RESEARCH Game Theory and Environmental Disputes ALAN L A M B E R T
Box 508 Downstate Medical Center Brooklyn, New York 11203 ABSTRACT / The courts have provided the traditional battleground for conflicts between environmental interest groups and those whose actions in some way have an adverse impact on the environment The judicial process is a time-consuming one in which all sides usually must concede to some points. Environmental disputes involve complex scientific issues which the court system is not set up to comprehend, so that the process gives the parties to a dispute the
Game Theory Each side in a conflict can either capitulate or hold firm to its demands. This leads to either one side winning, the other side winning, a conflict, or a compromise settlement. This two-person negotiated game predicts certain theoretical conditions under which the peaceful resolution of a conflict can occur. However, before an analysis of these conditions can take place, it is necessary to define some game theory terminology. There is a definite utility associated with each of the four possible outcomes. In game theory, the utility is defined as the payoff expected with a given outcome (Rapaport 1966, p. 23). It should also be understood that a payoff can have a negative value associated with it. Let u stand for utility, i stand for one side, o stand for other side, A stand for win, and C stand for conflict. A given side will negotiate only when the utility of the other side winning is worth more to it than the utility of a conflict (Harsanyi 1977, p. 149). In equation form
sense of having lost control of their own destinies. An increasing number of parties to environmental disputes are turning to negotiation, or mediation, as an alternative in which they can be active parties in the settlement-making process rather than the victims of a court-imposed solution When do the parties to a dispute choose a negotiated settlement over a court battle? To what extent does each party make the concessions necessary to reach an agreement? These questions can be answered by the game theory that provides a model for analyzing the negotiation process. This paper will apply game theory to two environmental conflict cases A series of questions pertinent to the analysis of all environmental disputes will be raised
Once the above analysis tells us that at least one side has a negotiation equation, the Zeuthen model of the bargaining process allows us to predict which side will be the first to concede (Abrams 1980, p. 193). We begin with an analysis of the probabilities of the first side winning and of a conflict. Let p be the probability of winning and l - p be the probability of conflict. The utility is then downgraded in value by the probability it will occur, pui(Ai) or (1 - p)ui(C). Then, according to Zeuthen: pui(Ai) + (l - p ) u ( C ) < ui(Ao) pui(Ai) + (l - - p)ui(C ) > ui(Ao)
The above relation is then calculated for the other side. If both sides should not concede, the analysis must be carried one step further. The next stage is the calculation of what is called the risk limit (Abrams 1980) ui(Ai) - ui(Ao) r i = ui(Ai) -- ui(C)"
ui(Ai) > ui(Ao) > ui(C).
In contrast, if the situation is
side 1 should concede side 1 should hold firm.
According to our established condition for negotiation,
ui(Ai) > ui(C) > ui(Ao),
ui(Ao) > ui(C).
a conflict is preferred to a victory for the other side and the first side will not negotiate. What is, in fact, a win for the other side? The maximal position of the other side may be unacceptable. As the range of possible outcomes moves away from the maximal position of the other side, there may be some point at which the utility of that outcome will be worth more to the first side than the utility of a conflict. This outcome is defined as a win for the other side as long as the outcome is less than the first side's maximal position.
Therefore, 0 < r / < 1 is the range of the risk limit. When ri increases, the utility of a conflict to side 1 increases and the utility of the other side winning gets smaller. Therefore, when ri is large, conflict is more likely to occur. When ri is small side 1 is more likely to concede. The risk limit of the other side, ro, is then calculated. The following is the relationship of ri to ro (Harsanyi 1977):
KEY WORDS: Game theory; Environmentalmediation;Legal decision-making Environmental Management, Vol 7, No 5, pp 427-432
r i > ro
the other side should concede
ri < ro
Side 1 should concede
ri = ro
both sides will have to offer a concession. 9 1983 Springer-Verlag New York Inc
428
A. Lambert
Is this a valid theory and is it useful in analyzing conflicts such as environmental disputes? An analysis of two recent environmental cases should be a useful application and test of the theory.
