Lecture Notes: Self-enforcing agreements

Transcription

1 Lecture Notes: Self-enforcing agreements Bård Harstad ECON 4910 April 2017 Bård Harstad (ECON 4910) Self-enforcing agreements April / 15

2 Outline for today Motivation a. Concepts b. Repeated games and Folk theorem c. Repeated games with emission and technology d. Stocks Bård Harstad (ECON 4910) Self-enforcing agreements April / 15

3 Motivation Many environmental problems are international By definitition, an "externality" crosses some kind of border Ozone layer, acid rain, climate change There is no world government which can impose taxes or quotas We must rely on agreements and negotiations Distinguish between self-enforcing agreements and legally binding agreements. Must use game theory to better understand the countries strategic actions Many environmental problems are dynamic The relationship is ongoing Pollution stocks accumulate over time Technology are invested in and accumulates over time Bård Harstad (ECON 4910) Self-enforcing agreements April / 15

4 Motivation - Kyoto 1997 The Kyoto Protocol (first commitment period): 35 countries negotiated quotas 5% average emission reduction (from 1990-levels) 5y: Durban Platform and Doha 2012: EU promised to continue similar commitments, if other countries specify targets by 2015 for 2020 Investments in new technology Importance of technology transfer/develop recognized.. "technology needs must be nationally determined, based on national circumstances and priorities" ( 114 in the Cancun Agreement, confirmed in Durban) Bård Harstad (ECON 4910) Self-enforcing agreements April / 15

5 Motivation - Paris 2015 Countries had to suggest, before the Paris meeting, their "intended nationally determined contributions" (INDCs) No formal commitments to reduce carbon emissions by a numerical target during a specific time frame. The agreement calls for the U.N. Framework Convection on Climate Change to publish all national action plans on its Web site and for scientists to calculate the contributions these plans make to curbing emissions. (WP) A Climate Accord Based on "Global Peer Pressure" (NYT) Climate is the ultimate public good International agreements must be self-enforcing There is no explicit sanctions Compliance is the main problem Bård Harstad (ECON 4910) Self-enforcing agreements April / 15

6 a. Important Concepts and Equilibria Refinements Normal form game Extensive form game Repeated game and stage game Stochastic/dynamic game Nash equilibrium Subgame-perfect equilibrium Renegotiation proofness Markov-perfect equilibrium Bård Harstad (ECON 4910) Self-enforcing agreements April / 15

7 b. The Prisoner Dilemma Game Climate is the ultimate public good Abatements are costly and benefit others The prisoner dilemma game is a reasonable stage game Let g i be the emission of i {1,.., n}, B (g i ) the benefit of polluting, c the marginal cost of greenhouse gases: u i = B (g i ) c n g i. i=1 If g { g, g }, the first-best agreement is simply g = g if: B (g) B ( g ) < ( g g ) cn. But polluting more is a dominant strategy if: B (g) B ( g ) > ( g g ) c. The emission game is a prisoner dilemma game if both holds: 1 < B (g) B ( g ) c ( g g ) < n. Bård Harstad (ECON 4910) Self-enforcing agreements April / 15

8 b. The Repeated Prisoner Dilemma Game Folk theorem with Nash equilibrium and SPE: Every v F is possible if v i v i min max v i and δ large. In PD, the minmax strategy is simply g = g. With (grim) trigger strategies, cooperation (g = g) is an SPE if B ( g ) cng B (g) cng B (g) cg c (n 1) g + δ 1 δ 1 δ B (g) B ( g ) c ( g g ) [δn + (1 δ)] So, as long as the first best requires g = g, cooperation is possible for suffi ciently high discount factors: [ δ δ 1 ( ) ] B (g) B g n 1 c ( g g ) 1 < 1. If δ < δ, the unique SPE is g = g. Bård Harstad (ECON 4910) Self-enforcing agreements April / 15

