ENVIRONMENTALPOLICY ANALYSIS
REGULATIONS
Game-Theoretic Framework for Risk Reduction Decisions SHARON A. JONES Rose-HulmanInstituteof Technology Department of Civil Engineering Terre Haute, IN 47803 Traditionally, regulators make risk reduction decisions using either technology-based or performance-based standards. However, the objectives of the regulated community are often in conflict with those of the regulators. Regulators who ignore the regulated communities' objectives in developing regulations may find that the regulation produces unexpected results. I propose using a game-theoretic framework that models regulator decision making as an interactive process between the regulator, who makes the decision, and the regulated community, which responds to that decision. I capture the strategic interaction using a Stakelberg model to evaluate a range of risk management strategies available to the regulator, including mandating pollution prevention goals versus setting technological and performance standards. I demonstrate the Stakelberg model using economic and risk reduction data for options to control benzene emissions at a petroleum refinery. Conflict occurs because the regulator's objective is to maximize risk reduction, whereas the objective of the regulated party—in this case, a refinery—is to minimize control costs. The primary advantages of using game theory are, for the regulator, to incorporate the expected behavior of the regulated party formally into decision making and enhance understanding of the decision, to suggest broad policy guidelines, and to explore the decision's sensitivity to changes in the regulator's preferences and payoffs.
1 2 8 A • VOL. 30, NO. 3, 1996 / ENVIRONMENTAL SCIENCE & TECHNOLOGY / NEWS
Risk reduction strategies imposed on industry result from interlocking decisions that often begin at the federal level. Typically, risk reduction policy is embodied in a law or statute passed by Congress. Enforcement of this law is then delegated to the respective administrative agencies. These agencies establish specific compliance requirements for the regulated community. These requirements typically align with a particular regulatory strategy, such as technology, or performance-based standards. Regulated parties then must decide upon a compliance strategy. Traditionally, compliance has meant relying on end-of-pipe treatment strategies; however, interest is increasing in designing regulations that advance pollution prevention measures. Agencies such as the Environmental Protection Agency often assess the impact a regulation has on the regulated community, but these assessments typically assume a predetermined industry compliance strategy and ignore the regulated party's conflicting objectives that may affect the outcome of these regulations. For example, EPA may set a pollutant limit for waste entering a particular medium based on an expected or desired risk reduction. The regulated industry, to minimize costs, may respond by diverting the waste to a different medium. The actual risk reduction may be less than intended because the regulator failed to consider industry's motivations and decision options. An alternative approach based on game theory can be applied. Game theory models interactive decision making between two or more decision makers with conflicting objectives. The method has been applied in several environmental areas including monitoring and enforcement (i), risk management (2), and international environmental agreements (3). In this article, I suggest a game-theoretic framework that enhances regulatory decisions by capturing this interactive decision making. I demonstrate this with an example of benzene regulation at a petroleum refinery. Defining game theory Game theory enables mathematical analysis of the behavior of people in situations of conflict (4). A "game" includes a starting point, players (i, i = 1, ri), available strategies for each player that are difficult to change once committed (Sy, j = 1,ri),and the payoffs for each player as a result of each of the possible strategy combinations (w(-(s,-, i - 1, n &/= 1, ri)). Players are payoff maximizers, unconcerned with the other players' payoffs, although each knows that the others also are payoff maximizers. Players choose an optimal strategy simultaneously but independently of each other while considering the possible strategies the other players may select. The result de0013-936X/96/0929-128A$12.00/0 © 1996 American Chemical Society
