Introduction The Game The Model General Results Numerical Simulations The Thin Green Line: Transboundary Pollution Problems in Coupled Lake Systems W. Davis Dechert Sharon O’Donnell and Stuart McDonald 2nd Workshop Game Theory in Energy, Resources and the Environment 2008 29 June 2008 W. Davis Dechert Sharon O’Donnell and Stuart McDonald The Thin Green Line
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IntroductionThe GameThe Model
General ResultsNumerical Simulations
The Thin Green Line:Transboundary Pollution Problems in Coupled Lake
Systems
W. Davis DechertSharon O’Donnell and Stuart McDonald
2nd Workshop Game Theory in Energy, Resources and theEnvironment 2008
29 June 2008
W. Davis Dechert Sharon O’Donnell and Stuart McDonald 2nd Workshop Game Theory in Energy, Resources and the Environment 2008The Thin Green Line
IntroductionThe GameThe Model
General ResultsNumerical Simulations
I The Game
I Non Cooperative Solution
I Dynamic Programming
I Numerical Results
I Stochastic Elements & Droughts
W. Davis Dechert Sharon O’Donnell and Stuart McDonald 2nd Workshop Game Theory in Energy, Resources and the Environment 2008The Thin Green Line
IntroductionThe GameThe Model
General ResultsNumerical Simulations
Single Lake ProblemCoupled Lake Problem
The Single Lake Game
I Players: Communities that share the lake
I Pollution: Phosphorus applied to land (controls)Accumulation in the lake (state)
I Benefits: Increased crop production −→ profits
I Costs: Phosphorus −→ nutrients for weeds and algæ
W. Davis Dechert Sharon O’Donnell and Stuart McDonald 2nd Workshop Game Theory in Energy, Resources and the Environment 2008The Thin Green Line
IntroductionThe GameThe Model
General ResultsNumerical Simulations
Single Lake ProblemCoupled Lake Problem
The Single Lake Game
I Players: Communities that share the lake
I Pollution: Phosphorus applied to land (controls)Accumulation in the lake (state)
I Benefits: Increased crop production −→ profits
I Costs: Phosphorus −→ nutrients for weeds and algæ
W. Davis Dechert Sharon O’Donnell and Stuart McDonald 2nd Workshop Game Theory in Energy, Resources and the Environment 2008The Thin Green Line
IntroductionThe GameThe Model
General ResultsNumerical Simulations
Single Lake ProblemCoupled Lake Problem
The Single Lake Game
I Players: Communities that share the lake
I Pollution: Phosphorus applied to land (controls)Accumulation in the lake (state)
I Benefits: Increased crop production −→ profits
I Costs: Phosphorus −→ nutrients for weeds and algæ
W. Davis Dechert Sharon O’Donnell and Stuart McDonald 2nd Workshop Game Theory in Energy, Resources and the Environment 2008The Thin Green Line
IntroductionThe GameThe Model
General ResultsNumerical Simulations
Single Lake ProblemCoupled Lake Problem
Upstream/Downstream Game
I Players: Upstream and downstream communities
I Pollution: Upstream and downstream application of P
I Interconnection: Some upstream pollution flows downstream
I Benefits: Increased crop production
I Costs: Accumulation of phosphorus in the lakes
W. Davis Dechert Sharon O’Donnell and Stuart McDonald 2nd Workshop Game Theory in Energy, Resources and the Environment 2008The Thin Green Line
IntroductionThe GameThe Model
General ResultsNumerical Simulations
Single Lake ProblemCoupled Lake Problem
Upstream/Downstream Game
I Players: Upstream and downstream communities
I Pollution: Upstream and downstream application of P
I Interconnection: Some upstream pollution flows downstream
I Benefits: Increased crop production
I Costs: Accumulation of phosphorus in the lakes
W. Davis Dechert Sharon O’Donnell and Stuart McDonald 2nd Workshop Game Theory in Energy, Resources and the Environment 2008The Thin Green Line
