The 1985-86 oil price collapse and afterwards: what does game theory add?

Griffin, James M. ; Neilson, William S.

I. INTRODUCTION

Between August 1985 and August 1986, crude oil prices plummeted from $28 per barrel to $8 per barrel before stabilizing at $18 per barrel in the fall of 1986. Traditional oligopoly theory explanations point to the inherent fragility of cartel agreements due to the proclivity to cheat. While the tendency to cheat may be the correct explanation, these theories do not take us very far in answering the following deeper set of questions: Why do some cartels expire quickly while others tend to be long-lived? Alternatively, why do we observe price collapses under one set of conditions and not others?

The purpose of this paper is to consider whether game theory can help to motivate richer behavioral hypotheses which enhance our ability to answer this deeper set of questions. OPEC and the world oil market offer a particularly fascinating arena within which to test the applicability of game theoretic models. Because of the enormous complexity of this market, models of OPEC behavior must necessarily be incomplete. For example, because oil is a non-renewable resource, important complications of user costs arise, as in Pindyck [1985], along with issues of dynamic consistency, as in Newbery [1981]. Furthermore, the existence of a backstop fuel implies a price ceiling and a finite time period over which OPEC can manipulate price. Behaviorally, OPEC countries do not fit neatly into either a monolithic cartel model or the dominant firm/competitive fringe models that are so appealing because of their tractability, as shown by Griffin [1985] and Geroski, Ulph, and Ulph [1987].(1) Yet a further complication is the existence of a large non-OPEC competitive fringe, as discussed by Salant [1976], which supplies roughly one-half of world oil consumption.

In tailoring game theoretic models to particular market phenomena, one must first have a clear grasp of the underlying events to be explained. Accordingly we provide details on OPEC meetings, violations of production quotas, and price histories over the period 1983-90. This information serves as a backdrop to our focus on OPEC strategies to earn supracompetitive profits. Specifically, three alternative game theoretic strategies are outlined: the Cournot strategy, the swing producer strategy, and the tit-for-tat strategy. The Cournot solution is important because it describes a profit floor, which can always be attained if alternative strategies fail. The empirical tests are designed to show that (a) from 1983 to August 1985 Saudi Arabia played the role of swing producer, (b) when profits fell below the Cournot profit floor, the swing producer strategy was abandoned, and (c) a tit-for-tat strategy was implemented thereafter. For comparative purposes, other explanations of events over this period are briefly reviewed. The final section recapitulates our key findings and examines the relevance of game theory to explain oil price movements over this period.

II. ANECDOTAL EVIDENCE

Since March 1983 when OPEC initiated monthly production quotas for its individual members, Saudi Arabia has, we believe, attempted to enforce cartel cohesion through two separate behavioral devices. We posit that for the period March 1983 to August 1985, Saudi Arabia followed a swing producer strategy, adjusting output so as to stabilize price. In return, other OPEC members were expected to abide by their production quotas. After August 1985, Saudi Arabia abandoned the role of swing producer and adopted instead a tit-for-tat strategy. The empirical implications of these two strategies are straightforward. In the swing producer regime, one would expect to observe stable prices coupled with Saudi output falling below its assigned quota when the other producers cheat. In contrast, with a tit-for-tat strategy no effort is made to stabilize prices; there should be much greater price variation than in the swing producer regime. Anecdotal evidence appears to support these conjectures.

When formal production quotas were first instituted in March 1983, the Saudis were nominally assigned a production quota, but as noted in Petroleum Intelligence Weekly: "Saudi Arabia was cast without a formal quota as 'swing producer' balancing supply and demand according to the market."(2) Subsequent anecdotal evidence from the trade publications and plots of actual versus quota production levels indicate that the swing producer behavior lasted through August 1985, when Saudi Arabia initiated "netback pricing."(3) Figure 1 contrasts aggregate actual production data against the production quotas for Saudi Arabia and the other OPEC producers.(4) Even though quotas were reduced in November 1984 due to falling consumption, cheating persisted. Saudi Arabia saw its production plummet to 2.2 million barrels per day (MMB/D) by August 1985.

Figure 2 reports the spot price for Saudi light crude at the end of each month. Under the swing producer strategy, the production of the swing producer must be adjusted to stabilize prices at the desired level. From April 1983 through summer 1985, the spot price of Saudi light marker crude fluctuated between $26.90 and $28.90 per barrel and the official sales price changed only once over the period, being reduced from $29.00 per barrel to $28.00 per barrel in February 1985.