pends on the final choices made by all players. Several techniques are available to solve for the game's equilibrium, the point at which both players have selected their optimal strategies, given what the other player has done (4). The original approach developed in the 1940s by John Von Neumann and Oskar Morganstern (4) provides a static analysis, but several modifications have added a dynamic dimension. One such modification is the Stakelberg game (4), in which a leader selects a strategy, followed by a second player who knows the strategy of the first. The game assumes that complete and perfect information is available at each decision point in the game and that each player knows the game's history. The payoffs for players 1 and 2 are a function of the combination of strategies selected, u2(svs2) and u2{svs2) (4). Games become more complicated as the number of players and strategies increases. Several heuristic techniques such as backwards induction have been developed to solve more complicated games. This often is used to solve games that are limited to two rounds of play, like the Stakelberg game. Players select among multiple equilibria that may exist within a game by first calculating the payoffs for all combinations of strategies available to both players. Player 2 first determines his or her optimal strategy, in terms of payoff, for each of Player l's available strategies. This eliminates less attractive strategies from further consideration, max u2(.s1,s2). You assume that for each strategy available to Player 1 [s^, Player 2's optimization results in a unique solution denoted by R2Ui). Player 1 can then anticipate Player 2's optimal reactions to determine which strategy is optimal from his or her perspective, max u^SyR^s^). If Player l's solution is unique, it may be denoted by Sj*. Therefore, (s/, R2(s1*)) is the backwards induction solution for the game's equilibrium (4). Amoco Yorktown Refinery example In the early 1990s, the Amoco petroleum refinery in Yorktown, Va., was the subject of a well-publicized pollution prevention project (5). The Benzene Waste Operations National Emissions Standard for Hazardous Air Pollutants (NESHAP) was one of the final air toxics regulations developed before the Title III Maximum Achievable Control Technology (MACT) program mandated by the 1990 Clean Air Act amendments. At the time of the Amoco pollution prevention project, MACT requirements for benzene had not been set. The benzene NESHAP, a technologybased strategy, required refinery compliance between 1993 and 1994. The NESHAP required endof-pipe treatment that would reduce benzene emissions by 5267 tons per year for the Yorktown facility (5).
TABLE
1
Amoco Pollution Prevention Project benzene control strategies (5)
Control option
1. Reroute desalter water 2. Eliminate coker blowdown pond 3. Secondary seals on tanks 4. Blowdown system upgrade 5. Drainage system upgrade 6. Treatment plant upgrade 7. Reduce barge loading 8. Quarterly LDARa
Pollutant Benzene Waste Annualize management reduction, risk cost, classification tons/year reduction, "id $ billion
52
1
0.33
Source 130 reduction 541 Source reduction End-of-pipe 5096 treatment End-of-pipe 113 treatment End-of-pipe 58 treatment Recycle 768
2
0.63
18
0.16
11
1.6
5
5.9
5
7.4
55
1.6
3
0.14
Recycle
Source reduction
511
" teak detection and repair. Note: Options 3 and 8 are only two of several available strategies for secondary seals and LDAR. All costs in 1991 dollars. Percentage of benzene risk reductions were calculated with the assumption that the eight options represented 100% of controllable benzene risk and that no interactions occurred among these control options.
Several compliance options were evaluated for cost and benzene risk reduction. Benzene exposure at a nearby residence was used as a proxy for risk associated with the population's exposure to the refinery's emissions. For each option, modeling and calculations were conducted to obtain a new emissions inventory, a new concentration at the nearby residence, and changes in relative population risk as compared with the no-controls baseline. Percentage of benzene risk reductions were calculated with the assumption that the eight options represented 100% of controllable benzene risk and that no interactions occurred among these control options. In other words, the percent risk reductions are additive (5). Compliance options were classified according to EPA's waste management hierarchy, detailed in the 1990 Pollution Prevention Act (6). The options, their designation in the waste management hierarchy, and benzene risk reduction are described in Table 1. I used the Stakelberg game to model the regulatory decision-making process. I assumed that, instead of a technology-based standard such as NESHAP, the regulators could select among several regulatory strategies. Player 1, the leader, was the regulator, and Player 2 was the Yorktown facility reVOL. 30, NO. 3, 1996 /ENVIRONMENTAL SCIENCE & TECHNOLOGY / NEWS • 1 2 9 A
TABLE 2 Optimal control options for industry under alternative regulatory strategies Regulator's strategy, s,
Industry's strategy, %"
Technology
5. Drainage system 6. Treatment plant 8. LDAR"
Performance— quantity Performancerisk 10% Mandatory pollution prevention goal 20% Mandatory pollution prevention goal 33% Mandatory pollution prevention goal
Waste management classification
% Benzene risk Control costs, i/2 reduction, ($ billion) « i
End-of-pipe
13.3
Pollution prevention 3. Secondary Pollution seals prevention 3. Secondary Pollution seals prevention
10
0.14
3
0.16
18
0.16
18
3. Secondary Pollution seals prevention 8. LDAR
0.3
21
3. Secondary
1.7
70
seals 7. Reduce barge loading (partial) 8. LDAR
Pollution prevention
3
Taken from Table 1 control options. Leak detection and repair. Note: Pollution prevent for this analysis can be either source reduction or recycling. All costs and risk reductions are those in addition to option 4. All costs in 1991 dollars. 5
FIGURE 1
Stakelberg framework for risk management decisions by regulators
Adapted from Reference 2.
