COALITION FORMATION UNDER UNCERTAINTY AND RISK: THE SUCCESS OF INTERNATIONAL ENVIRONMENTAL AGREEMENTS Michael Finus University of Exeter Business School, Department of Economics, UK 1
1. Coalition Formation and Uncertainty (No Risk) 2. Optimal Transfer Scheme 3. Introducing Risk in a Simple PD-Game 4. Possible Extensions 2
Coalition Formation and Uncertainty (No Risk) Dellink, R. and M. Finus (2009), Uncertainty and Climate Treaties: Does Ignorance Pay? Stirling Economics Discussion Paper No. 2009-16, UK. Dellink, R., M. Finus and N. Olieman (2008), The Stability Likelihood of an International Climate Agreement. Environmental and Resource Economics , 39 : 357-377. Finus, M. and P. Pintassilgo (2010), International Environmental Agreements under Uncertainty: Does the Veil of Uncertainty Help? Economics Department Discussion Paper Series, 10/03, 2010, University of Exeter, UK. Kolstad, C. (2007), Systematic Uncertainty in Self-enforcing International Environmental Agreements. Journal of Environmental Economics and Management , 53 : 68-79. 3
Kolstad, C. and A. Ulph (2008), Learning and International Environmental Agreements. Climatic Change , 89 : 125-141. Kolstad, C. and A. Ulph (2009), Uncertainty, Learning and Heterogeneity in International Environmental Agreements. Na, S.-L. and H.S. Shin (1998), International Environmental Agreements under Uncertainty. Oxford Economic Papers , 50 : 173-185. 4
Theme ● climate change ● uncertainty ● learning (research, Stern Report, IPCC) ● international environmental agreements (IEAs) 5
Motivation of Research Result: Learning can be bad in the context of IEAs! Ulph (1998), Na/Shin (1998), Kolstad (2007), Kolstad/Ulph (2008, 2009) Question 1: How general is this result? Question 2: What are the driving forces? Question 3: Can the problem be fixed? Dellink et al. (2008) and Dellink and Finus (2009). 6
Basic Setting Stage 1: Membership Π ≥ Π ∀ ∈ internal stability: S * * ( S ) ( S \{i }) i i i {{S}, {i}, …., {m}} Π ≥ Π ∪ ∀ ∉ external stability: S * * ( S ) ( S { j }) j j j Stage 2: Abatement Decision ∑ − Π ∀ ∈ Coalition Members: S S S max. ( q ,q ) i i S q ∈ i S ⇒ q ( S ) ⇒ π * * ( S ) Π − ∀ ∉ Singletons: S j max. ( q ,q ) j j j q j 7
Basic Setting ● symmetric uncertainty (analytical uncertainty; vs asymmetric= strategic uncertainty) ● risk neutrality ● uncertainty about the parameters of the payoff function 8
Assumptions ⇒ 1) Number of Players: 3 N players ⎛ ⎞ n Π = − ∑ 2) Payoff Function : 2 ⎜ ⎟ b y c y i i ⎝ k ⎠ i i = k 1 ⎛ ⎞ n b Π = θ − = = , θ = ∑ 2 ⎜ ⎟ if y y c c c i i i ⎝ k ⎠ i c i j i = k 1 ⎛ ⎞ 1 n = = , Π = − θ = ∑ bc 2 ⎜ ⎟ if b b b y y θ i ⎝ k ⎠ i i j i = k 1 i i 9
Assumptions 3) Learning Scenarios: No, Full and Partial Learning (NL, FL, PL) 10
Three Scenarios of Learning Stage 1: Membership NL PL FL π π π expected expected true i i i Stage 2: Abatement Decision NL PL FL θ θ θ expected true true i i i 11