The swing producer role ultimately proved to be very costly to the Saudis. By December 1984, as oil consumption dropped sharply and cheating averaged almost 1.4 MMB/D, the Saudis saw their market share erode to 21.6 percent. By August 1985, the Saudis' market share had fallen to 15.8 percent. Saudi Arabia initiated netback pricing, announced its intention of regaining lost market share, and proceeded to increase production from 2.3 MMB/D to 6.4 MMB/D twelve months later. In the process, prices plummeted to below $8 per barrel. At the August 1986 pricing accord, the Saudis and other OPEC producers agreed to reinstitute cartel discipline and to reduce production levels back to their quota levels.

Following the pricing accord of August 1986, the Saudis show no evidence of reverting back to the swing producer strategy. In the face of much greater levels of cheating in the 1987-90 period, Saudi Arabia appears to maintain its production at or above its quota. This meant that because of rampant cheating, the Saudi's market share fell 2-3 percent below its quota share. Then during autumn 1988 when cheating by the other OPEC countries reached over 3 MMB/D, the Saudis appear not only to sustain production but to aggressively match cheating by the other cartel members. From autumn 1988 on, the Saudis' behavior appears to be a classic tit-for-tat strategy as both the Saudis and other OPEC producers exceeded their quotas, with the Saudis maintaining market share.

III. VARIOUS OPEC STRATEGIES

The Cournot Strategy

In the absence of a binding collusive agreement to restrict output, the OPEC countries are involved in a repeated Cournot game between quantity-setting producers.(5) In the case of OPEC, there are thirteen producers within OPEC, as well as the non-OPEC producers. Ostensibly, this means that there should be one best-response function for each producer, with each best-response function mapping the output of all other producers into the output for the producer in question. The Cournot equilibrium is the output combination such that each producer's output is a best response to the equilibrium output of all the other producers. Note that since the combined output of all producers determines the price according to the world demand function [Q.sup.W](p), best-response functions can be written as functions of price.(6) Let [R.sup.SA](P) denote Saudi Arabia's best-response function, [R.sup.OO](P) denote the other OPEC countries' best-response function, which is simply the sum of the individual best-response functions, and let [R.sup.NO](P) denote the sum of the non-OPEC producers' best-response functions. The price [P.sup.C] is the Cournot equilibrium price satisfying the following supply/demand relationship:

(1) [Q.sup.W]([P.sup.C]) = [R.sup.SA]([P.sup.C]) + [R.sup.NO]([P.sup.C]) + [R.sup.OO]([P.sup.C]).

Accordingly, each country is producing along its best-response function and the market clears at the Cournot price, [P.sup.C].

When looking for equilibrium strategies, attention can be restricted to the Cournot solution if (a) the game has a finite number of periods, (b) the last period is known, and (c) there is complete information. Under these conditions it is well known that in the last period, collusion is not viable and the game unravels to the Cournot solution, as shown by Tirole [1988, 245] for example. Despite the appeal of this result, its applicability to OPEC and the world oil market is tenuous. Even though the stock of oil reserves is finite, the date when exhaustion occurs or when a backstop fuel becomes economically feasible is not known with any certainty because the magnitude of the stock of ultimately discoverable reserves is not known. Whether or not this game should be treated as an infinite game or a finite game depends on how the continuation probability evolves through the course of the game. If the probability that the game continues for another period is approximately constant and sufficiently high, the folk theorems of infinitely repeated games apply. If, instead, the continuation probability declines to zero, so that as the game goes on it becomes increasingly likely that the game will end in that period, the folk theorems of infinitely repeated games cannot be applied, and the game must be treated as a finite game. We believe that the infinitely repeated case is more realistic, but for completeness we discuss both the finite and infinite repeated-game cases.

According to the folk theorems of infinitely repeated games, a cartel might employ a variety of collusive equilibrium strategies.(7) It is impossible, however, to determine, a priori, what strategies a cartel might employ. The only restriction that can be placed on behavior is that all parties are at least as well off as in Cournot equilibrium. In view of the previous anecdotal evidence, we turn our attention to the swing producer and tit-for-tat strategies.

The Swing Producer Strategy

The nonbinding agreement governing OPEC behavior in 1983-85 assigned the role of swing producer to Saudi Arabia and assigned production quotas to the other members. To formalize swing producer behavior, let [Q.sup.W](P) denote world demand for oil at price P, let [Q.sup.NO](P) denote the supply of non-OPEC countries, and let [Q.sup.OO](P) denote the output of other OPEC countries, that is, all the OPEC countries except Saudi Arabia. If Saudi Arabia is acting as a swing producer, its output, [Q.sup.SA], is determined by

(2) [Q.sup.SA]([P.sup.A]) = [Q.sup.W]([P.sup.A]) - [Q.sup.NO]([P.sup.A]) - [Q.sup.OO]([P.sup.A]),

where [P.sup.A] denotes the price specified in the OPEC agreement. Swing production is only rationalizable, in the sense of Bernheim [1984] and Pearce [1984], if Saudi profits under swing production are at least as great as in Cournot equilibrium. The viability of this strategy depends critically on other OPEC producers' willingness to restrict output below the Cournot levels.