sponding to the regulatory decision. I assumed that the game is sequential but limited to one round, and complete information is available. The optimal solution was determined using the backwards induction technique previously described. 1 3 0 A • VOL. 30, NO. 3, 1996 / ENVIRONMENTAL SCIENCE & TECHNOLOGY / NEWS
I evaluated several regulatory approaches, as well as several combinations of compliance strategies available to industry to achieve the benzene emissions reduction. The regulatory strategies include technology-based standards, performance-based standards (quantity), performance-based standards (risk), and a range of mandatory pollution prevention goals. The technology-based strategies correspond to the benzene NESHAP. Industry's compliance strategies were categorized as either pollution prevention or end-of-pipe treatment. I assumed that industry's objective is to minimize its compliance costs, whereas the regulator's objective is to maximize the amount of risk reduction achieved. I discuss both of these assumptions later because, in recent years, regulators and industrial facilities often have multiple objectives. To estimate the payoffs, I used a linear algorithm to select the combination of compliance strategies that minimized the compliance costs and met the constraints imposed by each corresponding regulatory strategy. I determined the payoffs for each analysis as the minimum cumulative cost and maximum benzene risk reduction for that combination. The required benzene reduction could not be obtained under any of the regulatory strategy constraints unless option 4, an end-of-pipe treatment, was included in combination with other compliance strategies. However, for all cases analyzed, the optimal compliance combination used Option 4 and either another end-ofpipe treatment or pollution prevention, but not both. The resulting payoffs for the optimal responses by industry, beyond Option 4, are shown in Table 2. For example, one analysis used the performance-based standard (quantity) of a 5267 tons per year minimum as the regulatory constraint, while optimizing for the combination of compliance strategies with the minimum cost. For that example, the optimal compliance strategy combination included control options 4 and 8. Option 4 accounts for 11% risk reduction for the regulator and $1.6 billion for industry; Option 8 payoffs were 3% risk reduction and $140 million. Game-theoretic analysis at the Yorktown refinery As shown in Figure 1, the Stakelberg game is solved using backwards induction, in which die regulator anticipates industry's likely response to each regulatory strategy. Figure 2 summarizes the "game" between the regulator and the Yorktown refinery. Once the likely responses for each of the six strategies are known, tbe regulator selects the optimal strategy (s^). For this "game," the optimal solution is to adopt a 33% mandatory pollution prevention goal, resulting in a combination of options 3, 7, and 8, in addition to option 4. The thought process demonstrated in this analysis forces the regulator to anticipate the various combinations of control strategies that may be adopted and provides a much clearer picture of the risk management decision as shown in Figure 2. This contrasts the more traditional approaches that assume a predetermined compliance strategy by industry and often limit the focus to a single regulatory strategy.