Case Applications Grayrocks Dam The Grayrocks Dam case pits a large power company against a coalition of environmentalists, farmers, and state officials. Six utilities formed the Missouri Basin Power Project (MBPP) to build a 1.6 billion dollar coal-fired facility on the Loraine River near Wheatland, Wyoming (Susskind, unpublished manuscript). It would provide power for industrial expansion in eastern Montana, Wyoming, and Colorado. Cooling water for the facility would be provided by a dam to be built on the Loraine River, a tributary of the North Platte River. Environmentalists were concerned that additional reduction in streamflow would have severe effects on North Platte River wildlife. In the past fifty years, the construction of 43 dams and numerous irrigation projects reduced the streamflow by seventy percent (Susskind unpublished manuscript). The environmentalists focused their attention on the whooping crane, which, as an endangered species, receives special protection under the endangered species act (Susskind unpublished manuscript). Colorado, Wyoming, and Nebraska are composed of semiarid plains. Each state has been concerned about obtaining the largest possible use of North Platte River water for its farmers. A 1956 United States Supreme Court decision allocated a share of the water to each state (Susskind unpublished manuscript). Because Nebraska is the state most downstream, it has been able to take its share plus the unused water from the upstream states. Nebraska opposed the facility because its supply of unused upstream water would be reduced. In terms of a game theory analysis, this case divides into three stages. Stage one covers the initial negotiations that began in 1973. The MBPP Environmental Advisory Committee recommended a smaller facility (Susskind unpublished manuscript). MBPP rejected its own internal study and disbanded the committee in 1976. From 1973 to 1976, over thirty meetings dealing with the water rights issue were held between Nebraska and MBPP officials (Susskind, unpublished manuscript). The MBPP claimed that it had made specific water level offers and all of them had been rejected. Nebraska claimed that the MBPP offered no concessions and had not yielded because it felt it was politically powerful enough to avoid lawsuits. In game theory terminology, the positions of the two
sides are water
uw(Aw) > Uw(C) > Uw(Ae)
power
ue(Ae) > ue(C) > ue(Aw)
where w is the coalition against the power plant, and e is the Missouri Basin Power Project. In this situation, conflict is possible and real negotiations are unlikely. Stage two is the period of litigation. The state of Nebraska filed suit against the Rural Electrification Administration (REA) for failing to prepare an adequate environmental impact statement (EIS) as required by law before approval for a loan for a power plant (Susskind unpublished manuscript)., Nebraska claimed that the report left out the impact of the dam on Nebraska's water supplies and the effect on the aquatic ecosystem of the portion of the North Platte River that flows through Nebraska. A similar suit was filed against the Army Corps of Engineers (ACE) to prevent the issuing of the required dredging permits (Susskind unpublished manuscript). Environmentalists also filed suit against the REA and ACE, citing inadequate EIS. In addition, the REA and ACE were also cited in environmental suits for violating the Endangered Species Act (ESA) (Susskind unpublished manuscript). According to the ESA, federal agencies must consult with the United States Fish and Wildlife Service to ensure that their actions do not jeopardize an endangered species. Permits may then be refused or mitigating procedures may be ordered. The suits were designed to stop the construction of the dam until water rights and habitats could be protected. All of the suits were consolidated into one suit. During the court hearings some negotiations were held. However, no progress was made because both sides were confident of victory. The court decided against the MBPP by turning down the loan guarantee and dredging permit (Susskind, unpublished manuscript). MBPP decided to appeal the decision to its allies in Congress. The House of Representatives voted to approve a bill exempting the Grayrocks Dam from almost all requirements of the Endangered Species Act provided that the newly created Endangered Species Committee (ESC) approved (Susskind, unpublished manuscript). It then became clear to both sides that a quick decisive victory was no longer possible. A conflict in the courts and committees could last for years and prove to be very costly. In game theory terminology, the utility of conflict had become lower for each side. Because the ESC had never previously heard a case of this nature, it was unclear which way the committee would vote. The MBPP faced the prospect of losing over 500 million dollars if the hearings lasted for a one year period (Susskind unpublished manuscript). Environmental groups did not desire an expensive court appeal. Their only
Game Theory and Environmental Disputes
goal was to protect the ecosystem. Nebraska only wanted to protect its water rights. At the end of stage two, the game theory position of each side was uw(Aw) > uw(A,) > u(C) ue(Ae) > ue(Aw) > ue(C).