If the game is repeated infinitely, it is possible to construct a set of strategies which generate swing production behavior by Saudi Arabia in equilibrium. This is done formally in appendix A. The intuitive argument goes as follows. Assuming that world demand is constant through time, and treating all other producers (both inside and outside OPEC) as a single player (referred to as the other player),(8) the strategy used by Saudi Arabia is to behave as a swing producer as long as other production is below some level Q*. If other production exceeds Q*, then the Saudis' produce according to the Cournot best-response function for the remainder of the game. Intuitively, the interval (0, Q*) gives a range of output levels (which may include output above the pre-assigned quotas) over which Saudi Arabia behaves as a swing producer. But if other producers exceed the threshold output Q*, Saudi Arabia punishes them forever by playing Cournot. The strategy for the other player is to produce its most profitable output level within Q* unless Saudi Arabia fails to behave as a swing producer, in which case it produces according to its Cournot best-response function for the remainder of the game. In essence, the other producers accommodate swing production by not exceeding output Q*. For a given level of world demand, total world revenue is independent of the distribution of output across producers, since total world output and price are constant and designated by the OPEC agreement. Consequently, increases in production by other OPEC or non-OPEC producers directly transfer revenue from Saudi Arabia to the other producers, which gives the other producers the incentive to produce up to Q*. Since Q* may exceed the pre-assigned quota output of other OPEC countries, cheating may not be completely deterred with this strategy. Despite the possibility of some cheating, this strategy is potentially attractive to the Saudis, who can earn profit in excess of the Cournot equilibrium level. A similar result for the case of finitely repeated games establishes that, irregardless of whether the number of repetitions is finite or infinite, the swing producer strategy is one possible strategy for achieving profits in excess of Cournot profits.(9)

The Tit-for-Tat Strategy

The OPEC agreement plays a crucial role in the above argument, in that beliefs about Saudi behavior are governed to some extent by the role specified for Saudi Arabia in the agreement. The OPEC agreement reached after the 1985-86 price collapse did not detail any explicit behavior on the part of Saudi Arabia, but instead just specified production quotas for all members including Saudi Arabia. The class of feasible strategies adopted by the Saudis is potentially quite large, and more than one strategy could conceivably produce observationally equivalent responses. It is advantageous to first narrow the search by determining what characteristics a strategy should have. First, it should be rationalizable, which means that the strategy must be consistent with some set of beliefs. Unfortunately, however, there are many such strategies, so further restrictions must be made. A second set of restrictions comes from the work of Axelrod [1984] in his tournament comparing different strategies in a finitely repeated prisoner's dilemma. He concluded that a successful (but not necessarily equilibrium) strategy must both punish deviations from the Pareto efficient strategy combination and must also be forgiving if the other player repents.

The tit-for-tat strategy won Axelrod's tournament; moreover, tit-for-tat behavior is rationalizable. Consequently, it is a candidate for empirical testing. Even though tit-for-tat behavior is rationalizable, the tit-for-tat strategy, taken by itself, is not rationalizable, because it requires that one player cooperates while another player cheats, which is not optimal. The behavior can be rationalized as part of a "larger" strategy in the same manner as swing production. For the case of an infinite number of repetitions, Saudi Arabia plays tit-for-tat as long as other production is less than some level Q**, and produces according to the Cournot best-response function for the remainder of the game if other production ever exceeds Q**. The other producers select the optimal output level within Q** unless Saudi Arabia fails to play tit-for-tat, in which case the other countries produce according to their Cournot best-response functions for the remainder of the game. These strategies constitute an equilibrium in which Saudi Arabia plays tit-for-tat and earns profit in excess of the Cournot equilibrium level.(10)

Operationally, tit-for-tat involves punishing other OPEC members for producing in excess of the quotas specified in the OPEC agreement. Letting [Mathematical Expression Omitted] denote the quota specified for other OPEC members and [Mathematical Expression Omitted] denote the quota specified for Saudi Arabia, tit-for-tat specifies that Saudi production is determined by

(3) [Mathematical Expression Omitted]

If [Gamma] = 1, the Saudis match cheating by other OPEC members barrel for barrel. Other values of [Gamma] are consistent with a tit-for-tat strategy as well. Specifically, if the Saudis attempt to preserve their market share, then [Gamma]/1 - [Gamma] equals the Saudis' quota specified in the OPEC agreements. Note that when Saudi Arabia follows a tit-for-tat strategy, Saudi output in excess of its quota, as in equation (3), is independent of world demand and non-OPEC production. The Saudi response depends only on other OPEC production, which can be taken as predetermined because other OPEC members take Saudi Arabia's tit-for-tat behavior as given when deciding whether and how much to cheat. In effect, the problem becomes analogous to a Stackleberg price leadership model with Saudi Arabia as follower. Accordingly, we interpret equation (3) as a structural equation in which other OPEC production is predetermined.