As can be seen in Figure 1, a sensitivity analysis that explores the effects of uncertainty on the optimal solution is important both for understanding and improving the results. In this case study, the compliance cost and risk reduction estimates were uncertain. To evaluate the sensitivity to uncertainty of the optimal solution for this case study, I varied the per ton cost of each control option by 25% while holding the others at their nominal value. A similar analysis was conducted for the risk estimates. The 33% mandatory goal always remained the preferred regulatory strategy. The results of this case study indicate that a regulatory strategy of mandatory pollution prevention goals is preferable to technology-based standards. Because the replacement for the NESHAP program, MACT, is also a technology-based program, and pollution prevention is receiving increased regulatory interest, it is worthwhile to explore the results in more detail. As demonstrated, the 33% mandatory goal results in a benzene risk reduction that is significantly more than that intended by the original NESHAP regulation. This is primarily because of the compliance strategies that, if adopted, result in this higher risk reduction. However, the framework shows that several regulatory strategies that include lower pollution prevention goals can also surpass the original NESHAP regulation, but at a significantly lower cost than the 33% mandatory goal (and the NESHAP). Again, this implies that regulators should not adopt seemingly modest pollution prevention goals without first considering the regulated community's likely compliance strategy and its economic implications. It also indicates that technology-based standards may not be the best choice for either the regulator or the regulated party. Model limitations I made several assumptions to develop and apply the framework. The analysis assumes that regulatory decision making can be quantitatively modeled as two rational players arriving at an optimal solution. However, an alternate view assumes that policy decisions do not have one optimal solution but result from the dynamics of the negotiation and decisionmaking processes in which the criteria for judgment evolve (7). Although this paper does not address this assumption direcdy, the game-theoretic approach recognizes risk management as the result of an interlocking set of values and decisions. The explication of the thought process suggested by a gametheoretic analysis is its greatest asset. The game-theoretic framework assumes that industry responds once to a fixed decision by the regulator. Although the Stakelberg model is dynamic in the sense that industry responds to known actions by the regulator, it is not repeated over time. A review of the history of environmental policy for two pollutants, benzene and vinyl chloride, demonstrates that regulations are not static because of various congressional, technical, and court-driven reasons (8). Changes in regulations can make industry reluctant to commit to compliance strategies that are not adaptable over time. In fact, Amoco identified fu-
FIGURE 2
Normal form of the Stakelberg regulatory decision model for the Yorktown Refinery The boldface entries show the optimal response for industry under each of the possible regulatory strategies; the double-bordered box shows which of those optimal responses results in the optimal strategy for the regulator. Industry's strategy
Regulator's strategy
Pollution prevention
End-of-pipe treatment
Technology
[>10, > 13.31"
[10,13.3]
Performance—Quantity
[3, 0.14]
[10,13.3J 6
Performance—Risk
[18, 0.16]
[10, 13.3] 6
10% Mandatory pollution prevention goal
[18, 0.16]
[>10,>13.3] c
20% Mandatory pollution prevention goal
[21, 0.3]
[>10, >13.3] c
33% Mandatory pollution prevention goal
[70,1.7]
[>10, >13.3] c
" Any pollution prevention adopted by industry is in addition to the required end-of-pipe treatment and results in additional cost and risk reduction. * For these regulatory strategies, the optimal strategy for industry is pollution prevention. However, to complete the normal form of the game matrix, we hypothesized what the cost and risk reduction would be if end-of-pipe treatment options were selected instead of pollution prevention options. " For these regulatory strategies, the required and the optimal strategy for industry result in pollution prevention. However, to complete the normal form of the game matrix we hypothesized what the cost and risk reduction would be if end-of-pipe treatment options were selected in addition to the required pollution prevention options. Note: The normal form of a game displays the payoffs for the players in a matrix form. These payoffs are taken from Table 2. The payoffs represent (regulator's payoff in terms of risk reduction (%), industry's payoff in terms of compliance cost (% billion)]. Therefore, regulator's optimization is to maximize its payoff, whereas industry's optimization is to minimize its payoff.
