Int. Journal of Game Theory, Vol. 8, Issue 4, page 225-23~4. QPhysiea-Verlag, Vienna.

T h e U . S . - O P E C E n e r g y C o n f l i c t T h e P a y o f f M a t r i x b y the A n a l y t i c H i e r a r c h y P roces s

By Th.L. Saaty, Philadelphia 1 )

Abstract: In this paper we study the U.S.-OPEC oil conflict and compute the payoff matrix for each of the two players using the Analytic Hierarchy Process by first evaluating the strategies of each player according to their intrinsic merits and then according to their relative strengths when considered against each of the opponent's strategies. We compose the two results to derive the pay- off matrix. We then identify and study equilibrium payoffs and discuss their strategies.

1. Introduction

Because of the uncertainty in the availability of energy sources over the next two decades we have chosen to look at the problem of U.S. oil consumption and OPEC supply in a competitive framework. We draw on an extensive study of the literature and on our involvement in energy studies over the past few years to determine the pay- off matrix and equilibrium solutions. The payoff matrix requires that we evaluate both the "intrinsic" and the "engagement" values of strategies. We do this using the theory of analytic hierarchies [Saaty].

An intriguing problem in game theory is the assumption that it is possible to esti- mate payoffs for strategies in a game before the strategies of one player have been matched against those of the opponent in actual competition. Except for the simplest and most transparent situations it is impossible to spell out all the moves and tactics of a real-life strategy to really get a good idea of how well it would fare in competition. Some broad qualities of a strategy may be known, but exact prescriptions of its effec- tiveness may encounter such unanticipated problems in practice that it may be diffi- cult to get a "good" estimate of its worth when compared with other strategies.

We can distinguish two steps in arriving at the payoffs. The first is to evaluate strat- egies according to some intrinsic set of objectives to assess their relative strengths with- out regard to what strategies the opponent may have. This is useful, particularly when we do not have complete information on his strategies. We note that the objectives themselves must be evaluated according to importance with respect to some higher objective(s), etc. The process leads to a vector of the relative weights of the strategies with respect to all the objectives.

Next we analyze the relative effectiveness of the strategies if engaged against each strategy of the opponent. This yields a vector of the relative strengths of the strategies

1 ) Prof. Thomas L. Saaty, The Wharton School, University of Pennsylvania, Philadelphia, Pennsylvania 19174, USA.

226 Th. L. Saaty

against each strategy of the opponent. These vectors form the columns of a matrix. Each row of this "engagement" matrix is weighted by the corresponding "intrinsic" weight of the strategy from the first step to obtain the payoff matrix. The process is repeated to obtain the opponent's payoff matrix.

For the use of the scale 1-9 with reciprocals to indicate the relative strength of dominance with respect to a given property and for how to deal with hierarchical structures see Saaty [ 1977].

2. Prioritization of the Strategies of the United States and OPEC

Let us consider the problem of energy strategy options open to the U.S. in the face of oil price hikes and also oil shortages. Thus we let OPEC be the second player. For intrinsic value, energy policies for the United States will be evaluated according to their contribution in satisfying the following objectives:

P1 : Clean physical environment; P2 : Adequate supplies of petroleum and its products; and P3 : Reasonable prices for petroleum and its products.

The above objectives are prioritized according to their importance to the American consumer. Table 1 gives the pairwise comparison values and eigenvector weights.

Tab. 1: Which objective is more important to the consumer?

Consumer P1 P2 P3 Weight

P1 1 1/7 1/5 .072 P2 7 1 3 .649 /'3 5 1/3 1 .279

The second objective, namely adequate supplies of petroleum and its products, ranks the highest among the three. The behavior of the American consumer, regarding petroleum consumption, in the past few years has demonstrated that sufficient amounts of petroleum and its products are favored even if one had to pay higher pricks and even if there is some damage to the environment by greater consumption (although this is being gradually brought under control).

We now consider a select list of U.S. government energy policies. We use "strate- gies" and ,,policies" interchangeably.

L 1 - Conservation

By conservation we mean improving the efficient use of fuel by industries, insu- lating buildings and reducing interior winter temperatures, encouraging public trans. port and reducing the sizes of automobiles and their operating efficiency.

L2 - Storage o f petroleum

Petroleum could be stored in steel tanks underground in salt domes, or in devel. oped off fields. The purpose of storage is to provide a cushion against sudden acute shortages.

The U.S.-OPEC Energy Conflict 227

L 3 - Increasing interdependence with oil producers The purpose of this policy is to understand the needs and plans of oil-exporting

nations and to create a market which serves both the U.S. and its oil suppliers.

L 4 - Domestic oil price control This policy is intended to keep the domestic price of oil charged by the oil com-

panies sufficiently low for equity reasons. In other words, it prevents the oil industry from receiving windfall profits.