IV. EMPIRICAL TESTS OF ALTERNATIVE STRATEGIES

Tests of Swing Producer Behavior: March 1983-August 1985

When OPEC first began formal assignments of production quotas in March 1983, Saudi Arabia accepted the special role of swing producer. Unlike other OPEC producers, Saudi production could vary above or below its nominal quota for the purpose of stabilizing price at the official Saudi marker crude price. In effect, Saudi production became the residual necessary to meet world demand at the official "marker" price, given production from non-OPEC and other OPEC sources, as discussed by Al-Chalabi [1991]. Equation (2), describing the Saudi production response, is the basis for a direct test of swing producer behavior. Each determinant of Saudi production in equation (2) can be written as the sum of a deterministic component ([Q.sup.i]([P.sup.A])*) and a stochastic component ([[Epsilon].sup.i]) as follows: [Q.sup.i]([P.sup.A]) = [Q.sup.i]([P.sup.A])* + [[Epsilon].sup.i]. Subtracting out the deterministic components, we obtain the result that fluctuations in Saudi output ([[Epsilon].sup.SA]) should be positively related to demand shocks ([[Epsilon].sup.W]) and negatively correlated with non-OPEC and other OPEC supply shocks ([[Epsilon].sup.NO], [[Epsilon].sup.OO]) as follows:

(4) [[Epsilon].sup.SA] = [[Epsilon].sup.W] - [[Epsilon].sup.NO] - [[Epsilon].sup.OO].

In principle, the stochastic components for world demand, non-OPEC supply, and other OPEC supply could be calculated by first estimating structural models for each of these variables (i.e., world demand, non-OPEC production and other OPEC production). After solving for each respective quantity given the Saudi marker price ([P.sup.A]), the random shocks ([[Epsilon].sup.W], [[Epsilon].sup.NO], [[Epsilon].sup.OO]) can be calculated by the differences between actual and predicted quantities. Despite the intuitive appeal of this direct test of swing producer behavior, the requisite monthly data to estimate world demand and non-OPEC supply do not exist.(11)

Instead we have adopted an indirect test which utilizes available price data. Under the swing producer model, prices would be expected to fluctuate around the Saudi marker price. Three testable hypotheses emerge. First, under swing producer behavior, prices should not follow a random walk: rather they should exhibit stationarity around the Saudi marker price ([P.sup.A]). Second, the process generating prices in the swing producer period and the tit-for-tat period should differ structurally since in the latter there is no reason for prices to return to [P.sup.A]. Third, the variance of prices would be expected to be very small under swing producer behavior and potentially much larger under tit-for-tat. To test these conjectures, we posit the following general equation used to describe commodity price movements over time:(12)

(5) [P.sub.t] - [P.sub.t-1] = [Alpha] + [Beta] time + ([Gamma]-1)[P.sub.t-1] + [Delta]([P.sub.t-1] - [P.sub.t-2]) + [e.sub.t].

This formulation allows for prices to exhibit trend growth over time, to adjust to the previous price levels, and to fluctuate based on past price change. If prices follow a random walk ([Beta] = 0 and [Gamma] = 1), swing producer behavior is rejected because there would be no tendency for prices to revert to some market crude price.(13)

Table I reports the results of equation (5) as well as the restricted model implying random walk behavior ([Beta] = 0 and [Gamma] = 1) for both the swing producer period (May 1983 through August 1985) and the tit-for-tat period (October 1985 through March 1990). First, comparing the restricted equation (2) versus the unrestricted equation (1) for the swing producer period, it would appear that there was some negative drift in prices over time ([Beta] [is less than] 0).(14) Furthermore, the -.85 coefficient on lagged price suggests that increases in lagged prices result in subsequent price decreases, which is clearly inconsistent with a random walk. Furthermore, the implied stationary price of $27.70 per barrel is close to the $28 marker price in February 1985. Surprisingly, despite the apparent confirmation of the $28 marker crude price and the apparent rejection of a random walk, the unit root test shows a value of 6.53, which falls below the Dickey-Fuller critical value of 7.24. The hypothesis of a random walk cannot be rejected. Our interpretation of this result is that the Dickey-Fuller test is well known to be a low-power test, so failure to reject a random walk in no way leads us to reject the stationarity of the series and its consistency with the swing producer model.

