IEA model. We adopt the non-cooperative game framework referenced above to investigate abatement gains of self- enforcing partial coalitions in contrast with null-coalition and full-coalition behavior. The global profit function is defined as: (1) Each nation bears the cost, Ci, of its own abatement, qi, while all nations share the benefits of reduc- tion of harm, Bi, from global abatement Q. In a stable partial coalition, members have a collective profit that is at least as high as the sum of their individual profits operating alone. However, the allocation of abatement levels within the coalition that maximizes the coalition profit might not result in a higher individual profit for each member compared to their profit if they left the coalition. To overcome this problem, a transfer payment scheme redistributes the net burden among members. The “burden-sharing” rule ensures that the profit each nation receives as a coalition member exceeds what they receive outside the coalition. Nations that ▇▇▇▇▇ an amount greater than required under the agreement would receive a positive transfer, while nations that purchase permits are able to meet their abatement responsibilities under the agreement at a lower cost. Net transfers are zero-sum. Weikard (2009) presents a family of sharing rules that satisfy the internal and external stability re- quirements cited above. We adopt one rule from this set: the allocation rule for abatement requirements under a system of tradable pollution permits followed by ▇▇▇▇▇▇▇ (2007). This rule proposes transfers between coalition members that are “just sufficient to quell any incentive to deviate from the agreement” and distributes the remaining coalition surplus in proportion to the members’ benefit share-to-cost ratio. 3 Application of IEA Model to Debris Mitigation For this initial model of an IEA for space debris mitigation, we examine the effect of a self-enforcing market mechanism on parties’ choices regarding a single type of abatement action: deorbiting of space- craft after mission lifetime. We do not consider other actions parties might take that would affect the rate of debris generation such as active removal of debris, collision avoidance, or anti-satellite weaponry. 3.1 Elements of the model An IEA model requires the following elements: We specify the elements as follows for a space debris mitigation IEA: 3.1.1 Environmental resource and pollutant The environmental resource is taken to be the 900–1000 km altitude shell-of-interest (SOI) analyzed by ▇▇▇▇▇▇▇ and ▇▇▇▇ (2009). This is the region of near-Earth space with the highest object density. (The 700–900-km shell has a higher density of operational spacecraft but lower overall object density.) The “pollutant" is the population of orbital objects that might catastrophically collide with operational spacecraft, and thereby includes all objects from fragments through non-operational spacecraft as well as other operational spacecraft. Of particular concern is the future introduction of spacecraft that are launched but not deorbited from the SOI after completion of their operational lifetimes.2 3.1.2 Actors and actions Since our analysis relies on the long-term debris evolution model of ▇▇▇▇▇▇▇ and ▇▇▇▇, we adopt their baseline assumption of a total annual launch rate of three operational spacecraft per year to the 900–1000- 2The ▇▇▇▇▇▇▇ and ▇▇▇▇ model assumes a rapid deorbiting out of the SOI at end-of-life to an altitude of 600 km, in accordance with the NASA policy discussed earlier. km SOI (▇▇▇▇▇▇▇ and ▇▇▇▇, 2009). For a set of actors, we look at ownership data, by nation, for recent ▇▇▇ spacecraft whose orbits enter this SOI as indicated in the UCS database of operational spacecraft (Union of Concerned Scientists, 2009). We use a recent eight-year period3 and ignore spacecraft in orbits UCS classifies as “elliptical" (i.e., with eccentricity 0.14 and higher) because these spend only a small fraction of time in the SOI. (See Appendix: Spacecraft in the Shell of Interest.) We focus only on the pattern of launch distribution among nations (as “owners"), and ignore temporal variation in the ownership set. The one spacecraft identified as “international" we treat as having a single owner, and the one spacecraft with two identified co-owners we allocate equally between them. The resulting set contains seven actors, and we scale the launch distribution to match the total launch rate above. Reliance on the historical launch rates to the SOI results in a small set of actors, while the trend is arguably toward broader participation. Given this, we consider the seven-actor empirical distribution to be our Case I, and construct a “plausible" distribution for a larger set of actors, which we call Case II. We construct this pattern from UCS data for a broader ▇▇▇ ▇▇▇▇▇, from 700 to 1000 km. There were 15 single-nation “owners" of spacecraft recently launched to this shell.4 Of these nations, nine launched only one spacecraft. As benefit and cost in our model are both functions only of the parties’ launch rates, this launch distribution would yield a subset of nine identical actors out of the 15. To incorporate some measure of variety in this larger, hypothetical set of actors, we weight the distribution launches by orbit fraction in this larger shell. Figures 1 and 2 show share of eight-year launch rates for Cases I and II, listed in order from highest (designated as #1) to lowest. In Case III, we provide a preliminary sensitivity analysis of the relationship between coalition out- comes, number of nations, n, and the benefit and cost asymmetry by considering launch patterns based on the zeta distribution with a range of “steepness" parameters s (explained below).