Ls - Subsidies for energy production The purpose here is to encourage domestic energy production in general: oil,

natural gas, coal, nuclear, solar, and others.

To determine the constant values of these policies, we construct pairwise compari- son matrices for them with respect to each objective.

Tab. 2: Which policy is more effective in maintaining a clean physical environment?

P1

Zl L2 Lz L4 Ls

L1 L2 L3 L4 Ls Weight

1 3 3 5 3 .435 1/3 1 1/3 1/3 1 .094 1/3 3 1 1 1 .163 1/5 3 1 1 1/3 .131 1/3 1 1 3 1 .177

Tab. 3: Which policy is conducive to a greater supply of petroleum?

P2

Zl L2 La L4 Ls

L1 L2 L 3 L4 Ls Weight

1 5 1/5 5 1/3 .144 1/5 1 1/7 3 1/7 .055" 5 7 1 7 3 .490

1/5 1/3 1/7 1 1/7 .035 3 7 1/3 7 1 .276

Tab. 4: Which policy is better suited for maintaining a reasonable price of oil?

P3

Zl L2 L3 L4 Ls

LI L2 L3 L4 Ls Weight

1 7 1/5 1/5 1/3 .096 1/7 1 1/7 1/5 1/5 .035 5 7 1 3 3 .433 5 5 1/3 1 1/3 .188 3 5 1/3 3 1 .249

228 Th. L. Saaty

The intrinsic values of the policies are given by the composite vector of weights of the policy eigenvectors and the previously calculated vector of objectives. We have

LI (.435 144 096) 072) t152) L2 .094 .055 .035 / / . 0 5 2 La .163 .490 .433 .649 = [ . 4 5 1 L4 .131 .035 .188 ~ .085 Ls .177 .276 .249 \ . 2 7 9 \ . 2 6 1 ,

These are the priorities of the policies if everything else stays the same. Our next task is to determine the relative effectiveness of these policies should con-

ditions in the international oil market change. Thus it is essential to consider the pay- offs resulting from using these policies against the international oil market.

Suppose that the following changes are possible in the international oil market strategies imputed to OPEC:

11 : International oil price hike; I2 : Oil-production limitation by OPEC 13 : Sudden oil-supply interruption, and 14 : Do nothing.

Now, we evaluate the relative effectiveness of the U.S. policies against each of the policies 1/c, k = 1, 2, 3, 4.

Tab. 5: Which U.S. policy is more

11

L! L2 La L4 Ls

L~ L2

effective against an international oil-price hike?

L a L 4 L s Weight

1 5 1/6 7 1/5 .125 1/5 I 1/8 3 1/7 .047 6 8 t 9 3 .501

1/7 I/3 1/9 1 1/9 .027 5 7 1/3 9 1 .301

Tab. 6: Which U.S. policy is more effective against OPEC's production limitation?

&

Zl L2 L3 L4 Ls

LI L2 La L4 Ls Weight

1 1/4 1/6 5 1/7 .065 4 1 1/3 7 1/3 .159 6 3 1 9 1/3 .287

I/5 t /7 1/9 1 1/9 .027 7 3 3 9 1 .462

The U.S.-OPEC Energy Conflict 229

Tab. 7: Which U.S. policy is more effective against sudden oil interruptions?

ls

Zl L2 Ls L4 Ls

L 1 L2 Ls L4 L s Weight

1 1/8 1/7 5 1/3 .060 8 1 3 9 7 .525 7 1/3 1 9 3 .264

1/5 1/9 1/9 1 1/9 .025 3 1/7 1/3 9 1 .126

Tab. 8: Which U.S. policy is more effective to make OPEC "do nothing"?

14 LI L2 La L4 Ls Weight

Zl L2 L3 L4 Ls

1 1/2 1/7 5 1/5 .074 2 1 1/5 9 1/3 .131 7 5 1 9 3 .503

1/5 1/9 1/9 1 1/9 .026 5 3 1/3 9 1 .266

The payoff matrix to the U.S. is obtained by weighting each row of the matrix whose columns are the above four eigenvectors by the corresponding component from the intrinsic value eigenvector. It is given by

11 /2 I3 I4

La ( . 0 1 9 .0099 .0091 .0112 ) L2 .0024 .0083 .027 .0068 L 3 .226 .129 .119 .227 L4 .0023 .0023 .0021 .0022 L s , .079 .1206 .033 .069

We now continue our analysis by determining the payoff matrix for OPEC's strate- gies. First, we define OPEC's objectives as follows:

O1 : Revenue maximization; 02 : Petroleum conservation; and 03 : Using oil as a means to achieve political objectives.