Second, the price equations differ structurally in the two periods. Comparison of equation (1) versus equation (3) in Table I shows there was an apparent structural shift in the two periods. The computed F-statistic is 5.48, which exceeds the critical [F.sub.(.05,4,74)] value of 3.1, leading us to reject the assumption of a common structure. Perhaps our most striking finding is the third test to see if the variance of prices in the two periods were equal. Given that the standard error of prices is $.31 in the swing producer period and $1.56 in the tit-for-tat period, it should not be surprising that an F-test on the respective variances decisively rejects the hypothesis of equal variances (F = 24.6 [is greater than] [F.sub.(.05,50,24)] = 1.89).

To summarize, direct tests to see if Saudi output variation is positively correlated with demand shocks and negatively correlated with non-OPEC and other-OPEC supply shocks is an intriguing, but infeasible test. Indirect tests using monthly price data show that price variation in the 1983-85 period comports reasonably well with the predictions of the swing producer model despite our inability to rule out a random walk. It is clear that a structural break did occur after August 1985, separating the two periods. Moreover, the estimated variance of prices in the latter period was twenty-five times that of the swing producer period. While these results show that after August 1985 prices exhibited much greater variation and differed structurally from the swing producer period, it remains to be shown that the tit-for-tat strategy was in fact followed in the latter period.

TABULAR DATA OMITTED

Tests for Tit-for-Tat Behavior: October 1985--March 1990

Equation (3) describes the standard tit-for-tat model, which, depending on the value of [Gamma], can range from barrel-for-barrel matching of cheating to preserving a constant market share. The tit-for-tat period is assumed to begin in October 1985, although as noted above, Saudi Arabia's vigorous output expansion from October 1985 to August 1986 is observationally equivalent to a Cournot strategy.(15) As illustrated in equation (1) of Table II, this formulation estimates [Gamma] to be .215, which implies a type of market-sharing tit-for-tat behavior with a 27 percent market share. Interestingly, Saudi Arabia's quota market share fluctuated over the period between 24 and 27 percent.

This formulation of tit-for-tat may be overly restrictive, however, in that it implies the same marginal response to cheating, whether cheating is one barrel or three million barrels per day. A priori, a nonlinear punishment function might better capture the reality that certain low levels of cheating are likely to occur irrespective of the Saudis' actions. Accordingly, we modify equation (3) to include nonlinear punishment for cheating:

(6) [Mathematical Expression Omitted].

Under this generalized tit-for-tat strategy, we posit that [[Gamma].sub.2] is positive so that severe cheating is punished more than mild cheating. As shown by equation (2) of Table II, the nonlinear punishment formulation has considerably more explanatory power. The negative coefficient on [[Gamma].sub.1] coupled with a positive coefficient on [[Gamma].sub.2] implies that for other OPEC cheating below approximately two million barrels per day (approximately 15 percent of their quota), the Saudis reduce production as they would under a swing producer model.(16) However, cheating above this threshold results in increasingly severe reactions by the Saudis.

Equations (3) and (4) of Table II are included to deal with potential problems of autocorrelation and simultaneous equation bias, respectively. Equation (3) uses a first-order autocorrelation adjustment with a Prais-Winsten adjustment for the first data point. The estimated coefficient of first-order autocorrelation is .32. While the magnitude of the t-statistics is reduced, they remain strongly significant and the parameter estimates imply only a somewhat lower punishment threshold of 1,790,000 B/D.

Yet another potential objection is that other OPEC production, [Q.sup.OO], may be endogenously determined. As noted above, under the maintained hypothesis of tit-for-tat behavior, other OPEC production is exogenous; nevertheless, equation (4) of Table II shows that simultaneous equation bias is not serious.(17)

Equation (5) of Table II fits the tit-for-tat model to the swing producer sample period to see to what degree a tit-for-tat strategy might describe behavior in the swing producer period. Reassuringly, it TABULAR DATA OMITTED shows that the tit-for-tat model has no explanatory power in the swing producer period.(18)

Characteristics of the Cournot Solution

The theoretical section emphasizes that the Cournot equilibrium offers a floor level of profits, which the Saudis can always choose if experimentation with alternative strategies fails. The purpose of this section is to attempt to characterize the Cournot solution and to see whether it explains why the Saudis abandoned the role of swing producer in August 1985. Specifically, we address the following four questions: First, assuming all producers abide by their quotas, what is the payoff to Saudi Arabia under the swing producer strategy? Second, what is the Cournot price and the corresponding payoff to Saudi Arabia assuming noncollusive behavior by the other OPEC members? Third, what is the loss in Saudi market share under swing producer behavior necessary to reduce the Saudi revenues to that attainable under Cournot behavior? Fourth, does this calculated market share at which the Saudis should revert to Cournot behavior match observed market shares over this period?

