ENVIRONMENTAL POLICY ANALYSIS

REGULATIONS

Game-Theoretic Framework for Risk Reduction Decisions

SHARON A. JONES

Rose-Hulman Institute of 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.

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 de-

1 2 8 A • VOL. 30, NO. 3, 1996 / ENVIRONMENTAL SCIENCE & TECHNOLOGY / NEWS 0013-936X/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 technology-based strategy, required refinery compliance be­tween 1993 and 1994. The NESHAP required end-of-pipe treatment that would reduce benzene emissions by 5267 tons per year for the Yorktown fa­cility (5).

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 re-

T A B L E 1

Amoco Pollution Prevention Project benzene control strategies (5)

Waste Pollutant Benzene Annualize management reduction, risk cost,

Control option classification tons/year reduction, "i d $ billion

1. Reroute desalter Recycle 52 1 0.33 water

2. Eliminate coker Source 130 2 0.63 blowdown pond reduction

3. Secondary seals Source 541 18 0.16 on tanks reduction

4. Blowdown End-of-pipe 5096 11 1.6 system upgrade treatment

5. Drainage system End-of-pipe 113 5 5.9 upgrade treatment

6. Treatment plant End-of-pipe 58 5 7.4 upgrade treatment

7. Reduce barge Recycle 768 55 1.6 loading

8. Quarterly LDARa Source reduction

511 3 0.14

" 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.

VOL. 30, NO. 3, 1996 /ENVIRONMENTAL SCIENCE & TECHNOLOGY / NEWS • 1 2 9 A

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.

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-of-pipe 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.

TABLE 2 Optimal control options for industry under alternative regulatory strategies

% Benzene Waste Control risk

Regulator's Industry's management costs, i/2 reduction, strategy, s, strategy, %" classification ($ billion) « i

Technology 5.

6.

Drainage system Treatment plant

End-of-pipe 13.3 10

Performance— 8. LDAR" Pollution 0.14 3 quantity prevention

Performance- 3. Secondary Pollution 0.16 18 risk seals prevention

10% Mandatory 3. Secondary Pollution 0.16 18 pollution seals prevention prevention goal

20% Mandatory 3. Secondary Pollution 0.3 21 pollution seals prevention prevention 8. LDAR

goal 33% Mandatory 3. Secondary Pollution 1.7 70

pollution seals prevention prevention 7. Reduce

goal

8.

barge loading (partial) LDAR

3 Taken from Table 1 control options. 5 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.

FIGURE 1 Stakelberg framework for risk management decisions by regulators

Adapted from Reference 2.

1 3 0 A • VOL. 30, NO. 3, 1996 / ENVIRONMENTAL SCIENCE & TECHNOLOGY / NEWS

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 game-theoretic 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

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 two-player 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 game-theoretic framework may be to predict the outcome of several regulatory strategies on a local level to im­prove policy making from a broader perspective.

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] [10,13.3J6

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.

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 implement-ability 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).

Meeting the objectives My objective in this article was to present a game-theoretic 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

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.

References (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 Re­

sources; Pethig, R., Ed.; Springer-Verlag: Germany, 1992. (4) Gibbons, R. Game Theory for Applied Economists; Prince­

ton 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 Mak­

ing: A Multidisciplinary Perspective; Van Nostrand Rein-hold: 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 Protec­

tion; 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