Assumptions 3) Learning Scenarios: No, Full and Partial Learning (NL, FL, PL) 4) Four Cases of Uncertainty 12
Case 1: Uncertainty about the Distribution of Benefits without Transfers (Na/Shin Case) ⎛ ⎞ n b Π = θ − = = , θ = ∑ 2 ⎜ ⎟ if y y c c c i ⎝ ⎠ i i k i c i j i = k 1 ex-ante: symmetric; [ ] E Θ same for all players i ex-post : asymmetric; uniform probability distribution ⎧ 1 θ = ∈ ⎪ , for k k N ( ) θ = ⎨ Θ ≠ Θ ∀ ∈ i , f i k N n Θ i i k i ⎪ 0 ⎩ otherwise n { } ∪ Θ = 1,2,...,n i = i 1 13
Lemma 1: Second Stage in Case 1 In every possible coalition structure: = = Individual and Total Expected Abatement Levels: FL PL NL . = ≤ Individual and Total Expected Payoff Levels: FL PL NL with strict ≠ inequality if S N . Lemma 2: First Stage in Case 1 = ⎧ 1 3 if n ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ = ⎨ = = * * * 3 > PL NL FL E m E m E m ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ≥ 2 4 ⎩ if n 14
Proposition 1: Outcome in Case 1 = > 1) Total Abatement: NL PL FL = > = ⎧ 3 NL PL FL if n 2) Total Payoff: ⎨ . > > ≥ 4 ⎩ NL PL FL if n Intuition? 15
2 n q ∑ Π = θ − i q i i k 2 = k 1 Simple Example ● only two players ● only 2 learning scenarios: FL and NL ● only 2 cases of uncertainty: level and distribution ● only 2 realizations of parameter Three Driving Forces a) information effect from learning: zero b) strategic effect from learning: negative c) distributional effect from learning: negative 16
Case Uncertainty Example Ex-Post about Realizations 1 distribution (1,2 ) , ( 2,1) asymmetric 2 level (1,1) , ( 2,2 ) symmetric ∑ ∑ = ⇒ θ = 2 n ∑ q Full Cooperation : MB MC q Π = θ − i j i j i q i i k = ⇒ θ = 2 No Cooperation : MB MC q = k 1 i i i i 17
∑ ∑ 2 n = ⇒ θ = q ∑ Full Cooperation : MB MC q Π = θ − i q j i j i i i k 2 = ⇒ θ = = No Cooperation : MB MC q k 1 i i i i Full Cooperation No Cooperation θ Abatement Payoffs Abatement Payoffs i FL NL FL NL FL NL FL NL Case 1 Uncertainty about the Distribution of Benefits 1; 2 3; 3 3; 3 1.5; 7.5 4.5; 4.5 1; 2 1.5; 1.5 2.5; 4 3.38; 3.38 2; 1 3; 3 3; 3 7.5; 1.5 4.5; 4.5 2; 1 1.5; 1.5 4, 2.5 3.38; 3.38 ∅ 3; 3 3; 3 4.5; 4.5 4.5; 4.5 1.5; 1.5 1.5; 1.5 3.25; 3.25 3.38; 3.38 Case 2 Uncertainty about the Level of Benefits 1; 1 2; 2 3; 3 2; 2 4.5; 4.5 1; 1 1.5; 1.5 1.5; 1.5 3.38; 3.38 2; 2 4; 4 3; 3 8; 8 4.5; 4.5 2; 2 1.5; 1.5 6; 6 3.38; 3.38 ∅ 3; 3 3; 3 5; 5 4.5; 4.5 1.5; 1.5 1.5; 1.5 3.75; 3.75 3.38; 3.38 18
Case 2: Uncertainty about the Level of Benefits (Kolstad/Ulph Case) ⎛ ⎞ n b Π = θ − = = , θ = ∑ 2 ⎜ ⎟ if y y c c c i i i ⎝ k ⎠ i c i j i = k 1 Kolstad (2007) and Kolstad and Ulph (2008, 2009): systematic uncertainty ex-ante: symmetric; same expectations Θ = Θ ∀ ∈ ex-post: symmetric; once uncertainty is resolved, , i k N i k no assumption about probability distribution f Θ is required i 19