We perform these calculations with the use of a simulation model, OPEC GENIE, which was adapted by an earlier generation model in Daly, Griffin, and Steele [1982]. The model's basic structure is straightforward. Prices are set exogenously, aggregate demand determined, then non-OPEC production is determined, then other OPEC production is determined, and finally Saudi Arabia is the residual supplier. The aggregate demand function assumes an income elasticity of .93 and a long-run price elasticity (with respect to retail petroleum products) of -1.04. These estimates along with the non-OPEC supply response are well within the range of estimates reported by the Energy Modelling Forum's World Oil Project. For a schematic description of the model, see appendix B.

Our first step involved initializing OPEC GENIE to 1985 market conditions. The crude oil price was exogenously set at $28 per barrel, the official marker price for Saudi light crude in summer 1985. Assuming no cheating, Saudi Arabia's market share was set at 27.2 percent, while the market share of other OPEC producers was set at 72.8 percent based on assigned OPEC production quotas. Given the initial market price and initial market shares, the optimal future real escalation rate of crude prices is found to be 1.2 percent annually by a grid search over various escalation rates.(19) Thus, given an initial price of $28 per barrel escalating at 1.2 percent annually, and a 27.2 percent Saudi market share, we calculate the payoff to Saudi Arabia and other OPEC members if all parties abide by the quotas specified in the swing producer agreement. As shown in row 1 of Table III, the payoff would be $2.29 trillion for Saudi Arabia and $5.85 trillion for other OPEC countries, after applying a 5 percent discount rate to oil revenues computed in 1990 dollars.

Next, we utilize OPEC GENIE to compute the Cournot price which would maximize the Saudis' profits assuming no cooperation from the other OPEC producers. To model the other members' Cournot output response, behavior similar to that of the non-OPEC competitive fringe was assumed. Accordingly, a production path assuming vigorous output expansion was postulated, constrained only by the ability to expand existing facilities and the magnitude of the underlying resource base.(20) Given price-taking behavior by the other OPEC producers, Saudi Arabia was then assumed to search over the class of price paths selecting the one which maximizes the present value of its revenue stream. By searching over a grid consisting of various initial crude prices and various rates of annual price escalation, we found that the optimum noncollusive solution for Saudi Arabia was to select a low initial price--$8 per barrel and an annual escalation of 4.8 percent.(21) Quite plausibly, this result approximates the familiar Hotelling rule approximating the assumed 5 percent real discount rate. As reported in the last row of Table III, the present value of Saudi profits corresponding to the Cournot production strategy is $1.90 trillion, while other OPEC countries earn only $4.90 trillion.

TABLE III

Simulation Model Estimates of Saudi Arabia Net Present Value of Oil Revenues

 Saudi Saudi Payoff Other OPEC Payoff
Strategy Market Share ([10.sup.9] 1990 $'s) ([10.sup.9] 1990 $'s)

Swing Producer 27.2 2.290 5.851
 26.2 2.245 5.896
 25.2 2.200 5.941
 24.2 2.155 5.986
 23.2 2.109 6.032
 22.2 2.066 6.075
 21.2 2.022 6.119
 20.2 1.978 6.163
 19.2 1.936 6.205
 18.2 1.893 6.248
Cournot N.A. N.A. 1.897 4.901

Next, the swing producer model was solved under a variety of market share assumptions corresponding to different levels of cheating to calculate Saudi Arabia's profits under different levels of cheating. In all the swing producer cases, total OPEC profits are equal at $8.14 trillion because total OPEC production is the same, only the division between Saudi Arabia and other OPEC members varies.(22) Interestingly, despite resource limitations and a rising real price over time, it still pays other OPEC producers to cheat. As shown in Table III, every 1 percent loss in Saudi market share to the other OPEC members implies a $45 billion loss to the Saudis. Saudi profits fall to $1.89 trillion when its market share drops to 18.2 percent from its prescribed level of 27.2 percent. Thus, 18.2 percent represents a "trigger" market share at which Saudi Arabia should switch from swing producer behavior to Cournot behavior.(23) This result confirms that cheating had to reach epidemic proportions before the Saudis would abandon the role of swing producer.

By May 1985, when Saudi market share had fallen to 17.5 percent, and production stood at 2.6 MMB/D, these calculations suggest the Saudis would have preferred the Cournot solution. Nevertheless, the Saudis waited patiently until August 1985 when their market share had fallen even further to 15.8 percent and production had slipped another .3 MMB/D to 2.3 MMB/D before vigorously expanding production.(24) By July 1986, prices stood just below $8 per barrel--our estimate of the Cournot price. Then, following the August 1986 OPEC accord, OPEC members agreed to abide by new quotas, designed to stabilize prices in the $18 per barrel range. In the preceding empirical tests, we set October 1985 as the beginning of the tit-for-tat period. Alternatively, one could describe October 1985 to August 1986 as a Cournot period followed by a tit-for-tat period beginning in September 1986. Observationally, over this period of time, Saudi Arabia's vigorous expansion of production is consistent either with regaining market share under tit-for-tat or with Cournot behavior.