Although the last objective may not be the objective of OPEC as an organization, the Arab oil embargo of 1973 and some other related events have shown that some OPEC members are greatly in favor of using oil as a political weapon.

The above objectives are prioritized according to their importance to OPEC mem- bers. Table 9 gives the pairwise comparison values and eigenvector weights.

230 Th. L. Saaty

Tab. 9: Which objective is more important to OPEC members?

OPEC

O1 02 Os

O1 02 Os Weight

1 7 8 .763 1/7 1 5 .178 1/8 1/5 1 .058

OPEC strategies have been discussed in previous pages, namely, 11,12, la, 14. These strategies are prioritized according to their contributions to OPEC objectives. The pair- wise comparison matrices and the corresponding eigenvector weights are listed in tables 10, 11, and 12.

Tab. 10: Which OPEC strategy would contribute more to revenue maximization?

O1

I1 /2 Is /4

11 12 Is 14 Weight

1 7 9 3 .575 1/7 1 5 1/5 .099 1/9 1/5 1 1/7 .038 1/3 5 7 1 .288

Tab. 11 : Which OPEC strategy would provide more incentives for petroleum conserva- tion?

02

I1 /2 Is /4

11 I2 Is 14 Weight

1 7 8 3 .597 1/7 1 1 1/4 .071 1/8 1 1 1/5 .065 1/3 4 5 1 .266

Tab. 12: Which OPEC strategy would be more effective in enhancing the political power of oil?

Os

11

ls /4

11 I2 13 !4 Weight

1 1/5 1/7 3 .086 5 1 1/3 7 .293 7 3 1 8 .576

1/3 1/7 1/8 1 .045

The intrinsic values of OPEC strategies are given by the composite vector obtained as follows

The U.S.-OPEC Energy Conflict 231

O1 02 03

I2 ~ .099 .071 .293 I3 ~ .038 .065 .576 .178 /4 \ .288 .266 .045 .058

.550 = .105 |

.074 ]

.270 /

We next determine the relative effectiveness of these strategies against the U.S. strategies L i , i = 1 . . . . , 5 .

Tab. 13: Which OPEC strategy is more effective if the U.S. encourages energy conser- vation?

L1

/I 12 Ia I4

11 I2 13 14 Weight

1 1/7 1/5 1/3 .056 7 1 2 4 .486 5 1/2 1 5 .345 3 1/4 1/5 1 .113

Tab. 14: Which OPEC strategy is more effective if the U.S. develops adequate petro- leum storage?

L2

/1 /2 13 /4

11 12 Ia 14 Weight

1 3 7 1/3 .285 1/3 1 5 I/3 .149 1/7 1/5 1 1/9 .041 3 3 9 1 .525

Tab. 15: Which OPEC strategy is more effective if the U.S. increases its interdepend- ence with OPEC members?

L3

/1

13 /4

11 12 Ia 14 Weight

1 1/3 5 1/7 .105 3 1 7 1/5 .213

1/5 1/7 1 1/9 .037 7 5 9 1 .645

Tab. 16: Which OPEC strategy is more effective if the U.S. controls the domestic prices of oil?

L4

/1 /2 /3 /4

11 12 Ia /4 Weight

1 1/3 1/5 3 .139 3 1 1/3 2 .236 5 3 1 4 .535

1/3 1/2 1/4 1 .091

232 Th. L. Saaty

Tab. 17: Which OPEC strategy is more effective if the U.S. encourages energy produc- tion through subsidies?

L5

11 h I3 /,

Is 12 13 14 Weight

1 1/7 1/3 1/5 .057 7 1 3 2 .472 3 1/3 1 1/4 .133 5 1/2 4 1 .338

The payoff matrix to OPEC may be calculated as we did for the U.S. Thus we final- ly have the following payoff matrix for a nonzero-sum U.S.-OPEC game. The first set of components give rise to U.S. payoffs and the second to those of OPEC.

Is 12 I3 14

L1 / (.019, .031) (.010, .051) (.009,.026) (.011, .031) \ L2 / (.002, .157) (.008, .016) (.027, .003) (.007, .142) L3 (.226, .058) (.129, .022) (.119, .003) (.227, .174) L4 (.002, .077) (.002, .025) (.002, .040) (.002, .025) Ls (.079, .031) (.121, .050) (.033, .010) (.069, .091)

3. Analysis of the Results

We focus here on identifying Nash equilibrium solutions with and without the crucial mutually beneficial strategies L 3 (U.S. interdependence) and/4 (OPEC "do nothing"). We have kept in mind the variable threat idea to look for cooperative solu- tions. As characterized here the situation gives rise to a Pareto optimal dominant equi- librium in the (L3,/4) position. We believe that this solution has gradually emerged as a result of both competition and cooperation between the U.S. and OPEC. The solu- tion or a slight variant of it with small price hikes, is a result of several perturbations of these two strategies by the corresponding players. The U.S. has friendly relations with some members of OPEC and has succeeded in maintaining cooperation and en- couraging the adoption of these two strategies. This is in addition to the adverse in- fiationary effects of price hikes on the western economies which nullified its benefits to OPEC, inducingI4. Both sides also showed restraint in the use of threats and have frequently made declarations of good intentions.