Proposition 2: Outcome in Case 2 = = 1) Total Abatement: FL PL NL = > FL PL NL 2) Total Payoff: . Three Driving Forces a) information effect from learning: positive b) strategic effect from learning: positive c) distributional effect from learning: zero 20
∑ ∑ 2 n = ⇒ θ = q ∑ Full Cooperation : MB MC q Π = θ − i q j i j i i i k 2 = ⇒ θ = = No Cooperation : MB MC q k 1 i i i i Full Cooperation No Cooperation θ Abatement Payoffs Abatement Payoffs i FL NL FL NL FL NL FL NL Case 1 Uncertainty about the Distribution of Benefits 1; 2 3; 3 3; 3 1.5; 7.5 4.5; 4.5 1; 2 1.5; 1.5 2.5; 4 3.38; 3.38 2; 1 3; 3 3; 3 7.5; 1.5 4.5; 4.5 2; 1 1.5; 1.5 4, 2.5 3.38; 3.38 ∅ 3; 3 3; 3 4.5; 4.5 4.5; 4.5 1.5; 1.5 1.5; 1.5 3.25; 3.25 3.38; 3.38 Case 2 Uncertainty about the Level of Benefits 1; 1 2; 2 3; 3 2; 2 4.5; 4.5 1; 1 1.5; 1.5 1.5; 1.5 3.38; 3.38 2; 2 4; 4 3; 3 8; 8 4.5; 4.5 2; 2 1.5; 1.5 6; 6 3.38; 3.38 ∅ 3; 3 3; 3 5; 5 4.5; 4.5 1.5; 1.5 1.5; 1.5 3.75; 3.75 3.38; 3.38 21
Case 3: Uncertainty about the Distribution of Benefits with Transfers ● almost ideal transfer scheme ● cannot influence negative strategic effect (FL, PL ≺ NL) ● counterbalances negative distribution effect from learning and even turns it into positive effect (improves FL over PL and NL) ≤ ⎧ 3 8 if n ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ = ⎨ = = * * * 3 ≤ PL NL FL E m E m E m ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ( ) > ≥ 3 9 f n if n ⎩ = = = ⎧ 3 FL PL NL if n ⎪ > = ≤ ≤ 4 8 ⎪ NL FL PL if n Total Payoff: ⎨ > > = 9 NL FL PL if n ⎪ ⎪ > > ≥ 10 ⎩ FL NL PL if n 22
∑ ∑ 2 n = ⇒ θ = q ∑ Full Cooperation : MB MC q Π = θ − i q j i j i i i k 2 = ⇒ θ = = No Cooperation : MB MC q k 1 i i i i Full Cooperation No Cooperation θ Abatement Payoffs Abatement Payoffs i FL NL FL NL FL NL FL NL Case 1 Uncertainty about the Distribution of Benefits 1; 2 3; 3 3; 3 1.5; 7.5 4.5; 4.5 1; 2 1.5; 1.5 2.5; 4 3.38; 3.38 2; 1 3; 3 3; 3 7.5; 1.5 4.5; 4.5 2; 1 1.5; 1.5 4, 2.5 3.38; 3.38 ∅ 3; 3 3; 3 4.5; 4.5 4.5; 4.5 1.5; 1.5 1.5; 1.5 3.25; 3.25 3.38; 3.38 Case 2 Uncertainty about the Level of Benefits 1; 1 2; 2 3; 3 2; 2 4.5; 4.5 1; 1 1.5; 1.5 1.5; 1.5 3.38; 3.38 2; 2 4; 4 3; 3 8; 8 4.5; 4.5 2; 2 1.5; 1.5 6; 6 3.38; 3.38 ∅ 3; 3 3; 3 5; 5 4.5; 4.5 1.5; 1.5 1.5; 1.5 3.75; 3.75 3.38; 3.38 23
Two effects from forming a coalition: 1) Interalization of an externality (non-exclusive to coalition) 2) Equalizing marginal abatement costs (exclusive to coalition) 24
Case 4: Uncertainty about the Distribution of Costs ● information and strategic effect from learning positive (FL, PL � NL) ● without transfers: distributional effect from learning negative for FL ● transfers: mitigate distributional effect, but does not turn it into positive effect ● with transfers: Total Payoffs and Abatement: FL=PL>NL 25
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