water
power
Each side was in a position where it should negotiate. Each utility is downgraded in value by the probability it will occur. For both sides, pui(Ai) w a s low in value since there was almost no probability (p) of a peaceful victory. Since (l - p) was high, each side would receive the full impact of a costly ui(C). The probability equations are presented as the following: water
puw(Au,) + (l -- p)uw(C) < uw(Ae)
power
pue(Ae) + (l -- p)ue(C) < Ue(Aw).
Both sides are in a position where they should concede. An analysis of risk limits is necessary to determine which side should concede first: uw(Aw) - uzo(Ae) ,,o = u w ( A w ) -
uw(C)
ue(Ae) - ue(Aw)
re = u e ( A e ) -
ue(C)"
The uw(Aw) is much greater than the uw(Ae) that would result in a loss of water rights and a damaged ecosystem. The uw(Ae) is only moderately greater than the uw(C) because most of the cost is expressed in legal fees. Therefore, rw is relatively large. The ue(Ae) is much greater than the ue(Aw). However, the ue(Ae) is infinitely greater than the ue(C) which, with its potential one year 500 million dollar delay cost, could end the project. Therefore, re is relatively small. Since rw > re, M B P P should make the first concession. Basing its decision on what it thought it could afford, how much it stood to lose if the case was not settled quickly, and the minimum needed to satisfy its opponent, MBPP offered fifteen million dollars to the plaintiffs in return for dropping the case (Susskind unpublished manuscript). The money was intended for purchasing water rights to maintain the streamflow and to protect the ecosystem. As offered, the cash payment could be perceived as a payoff. Also, Nebraska really wanted to maintain the streamflow and was unsure that the payment was large enough. Environmentalists doubted that the ecosystem could be protected by purchasing water rights because Nebraska allocates water rights for beneficial uses that usually involve the removal of water from the river (Susskind unpublished manuscript). Therefore, a state court might not approve of the purchase of water rights just to maintain the streamflow. The offer was rejected. M B P P then designed a proposal to correct the flaws in the initial offer, M B P P would guarantee minimum seasonal
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streamflow levels for the North Platte River. Also, 7.5 million dollars would be provided to purchase additional water rights as needed and protect the ecosystem artificially (Susskind unpublished manuscript). A trust fund for the preservation of the whooping crane and its habitat would be set up with an independent board of trustees to administer the money. The plaintiffs accepted this offer and all parties signed a binding agreement with joint monitoring provisions to insure implementation (Susskind unpublished manuscript).
Tennessee Eastman Company The next case deals with the Tennessee Eastman Company (TEC), which is one of the largest chemical factories in the United States, occupying over 400 acres and employing 11,900 people. Over 1,800 scientists and engineers work in research and development laboratories in a main facility on the site. Over 500,000 pounds of chemical wastes are produced each day. The waste is incinerated or processed in a waste water treatment facility. Congress passed the Federal Water Pollution Control Act Amendments in 1972 (Jaegerman 1980). This act, PL-92-500, is an attempt to base effluent limitations on technological capabilities, subject to economic and social constraints. The United States Environmental Protection Agency EPA is charged with the responsibility of implementing PL-92-500, and with issuing national pollution discharge elimination system (NPDES) permits. Computerized water quality models are used to determine and substantiate the terms of discharge permits. To control its waste discharge, T E C was required to install the "best practicable technology" (BPT), taking into account costs and benefits, by July 1, 1977. This technology must meet existing state effluent limits if they are stricter than those established by the EPA model. By July 1, 1983, the "best available technology" (BAT) that is economically feasible must be installed. An understanding of a few scientific concepts is essential to analyzing the T E C case. When organic waste is discharged into a stream, a decomposition process takes place in which microorganisms digest the waste (Jaegerman 1980). The waste is broken down into its essential elements, which are nitrogen, phosphorous, and carbon. During the waste assimilation proeess, oxygen dissolved in the stream water is consumed in chemical reactions with the elements. The amount of oxygen consumed is dependent on the volume and composition of the waste materials. The concentration of oxygen in a stream varies inversely with temperature: a lower temperature supports a higher concentration. The oxygen concentration also depends on turbulence, depth, upstream conditions, bottom deposits, and aquatic needs. If the oxygen concentration falls below 3-5 mg parts per million, the fish population will be