V. ALTERNATIVE EXPLANATIONS

A variety of other explanations have been offered for the oil price collapse of 1986. For example, articles in Petroleum Intelligence Weekly attribute the price collapse to the Saudis' experimentation with netback pricing, which was abandoned in late summer 1986.(25) Stated simply, netback pricing was the culprit, rather than a tool used to deliberately punish cheaters. Other commentators, such as Dermot Gately [1986], interpret the Saudi actions as more planned, but a severe mistake, nevertheless. Adelman [1986] and Al-Chalabi [1991], on the other hand, suggest that the Saudi's sharp decline in market share gave them little choice but to regain it.(26) Still another explanation is that the price collapse of 1986 signalled the end of OPEC.(27)

One exception to the ad hoc explanations is a game-theoretic interpretation offered by Alt, Calvert and Humes [1988]. They construct a finitely repeated game in which Saudi Arabia's punishment costs vary randomly from period to period, with the Saudis knowing their current punishment costs but not future punishment costs. To them, the price collapse of 1985-86 should be interpreted as a random (and therefore unpredictable) effort by Saudi Arabia to reinforce its reputation as a low-cost producer and in the process discipline high-cost non-OPEC producers, such as Britain and Norway.

In contrast, our analysis leads us to conclude that the 1985-86 oil price collapse was neither a random event, nor a Saudi mistake, nor the end of OPEC. Like Adelman and Al-Chalabi, we interpret Saudi behavior as a rational response to its precipitous loss in market share. Interestingly, our simulation results confirm that the Saudi market share had fallen below the trigger level at which profits under a Cournot strategy would be preferable. The decision to punish cheaters had reached the point at which it was costless to do so. An important distinction between our analysis and that of Adelman and Al-Chalabi is that following the punishment phase we claim that the Saudis abandoned the swing producer strategy, adopting a tit-for-tat strategy. This explanation makes the greater price variability following the August 1986 pricing accord intelligible and suggests that the Saudis will not sustain the large losses in market shares experienced in 1984-85.

VI. CONCLUSIONS

Our approach in this paper has been (i) to identify two strategies employed by Saudi Arabia to foster cartel cohesion over the period 1983 to 1990 and (ii) to ask what insights game theory offers as to the sustainability of these strategies. Support for the swing producer strategy rests on several pieces of evidence which taken together form a persuasive explanation. Empirical tests on price data show apparent price stationarity approximating the Saudi marker price, a structural shift in prices after August 1985, and a phenomenal increase in the variance of prices after departing from the swing producer strategy after August 1985. Our simulation model results indicate that the trigger market share was 18.3 percent, and the Cournot price was $8.00 per barrel. By August 1985 the Saudis' market share had fallen to 15.8 percent--a level well below the trigger market share at which Cournot profits would be higher. The ensuing abandonment of the swing producer strategy and adoption of a tit-for-tat strategy drove price down to $8 per barrel in the summer of 1986 before OPEC members agreed to abide by new quotas.

The exact tit-for-tat strategy adopted punishes cheating differently, depending on the magnitude. The Saudis do not appear to react to low levels of cheating and may absorb some minor cutbacks, but high levels of cheating evoke a forceful response.

But what does game theory add? Game theory appears useful to the extent that it focuses empirical analysis on strategies to achieve cooperation. While game theory does not identify, a priori, the strategy employed, empirical validation of a strategy, as in this paper, is helpful. By identifying such strategies, events over the period 1983 to 1990 become more intelligible. For example, given the swing producer strategy, it was possible to predict the market share threshold at which Saudi Arabia would wish to punish the other producers' cheating. In this way the price collapse of 1985-86 was a predictable consequence. Likewise, tit-for-tat behavior suggests that short-run price volatility should increase, but price collapses of the magnitude of the 1985-86 period, paradoxically, become less likely.

Unfortunately, game theory does not explain the choice of strategies and offers few insights as to their sustainability. Except under very restrictive conditions, the number of rationalizable strategies is very large. Interjecting different sets of prior beliefs allows the theory to generate a plethora of different strategies. Without specifying the reasons for the prior beliefs and strategy selection, game theory is of negligible predictive value. Likewise, the folk theorems of infinitely repeated games allow too many equilibrium strategies to make prediction possible. The alternative of limiting the number of equilibrium strategies to one (the Cournot outcome) by assuming, for example, perfect information and a finitely repeated game, seems unsatisfying as well.