The policy of interdependence is a natural one. By exercising restraint in price hikes and by investing in U.S. business, OPEC has encouraged this type of outcome. (L3, I4) places the U.S. in a good position against threats by OPEC regarding the supply of oil and hikes in oil prices. It also boosts U.S. exports, providing more jobs in the Ameri- can economy, and improves the U.S. balance of payments. From OPEC's viewpoint, interdependence not only ensures an oil market, but also provides OPEC countries with U.S. technology, capital, and management skills needed for their development.

In the short run, OPEC prices for oil were sufficiently low that the U.S. did not

The U.S.-OPEC Energy Conflict 233

find it economically necessary to develop its own domestic oil or alternate sources of energy. Vast amounts of coal reserves in the United States and advanced technology are available to reduce dependence on imported oil. The U.S. could probably become self-sufficient in energy in the long-run. On the other hand, it has been to the benefit of OPEC to "do nothing". Otherwise, higher oil prices and/or production limitation would have speeded up the efforts of the industrialized countries, especially the U.S., to reach the "backstop" technology which would make other sources competitive with oil. This would certainly have reduced the world demand for OPEC oil.

OPEC maintained price hikes that were not disastrous to the U.S. and was able to keep its oil flowing thus drawing capital for development and for greater economic in- fluence. In the long run OPEC does not do the U.S. a favor since alternative supplies are being developed at a slower rate than they must in order to be available when the oil actually runs out. Thus keeping the price down has encouraged interdependence. In this manner the U.S. becomes dependent on OPEC oil. There is a trade-off between immediate economic advantages to the U.S. in the face of inflation and political co- operation with OPEC. There is considerable stability in this state of affairs and because of its dominance it is hard to dislodge even if outside political influences are brought to bear on it (i.e. the Israeli situation).

If we remove the U.S. interdependence strategy L3 and OPEC's "do nothing" strat- egy 14, we have two Pareto optimal payoffs at (L2, 11 ) and (L s, 12). Only the second of these is an equilibrium solution with the U.S. subsidizing energy production and OPEC limiting its oil supply. That is how the situation was immediately after 1973. Note that (L3,/4) is more than three times better for the U.S. and nearly twice better for OPEC.

We have also studied separately the effectiveness of the U.S. strategies in preventing OPEC from adopting each of its strategies (except for/4). There we had the optimum strategy (L3, 11 ) in which interdependence absorbs the effects of price hikes. When we left out the interdependence strategy L3, equilibrium was attained at (Ls, 12) with limited OPEC supplies and increased subsidies for domestic energy production. This is a reasonable outcome in which the parties would attempt to maximize their benefits Without cooperation.

4. Conclusion

We have found the Analytic Hierarchy Process and its generalization to systems with feedback a useful tool in the analysis of conflict situations. Among the applica- tions are the Conflict in Northern Ireland [Alexander/Saaty], a Study of Terrorism [Saaty/Bennett] carried out for the Arms Control and Disarmament Agency, corporate planning, and in forecasts of the likely future of higher education in the U.S. by 1985 [Saaty/Rogers].

This approach has a richness which enables one to include most of what is im- portant to people when they think of a conflict problem. There is flexibility both in forming the hierarchy and in providing the judgments. Repetition of the process by projecting judgments over two or three time periods gives an overview of the dynamic

234 Th. L. Saaty

stability. Finally, implicit in our findings are areas for bargaining between the parties.

Addit ional work is now underway to highlight and to make explicit the bargaining process. I am grateful to my student, Hamid Gholemnezhad, for his help in constructing the example.

R e f e r e n c e s

Alexander, JAl., and T.L. Saaty: The forward and backward processes of conflict analysis. Behav- ioral Science 22, 1977, 87-98.

- : Stability analysis of the foreward-backwaxd process: Northern Ireland ease study. Behavioral Science 22, 1977, 375-382

Saaty, T.L.: A scaling method for priorities in hierarchical structures. Journal of Mathematical Psychology 15, 1977, 234-281.

Saaty, T.L., and P.C. Rogers: The future of higher education in the United States. Socioeconomic Planning Sciences 10, 1976, 251-264.

Saaty, T.L., and &P. Bennett: Terrorism: patterns for negotiations; three case studies through hierarchies and holarchies. A Study for the Arms Control and Disarmament Agency, August, 1977.

Received September, 1978 (revised version February, 1979 )