ture uncertainty of regulations as a key barrier to pollution prevention (5). To include these considerations, the game could be restructured to a multistage game in which each player has a decision in each of several stages (9). I assumed that I could model regulatory decision making as a two-party game. However, regulatory decision making is affected by internal organizational influences and external interests. The motivations of these other "players" may not reflect those used to develop the payoffs for a twoplayer game. In fact, the main objectives and intent of legislation are determined well in advance of the issuance of a specific rule or permit for a facility. Despite the simplification of the model, it still represents the regulatory process on a more local level, where a particular regulator is responsible for establishing policies for a facility. The individual facility typically is not in a position to influence the requirements it must meet. In fact, the benefit of a gametheoretic framework may be to predict the outcome of several regulatory strategies on a local level to improve policy making from a broader perspective. VOL. 30, NO. 3, 1996 / ENVIRONMENTAL SCIENCE & TECHNOLOGY / NEWS • 1 3 1 A
For this example, I assumed that the regulator's sole objective is to maximize risk reduction. However, it has been suggested that technology-based standards are easier to enforce and that implementability is a major consideration in formulating environmental regulations (10). Other regulatory objectives may include a preference for risk equity, pollution prevention, and multimedia risk reduction. Multiple objectives can be included in the game using a multiattribute utility analysis that assigns payoff designations based on preferences for the various objectives held by each player (11). In this example, I modeled industry's payoffs by cost effectiveness. However, the response of large ' firms to SARA's Title III information disclosure suggests public perception may be an important factor in industry's payoff. Again, the multiattribute utility analysis could include these and other objectives in the payoffs (11).
quired information is the same. Extra efforts would be needed to bring industry into the process to better understand its objectives and compliance options. Even if the quantitative modeling is beyond the scope of the regulator's budget, the thought process outlined in Figure 1 may be sufficient to identify regulations that consider both the regulator and the regulated party.
Acknowledgment Financial support for the preparation of this paper came from the Clare Booth Luce Fellowship Program. Advice in formulation and implementation of this research was provided by Mitchell Small. The following are also acknowledged for their suggestions and assistance: Christina Bicchieri, Scott Farrow, Ed Rubin, Lester Lave, Fran McMichael, and anonymous reviewers.
Meeting the objectives
References
My objective in this article was to present a gametheoretic approach that could be used to explicitly consider industry's actions when making risk management decisions. Although the example focused on a particular facility and pollutant, many of the observations can be generalized for regulatory decision making. A game theoretic analysis may benefit those regulators who must grant permits for industrial facility emissions or must determine cleanup levels and remediation options for various media at contaminated sites. The method is also suitable for consumer product decisions and other areas where risk levels are predetermined. I suggest that regulators stand a better chance of meeting their objectives if they consider the regulated community's likely responses. This type of analysis would complement rather than substitute for other decision-making tools, because much of the re-
(1) Kilgour, D. M.; Fang, L.; Hipel, K. W. Water Resourc. Bull. 1992, 28(2), 141-53. (2) Hong, Y.; Apostolakis, G. E. Risk Based Decision-making 1992, (Winter), 331-36. (3) Conflicts and Cooperation in Managing Environmental Resources; Pethig, R., Ed.; Springer-Verlag: Germany, 1992. (4) Gibbons, R. Game Theory for Applied Economists; Princeton University Press: Princeton, NI, 1992. (5) AMOCO-US EPA Pollution Prevention Project Summary: 1992; U.S. Environmental Protection Agency: Washington, DC, 1991. (6) Fed. Regist. 1991, 6(38), 7849-64. (7) Chechile, R. A.; Carlisle, S. Environmental Decision Making: A Multidisciplinary Perspective; Van Nostrand Reinhold: New York, 1991. (8) Brickman, R.; Jassanoff, S.; Ilgen, T. Controlling Chemicals; Cornell University Press: Ithaca, NY, 1985. (9) Brams, S. J.Am. Set 1993, 8J(Nov.-Dec), 562-70. (10) Portney, P. R. Public Policies for Environmental Protection; Resources for the Future: Washington, DC, 1990. (11) Clemen, R. T. Making Hard Decisions: An Introduction to Decision Analysis; Duxbury Press; Belmont, CA, 1991.
1 3 2 A • VOL. 30, NO. 3, 1996 / ENVIRONMENTAL SCIENCE & TECHNOLOGY / NEWS