9 c. Emissions and Technology Consider next a stage game with both emissions and technology investments (r i,t ): u i,t = B (g i,t, r i,t ) c (r i,t ) n i=1 g i,t kr i,t. B ( ) is increasing and concave in both arguments. Examples: "green" technologies: b gr <0 and c r =0 "brown" technologies: b gr >0 and c r =0 "adaptation" technologies: b gr =0 and c r <0 Linear investment-cost k is a normalization Will be added below: Uncertainty, heterogeneity, and stocks Bård Harstad (ECON 4910) Self-enforcing agreements April / 15

10 c. Benchmarks The first-best outcome is (g, r ) satisfying B g (g, r ) = nc (r ) and B r (g, r ) ng c r (r ) = k. The business-as-usual outcome is ( g b, r b) satisfying B g (g b, r b) ( = c r b) and ( B r g b, r b) ng b c r (r b) = k. Given g, every country will voluntarily invest optimally in r. Once g has been committed to, there is no need to negotiate r. If g { g, g }, the first-best agreement is simply g = g. Bård Harstad (ECON 4910) Self-enforcing agreements April / 15

11 c. Problem: Deriving the best SPE The maximization problem is: B (g, r) ngc (r) kr max r,g {g,g} 1 δ subject to the two "compliance constraints" (CC-r) and (CC-g): B (g, r) ngc (r) kr 1 δ B(g b ( r), r) [g b ( r) + (n 1) g b (r)]c ( r) k r + δub 1 δ r, B (g, r) ngc (r) δkr 1 δ B ( g, r) [ g + (n 1) g] c (r) + δub 1 δ g. Folk theorem: There exists δ r < 1 and δ g < 1 such that the first-best can be sustained as an SPE iff δ max { δ r, δ g }. Bård Harstad (ECON 4910) Self-enforcing agreements April / 15

12 c. Compliance Constraints Proposition CC-r never binds if an agreement is beneficial (i.e., δ r = 0). CC-g can be written as ( δ (r) can be defined such CC-g binds): B ( g, r ) ngc kr (1/δ 1) [ B (g, r) B ( g, r ) ( g g ) c ] u b. CC-g is more likely to hold for large δ, n, or c (r). Maximizing rhs of CC-g wrt r gives the best compliance technology r: ( ) B r g, r ngcr ( r) k ( ) ( ) = B r (g, r) B r g, r g g c ( r) 1/δ 1 ( g g ) [B gr c r ] r > r IFF B gr c r < 0. Bård Harstad (ECON 4910) Self-enforcing agreements April / 15

13 c. Equilibrium Technology Proposition Let c (r) hf (r). For every r, we have δ h (r) < 0 and δ n (r) < 0. Suppose δ δ g δ (r ). If h, n, or δ decreases, then r>r for "green" technologies (where B gr <0 and c r =0) r<r for "brown" technologies (where B gr >0 and c r =0) r<r for "adaptation" technologies (where B gr =0 and c r <0) Bård Harstad (ECON 4910) Self-enforcing agreements April / 15

14 c. Heterogeneity Proposition CC-g only depends on individual parameters. Suppose δ i δ i (ri ). If h i, δ i, n or i s size decreases, then r i >ri for "green" technologies (where B gr <0 and c r =0) r i <ri for "brown" technologies (where B gr >0 and c r =0) r i < ri for "adaptation" technologies (where B gr =0 and c r <0) Reluctant countries should contribute more! (i.e., invest more in green technologies and less in brown.) True: One problem is to persuade a reluctant country to participate. However, the harder problem is to ensure that they are willing to comply - once they expect others to comply. Reluctant countries should be helped to make such self-commitment, and this can be done with technology! Bård Harstad (ECON 4910) Self-enforcing agreements April / 15

15 d. Stocks We can reformulate the model to allow for stocks Consider a pollution stock G t = q G G t 1 + g i,t and if just c C / (1 δq G ). ũ i,t = B (g i,t, r i,t ) CG t kr i,t, Similarly, the technology r i,t can be a stock: r i,t = q R r i,t 1 + s i,t, where the investment s i,t has the marginal cost K, if just k K (1 δq R ). Bård Harstad (ECON 4910) Self-enforcing agreements April / 15