IntroductionThe GameThe Model
General ResultsNumerical Simulations
Single Lake ProblemCoupled Lake Problem
Upstream/Downstream Game
I Players: Upstream and downstream communities
I Pollution: Upstream and downstream application of P
I Interconnection: Some upstream pollution flows downstream
I Benefits: Increased crop production
I Costs: Accumulation of phosphorus in the lakes
W. Davis Dechert Sharon O’Donnell and Stuart McDonald 2nd Workshop Game Theory in Energy, Resources and the Environment 2008The Thin Green Line
IntroductionThe GameThe Model
General ResultsNumerical Simulations
Single Lake ProblemCoupled Lake Problem
Upstream/Downstream Game
I Players: Upstream and downstream communities
I Pollution: Upstream and downstream application of P
I Interconnection: Some upstream pollution flows downstream
I Benefits: Increased crop production
I Costs: Accumulation of phosphorus in the lakes
W. Davis Dechert Sharon O’Donnell and Stuart McDonald 2nd Workshop Game Theory in Energy, Resources and the Environment 2008The Thin Green Line
IntroductionThe GameThe Model
General ResultsNumerical Simulations
CharacterizationCooperative GameNoncooperative Game
Assumptions
I Separable functional form for costs and benefits
I Agreement on functional form of costs
I Player’s benefits are a function of his/her own loading
W. Davis Dechert Sharon O’Donnell and Stuart McDonald 2nd Workshop Game Theory in Energy, Resources and the Environment 2008The Thin Green Line
IntroductionThe GameThe Model
General ResultsNumerical Simulations
CharacterizationCooperative GameNoncooperative Game
Assumptions
I Separable functional form for costs and benefits
I Agreement on functional form of costs
I Player’s benefits are a function of his/her own loading
W. Davis Dechert Sharon O’Donnell and Stuart McDonald 2nd Workshop Game Theory in Energy, Resources and the Environment 2008The Thin Green Line
IntroductionThe GameThe Model
General ResultsNumerical Simulations
CharacterizationCooperative GameNoncooperative Game
Assumptions
I Separable functional form for costs and benefits
I Agreement on functional form of costs
I Player’s benefits are a function of his/her own loading
W. Davis Dechert Sharon O’Donnell and Stuart McDonald 2nd Workshop Game Theory in Energy, Resources and the Environment 2008The Thin Green Line
IntroductionThe GameThe Model
General ResultsNumerical Simulations
CharacterizationCooperative GameNoncooperative Game
Assumptions
I Separable functional form for costs and benefits
I Agreement on functional form of costs
I Player’s benefits are a function of his/her own loading
W. Davis Dechert Sharon O’Donnell and Stuart McDonald 2nd Workshop Game Theory in Energy, Resources and the Environment 2008The Thin Green Line
IntroductionThe GameThe Model
General ResultsNumerical Simulations
CharacterizationCooperative GameNoncooperative Game
State Equations
I Upper lake
xt+1 = bxxt +x2t
1 + x2t
+∑
i
ai ,t
I Lower lake
yt+1 = byyt +y2t
1 + y2t
+∑
i
ai ,t + µxt
W. Davis Dechert Sharon O’Donnell and Stuart McDonald 2nd Workshop Game Theory in Energy, Resources and the Environment 2008The Thin Green Line
IntroductionThe GameThe Model
General ResultsNumerical Simulations
CharacterizationCooperative GameNoncooperative Game
State Equations
I Upper lake
xt+1 = bxxt +x2t
1 + x2t
+∑
i
ai ,t
I Lower lake
yt+1 = byyt +y2t
1 + y2t
+∑
i
ai ,t + µxt
W. Davis Dechert Sharon O’Donnell and Stuart McDonald 2nd Workshop Game Theory in Energy, Resources and the Environment 2008The Thin Green Line
IntroductionThe GameThe Model
General ResultsNumerical Simulations
CharacterizationCooperative GameNoncooperative Game