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IEA model. We adopt the non-cooperative game framework referenced above to investigate abatement gains of self- enforcing partial coalitions in contrast with null-coalition and full-coalition behavior. The global profit function is defined as:
(1) Each nation bears the cost, Ci, of its own abatement, qi, while all nations share the benefits of reduc- tion of harm, Bi, from global abatement Q. In a stable partial coalition, members have a collective profit that is at least as high as the sum of their individual profits operating alone. However, the allocation of abatement levels within the coalition that maximizes the coalition profit might not result in a higher individual profit for each member compared to their profit if they left the coalition. To overcome this problem, a transfer payment scheme redistributes the net burden among members. The “burden-sharing” rule ensures that the profit each nation receives as a coalition member exceeds what they receive outside the coalition. Nations that ▇▇▇▇▇ an amount greater than required under the agreement would receive a positive transfer, while nations that purchase permits are able to meet their abatement responsibilities under the agreement at a lower cost. Net transfers are zero-sum. Weikard ▇▇▇▇▇▇▇ (2009) presents a family of sharing rules that satisfy the internal and external stability re- quirements cited above. We adopt one rule from this set: the allocation rule for abatement requirements under a system of tradable pollution permits followed by ▇▇▇▇▇▇▇ (2007). This rule proposes transfers between coalition members that are “just sufficient to quell any incentive to deviate from the agreement” and distributes the remaining coalition surplus in proportion to the members’ benefit share-to-cost ratio. 3 Application of IEA Model to Debris Mitigation For this initial model of an IEA for space debris mitigation, we examine the effect of a self-enforcing market mechanism on parties’ choices regarding a single type of abatement action: deorbiting of space- craft after mission lifetime. We do not consider other actions parties might take that would affect the rate of debris generation such as active removal of debris, collision avoidance, or anti-satellite weaponry.
3.1 Elements of the model An IEA model requires the following elements: We specify the elements as follows for a space debris mitigation IEA:
3.1.1 Environmental resource and pollutant The environmental resource is taken to be the 900–1000 km altitude shell-of-interest (SOI) analyzed by ▇▇▇▇▇▇▇ and ▇▇▇▇ (2009). This is the region of near-Earth space with the highest object density. (The 700–900-km shell has a higher density of operational spacecraft but lower overall object density.) The “pollutant" is the population of orbital objects that might catastrophically collide with operational spacecraft, and thereby includes all objects from fragments through non-operational spacecraft as well as other operational spacecraft. Of particular concern is the future introduction of spacecraft that are launched but not deorbited from the SOI after completion of their operational lifetimes.2
3.1.2 Actors and actions Since our analysis relies on the long-term debris evolution model of ▇▇▇▇▇▇▇ and ▇▇▇▇, we adopt their baseline assumption of a total annual launch rate of three operational spacecraft per year to the 900–1000- 2The ▇▇▇▇▇▇▇ and ▇▇▇▇ model assumes a rapid deorbiting out of the SOI at end-of-life to an altitude of 600 km, in accordance with the NASA policy discussed earlier. km SOI (▇▇▇▇▇▇▇ and ▇▇▇▇, 2009). For a set of actors, we look at ownership data, by nation, for recent ▇▇▇ spacecraft whose orbits enter this SOI as indicated in the UCS database of operational spacecraft (Union of Concerned Scientists, 2009). We use a recent eight-year period3 and ignore spacecraft in orbits UCS classifies as “elliptical" (i.e., with eccentricity 0.14 and higher) because these spend only a small fraction of time in the SOI. (See Appendix: Spacecraft in the Shell of Interest.) We focus only on the pattern of launch distribution among nations (as “owners"), and ignore temporal variation in the ownership set. The one spacecraft identified as “international" we treat as having a single owner, and the one spacecraft with two identified co-owners we allocate equally between them. The resulting set contains seven actors, and we scale the launch distribution to match the total launch rate above. Reliance on the historical launch rates to the SOI results in a small set of actors, while the trend is arguably toward broader participation. Given this, we consider the seven-actor empirical distribution to be our Case I, and construct a “plausible" distribution for a larger set of actors, which we call Case II. We construct this pattern from UCS data for a broader ▇▇▇ ▇▇▇▇▇, from 700 to 1000 km. There were 15 single-nation “owners" of spacecraft recently launched to this shell.4 Of these nations, nine launched only one spacecraft. As benefit and cost in our model are both functions only of the parties’ launch rates, this launch distribution would yield a subset of nine identical actors out of the 15. To incorporate some measure of variety in this larger, hypothetical set of actors, we weight the distribution launches by orbit fraction in this larger shell. Figures 1 and 2 show share of eight-year launch rates for Cases I and II, listed in order from highest (designated as #1) to lowest. In Case III, we provide a preliminary sensitivity analysis of the relationship between coalition out- comes, number of nations, n, and the benefit and cost asymmetry by considering launch patterns based on the zeta distribution with a range of “steepness" parameters s (explained below).
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