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A. Lambert
Table 1. Comparison of proposed effluent limitations by TWQCD, EPA, and TEC (Jaegerman 1980). TWQCD
Units lb/day
proposed limitations lb/day net
Effluent consituents Biochemical oxygen demand (BOD) Total Kjeldahl nitrogen (TKN) as N Total nitrogen (TN) as N Ammonia nitrogen as nitrogen Nitrates plus nitrites as N Phosphates as P Total dissolved solids (TDS) Total suspended solids (TSS) (gross) Zine as Zn Phenols Iron as Fe Manganese as Mn
3350 400 3310 400
EPA proposed effluent limitations
TEC proposed effluent limitations
Daily average
Daily maximum
Max. monthly average
2230 270 a
3350 400
10,000 9,000
.
__ .
__
.
100
700
7,500
213
140
210
800
--
--
--
2230 125 10
650,000 6,000 125 100 300 100
3350 250 20
--
--
100
200
Daily average
Instantaneous maximum
40,0 0.05 0.02 0.005
50.0 0.075 0.03 0.0075
17,000 18,000 __
.
2910
1,200,000 -250 100 1000
Max. day
Monthly average
11,000 1,500
1,200,000 15,000 250 175 1,000 200 Max. day
mg/l b
ml/1
Total suspended solids (TSS) Chromium Copper Mercury Lead Dissolved oxygen (DO) Settleable solids
0.05
0.075
>_5.0 0.5
-----
40 0.05 0.05 <0.005
--
0.08
>_5.0 --
5 <0.5
100 0.1 0.1 <0.0 0.9 --
0.5
aFor entries that containa dash (--), no valuehas been specified. bMeasured by Concentrationin each processdischarge. seriously threatened. At zero concentration anaerobic digestion occurs. This kills all fish life and causes the evolution of odorous gases. On September 15, 1972, EPA Region IV staff made their first of a series of field trips to the T E C complex to take discharge samples (Jaegerman 1980). They applied a waste load allocation model for determining the assimilative capacity of the Holston River. The EPA then issued a report entitled "Waste source investigations--Kingsport, Tennessee" (see Jaegerman 1980, p. 13). Its effluent limits were almost identical to those of a Tennessee state study. T E C claimed that no e-eonomically feasible technology could meet the EPA effluent limits and requested discussions before involving the public in the process. T E C took its own samples and issued a counterproposal entitled "Waste borne effluent limits" (see Jaegerman 1980, p. 18). Its limits were much higher than those of the EPA. In order to support these limits, the T E C hired a team of nationally recognized consultants to prepare a report entitled "The assimilative capacity of the South Fork Holston River and Holston River below Kingsport, Tennessee." The report concluded that the assimilative capacity of the river was much
higher than concluded by the EPA model (see Jaegerman 1980). The major areas of disagreement centered on the biochemical oxygen demand (BOD) and nitrogen effluent limits (Table 1). Each side questioned the validity of the model on which the other side's proposed limits were based. The two sides disagreed on the effect of nutrient discharge upon weed growth, and as a result, also disagreed on the oxygen variation based on weed growth. The disagreements could then be settled through the courts or through negotiations. The EPA had strong incentives to negotiate: the validity of its model was in question; the state of the art in effluent water modelling was such that either side's model could be viewed as acceptable; and it did not want to tie up its staff for years in technical studies and legal hearings, it had other cases on its agenda. In contrast, the T E C could expend almost unlimited resources to hire the technical experts needed to support its model; and during the years of court hearings, no controls would be in place so that the T E C could continue to dump waste into the river in unlimited quantities. A game theory analysis of the preceding information yields:
Game Theory and EnvironmentaI Disputes
u,(A,) > u,(A,) > u,(C) p u , ( A , ) + (l - p ) u e ( C ) < ue(At)
e is the EPA, t is the TEC. The probability of a conflict (l - p) was high because the T E C would rather have gone to court than accept the maximal demands of the EPA. Thus the probability of a peaceful victory for the EPA, p, was small. The cost of a conflict coupled with its high probability of occurrence puts the EPA in a position where it should concede. The T E C also had incentives for negotiation. Its model was also open to question, even if supported by a larger number of nationally recognized experts. The courts, whose main responsibility is resolving legal disputes, are not adept at analyzing technical issues. For the T E C the stakes were extremely high. A court victory for the EPA could have resulted in cutbacks in production and in employment. For the TEC, game theory analysis yields: ut(At) > ut(Ae) > ut(C) put(At) + (l - p ) u t ( C ) < ut(A,).
