coalitions and actions
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2x2 coalition-customer interaction
p2 Action priority of coalition 2
Indifference curve for customer 2
(1,1)
(0,2)
Indifference curve for customer 1
(2,0)
(1,1)
p1 Action priority of coalition 1
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Potential complexity of player-coalition
interaction
8 actors, 2 coalitions
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Limits to coalition size
Always support coalition
Never support coalition
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Major players in climate policy
US Umbrella
Consumers
Firms
NGOs
Media
Scientists (IPCC)
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Adaptive Control Where to Go and How Fast?
Critical threshold?
Loss of polar ice
Shutdown of thermohaline circulation
Sea-level rise
Floods
Collapse Amazon forest
Tropical Monsoon suppression
Water scarcity
Droughts
Glacier retreat
Control
Trend
Change in hydrological cycle
Diseases
Target
Loss of coral reefs
Species loss
Harvest loss
Storms

• Speed control?

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Adaptive Control Under Uncertainty
CO2 concentration
x
Limit
x
Control
Target
x-
x1
Trend
x0
Uncertainty
t0
t1
t2
Time
Adaptive decision rules ?x(t) w(x,t) D(x,t)

• Speed control ?x(t) ? w (x(t) x(t))

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Emission trading Multi-actor dynamic game
Value function for actor i
Incremental value of firm for emission reduction
ri
Threshold emission trading price
Threshold emission reduction
Response function between actors i and j
? Coupled multi-actor dynamics of emission
reduction and permit price
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Model specifications of multi-regional emissions
trading
Parameter settings GDP and emission data of 2005
(ICLIPS ref.) Exponents production/costs ? ?
1,5 Damage ? 2 Mitigation cost 5 reduction,
2 GDP loss
Regions AFR Sub-Saharan Africa CPA China,
Mongolia, Vietnam, Cambodia, Laos EEU Eastern
Europe FSU Former Soviet Union LAM Latin America,
Caribbean MEA Middle East,North Africa NAM North
America PAO Pacific OECD (Japan, Australia, New
Zealand) PAS Other Pacific Asia SAS South Asia
(India) WEU Western Europe
Scenarios BAU - Business as usual (emission
baseline ICLIPS) epc - equal per capita 10 red.
- 10 reduction of 2005 baseline level (only
ICs) stabilis. - stabilisation of emissions on
1990 levels
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Simulation of emission tradings among 11 world
regions

• Emissions/capita
• Tons Carbon

• Total emissions and market price

Years
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Coalition formation in energy use
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Coalitions in Energy and Climate Management

• Actions by providers AI produce energy of type k
• for budget CI, cost per energy unit cIk and
  allocation pIk.
• Customer Ai receives share
  of energy.
• Energy of type k received by customer Ai from all
  providers AI
• is used for production or consumption of economic
  output Qi and generates carbon emissions GI
  according to
• qik productivity for energy unit of type k, gik
  carbon emission per energy unit. Value of
  customer Ai

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Example

• Two energy paths A and B, two energy providers
  and six customers.
• Energy path B more expensive by factor 2,
  provider 1 (2) cheaper in energy A (B)
• Customers differ in energy efficiency of
  production, where efficiency for energy 1
  declines from customer 1 to 6 and vice versa for
  energy 2
• Carbon emissions for new energy are gi1 2 gi2
  1 for all i 1, ..., 6.
• Damages per emission unit increase from d1 0.2
  to d6 0.4.
• Benefit per unit of production ui 1 for all
  actors.
• Customers build capital
• Replication equations of evolutionary game in piI
  and p_Ik
• Growth in resources of actors and coalitions A1,
  A6 and coalition C2 strongest growth rates. C1
  specializes in the old energy path, C2 in new
  energy path, where both have cost advantages.

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Searching for compromise in climate negotiations
Value V
Player
Emissions q
Power C
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The compromise coalition
Value V
Coalition Value V12
Player

Position q
Power C
Coalition Power C12
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Factors influencing position change
Value V
Value V1
Value V2
Coalition value share
P1
P2

r1
r2
Emission reduction r
Reward, punishment, force
Capability C1
Cpability C2
Capability C
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Coalition Formation in Negotiations
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Emission Quota Setting Game for two Actors

x carbon concentration qi carbon emissions of
group i q0 recommendation emissions p market
price ?i profit of group i ?i, ?i cost parameter
of group i ?i lt0 penalty parameter group
i Vi value of group i
q0
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Cooperative Management of Energy and Climate
Change
ManagementAuthority
ScientificInstitution
Actor 1
COP
Actor 2
Energy Carbon pool
Modified from Eisenack, Scheffran, Kropp 2006