The probability of a T E C victory, p, was small given the fact that the EPA had to meet certain legal requirements in issuing the permit. The probability of a conflict, ( l - p), was high since the EPA would have to seek court action if the T E C refused to agree on permit limits. T E C is also in a position where it should concede. A risk limit analysis indicates which side should concede first r,-
ue(A,) - ue(A,) u,(A,) - ue(C)"
A conflict would drain limited EPA resources, while a victory for T E C would allow the EPA to move on to other cases. This implies a low risk limit: ~,(A,) - u , ( A , )
rt
ut(At) - ut(C)"
A victory for the EPA would certainly curtail T E C operations even though the T E C had the resources to survive an extended conflict, the result of which could be no worse than a total EPA victory. This implies a relatively high risk limit. Thus rt > re and the EPA should concede first. A series of technical meetings were held. As expected from the risk limit analysis, the EPA made the major concessions. The EPA conceded by agreeing to summer-winter BOD limits in order to utilize higher winter oxygen concentrations (Jaegerman 1980). The gap on BOD limits was narrowed as both sides moved from the positions listed in Table 1. The EPA had insisted on strict nitrogen and phosphorous limits to bring
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downstream nuisance weed growth under control. The T E C pointed out that a plentiful supply of nutrients was already available from bottom deposits, sediments, and from stream flow moving down from the North Fork Holston River. T E C also claimed that the biological nitrogen removal process was unproven. Because this biological process works less efficiently in cold winter weather and inhibitory chemicals could also block the process, the T E C feared it would be committed to an unworkable system. The EPA offered two concessions on nitrogen limits. It agreed to summer-winter nitrogen limits to compensate for the reduced efficiency of the process in cold weather. It also agreed that the technology must be proven feasible by a pilot facility. Against T E C wishes, the EPA finally involved the public and scheduled a permit hearing (Jaegerman 1980). T E C counterattacked with a 74 page document entitled "Comments by Tennessee Eastman Company." The report attacked all of the limits that T E C found unacceptable. The EPA made minimal efforts to generate attendance at the hearing (Jaegerman 1980). The major speaker for the EPA was a representative of the League of Women Voters. In contrast, T E C fielded several nationally recognized scientific experts in addition to local business and political personalities. The EPA realized that the state of Tennessee would not actively provide support for a restrictive permit. In contrast to the limited resources of the EPA, the team of experts working for the T E C was large. The EPA made all the necessary concessions and issued a permit acceptable to the TEC. The extent of the EPA final concessions is observable in Table 2.
Discussion and Conclusions The application of game theory to environmental cases raises a number of salient questions. 1) What are the relative effects of the other side winning as opposed to a conflict as perceived from each party's point of view ? 2) Considering the answer to question one, is there room for movement away from the maximal demands of each side? If the answer is yes, there may be points of overlap in the minimal demands of the two sides. If the answer is no, there is no basis for negotiation. One side will have to capitulate totally or there will be a conflict. 3) Which side, if any, can better survive negotiations or delays? Consider the effect of a one year 500 million dollar delay cost on the negotiating posture of MBPP. Remember that agencies or groups like the EPA have limited resources with which to cover many cases. 4) How valid is the scientific base of each side's position? 5) What resources in terms of recognized scientists and
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Table 2.
A. Lambert
Comparison of proposed permit limitations at public hearing with final NPDES permit. EPA draft permit
Units lb/day
ml/l mg/l
Effluent characteristics BODs (summer) a BOD5 (winter)a Total suspended solids Total dissolved solids Total nitrogen b (summer) Total nitrogenb (winter) Phosphorous, total Zinc, total Phenols Iron, total Manganese, total Settleable solids Chromium, total Copper, total Lead, total Mercury, total
Daily avg.
Daily max.
3,200 6,300 4,500 8,350 4,500 8,350 650,000 1,200,000 680 1,3501 970 1,800J 150 125 50 300 100 NA 0.05 0.05 0.08 0.005
300 250 65 1,000 200 0.5 0.1 0.1 0.5 0.0075
TEC draft permit Daily avg.
Final permit
Daily max.
Daily avg.
Daily max.
4,000 6,000 6,000 650,000
8,500 13,000 15,000 1,200,000
4,000 6,000 6,000 650,000
8,500 13,000 15,000 1,200,000
3,000
6,000}
3,000
6,000
300 125 50 300 100 NA 0.05 0.05 0.08 0.005
600 250 65 1,000 200 0.5 0.1 0.1 0.5 0.0075
300 125 50 300 100 NA 0.05 0.05 0.08 0.005
600 250 65 1,000 200 0.5 0.1 0.1 0.5 0.0075
aSummerand winter as designatedin the EPA draft permit were May 1 to October31, and November 1 to April 30, respectively.The TEC draft and final permit differedby a month, with summer May I to September30 and winter October 1 to April 30. bThere was a caveat on these limits to allow TEC to test the technologyin a pilot facility. The final permit containedthe followingnotation: "If TEC can demonstrateto EPA by July 1, 1975 that these total nitrogenand toal phosphorouslimits are unattainableby TEC's currentlyplannedwastewatertreatment plant and currentlyplannedin-plant controls,theselimitswill be revisedaccordinglyby EPA. The revisedlimitswill make proper allowancefor seasonaland operational variabilities."(Doe. 625) This wordingdosely resemblesthat suggestedby TEC in the comments. engineers can be employed to defend the scientific base of each side's position? 6) What priority does the satisfactory resolution of the dispute have relative to each side's other current or pending activities? Answering this question helps to determine just how much of the available resources are assigned to the case. Companies like T E C will commit almost unlimited resources to protect their operations. Agencies like the EPA approach each case with a different set of priorities. 7) Before negotiations begin, are all parties with legal power involved in the present case? If the answer is no, an agreement may be reached only to be blocked in the courts by an unrepresented party. Once these questions have been answered, it should be easy to estimate relative utility values and apply the game theory to any environmental case. In conclusion, game theory can have many useful applications in resolving environmental disputes. Initially it can be used to indicate if a given case will be resolved through negotiations or through conflict in the courts. Ideally the model can be used by all involved parties as a means by which to negotiate a peaceful solution to a dispute. If not, it can be used by one of the parties to analyze what its posture should be throughout the negotiation process. Finally, game theory can be used to analyze if an agreement was the best possible given the power relationship between the parties to the conflict.
Literature Cited Abrams, R. 1980. Foundations of political analysis: An introduction to the theory of collective choice. Columbia University Press, New York, NY. Harsanyi, J. 1977. Rational behavior and bargaining equilibrium in games and social situations. Cambridge University Press, Cambridge. Jaegerman, A. 1980. The Holston River case: Behind the scenes negotiation in the NPDES permit process. Rapaport, A. 1966. Two person game theory: The essential ideas. University of Michigan Press, Ann Arbor, MI. Susskind, Larry. Grayrocks Dam case study (unpublished manuscript) Massachusetts Institute of Technology, Cambridge, MA. Tennessee Eastman Company. Comments by Tennessee Eastman Company. Kingsport, TN. 74 pp.