APPENDIX A

Generating Swing Producer and Tit-For-Tat Behavior In Equilibrium

Two players, denoted SA and OO, are involved in a game with a finite number of periods. Each stage game has a Pareto efficient outcome, but the combined payoff in the Pareto efficient outcome is nonconstant over time, possibly shrinking to zero.(28) Both players have dynamic best-response functions, denoted [Mathematical Expression Omitted] and [Mathematical Expression Omitted], respectively, where [Mathematical Expression Omitted] denotes player i's output in period t, and [Mathematical Expression Omitted] denotes the function assigning player j's best response to player i's output in period t. Cournot equilibrium holds when both players set output according to [Mathematical Expression Omitted].

Before the game begins, the two players reach a nonbinding agreement specifying that player SA will produce output [Mathematical Expression Omitted] in period t, where [Mathematical Expression Omitted] is a function assigning SA's response to OO's output. Also implicit in the agreement is a set [Mathematical Expression Omitted] of output levels for player OO such that if [Mathematical Expression Omitted], player SA responds by playing [Mathematical Expression Omitted]. Let [Mathematical Expression Omitted] be the element of [Mathematical Expression Omitted] which maximizes the expected present value of profits for OO as of time t. It is assumed that the path [Mathematical Expression Omitted] is a Pareto efficient outcome combination. The final relevant attribute of the agreement is that if player OO ever chooses an output level outside of [Mathematical Expression Omitted], player SA responds by producing according to its best-response function for the remainder of the game. Likewise, if player SA ever fails to produce according to [Mathematical Expression Omitted], player OO responds by producing according to its best-response function for the remainder of the game.

The purpose of this appendix is to establish that there exist equilibria in which SA behaves according to [Mathematical Expression Omitted] and OO behaves according to [Mathematical Expression Omitted], at least for part of the game. First consider the case in which there are an infinite number of periods, or, equivalently, the case where the game has a high continuation probability at every stage. As Fudenberg and Maskin [1986] demonstrate, if there is sufficiently little discounting, the strategies outlined above are best-responses to each other, and there exists a perfect equilibrium in which SA behaves according to [Mathematical Expression Omitted] for the entire game.

For the case of finite repetitions, assume that player OO assigns probability p [is greater than] 0 to the event that SA must abide by the agreement, and that this probability is common knowledge. This assumption is equivalent to the assumption that OO assigns probability p [is greater than] 0 to the event that SA uses the grim strategy of playing the strategy which leads to the Pareto efficient outcome until OO deviates by producing an output level outside of the set [Mathematical Expression Omitted]. Applying the incomplete information folk theorem of Fudenberg and Maskin [1986], there exists a sequential equilibrium in which the path [Mathematical Expression Omitted] is followed at the beginning of the game.

APPENDIX B

Overview of OPEC GENIE 4.0

OPEC GENIE 4.0 is a fully dynamic simulation model of the world oil market describing non-communist oil demand (D), non-OPEC oil production ([Q.sub.no]) excluding net communist exports (X), and production from each of the thirteen OPEC countries ([Q.sub.1]...[Q.sub.13]).(29) The model assumes market clearing behavior at every period, that is,

(B1) D = [Q.sub.no] + X + [Q.sub.1] + [Q.sub.2] + ... + [Q.sub.13].

Econometric relationships form the basis for non-communist demand determination. Net communist exports, which have typically been very small, are treated exogenously. Supply from non-OPEC areas is based on judgmental estimates, which include considerations of present and anticipated reserves, absorptive capacity and political and engineering constraints. Key exogenous variables to the model include the real price of oil and an index of world economic activity. Since oil prices are treated as exogenous, the structure of the model is recursive, beginning with oil demand determination, then proceeding to supply determination.

World oil demand from non-communist areas in period t depends upon economic activity ([A.sub.t]) in period t and a distributed lag (L) on previous years' real price of retail petroleum products (P*) as follows:

(B2) [D.sub.t] = f[[A.sub.t], P*(L)].

In turn, the real price of retail petroleum products is determined by the price of crude oil ([P.sub.t]) plus the costs of refining, marketing, and taxes reflected in the margin (M), which is assumed constant.

(B2a) [P*.sub.t] = [P.sub.t] + [M.sub.t].

Given assumptions about world economic growth and the price path of crude oil, equation (B2) solves for non-communist world oil demand.(30) Implicit in this formulation is a long-run retail petroleum product's price elasticity of -1.04 and an elasticity of .93 with respect to economic activity.

Next, the model determines non-OPEC, non-communist oil production ([Q.sub.no]) as a function of the real price of crude oil and existing institutional and technical constraints ([Z.sub.t]):

(B3) [Q.sub.[no.sub.t]] = g([P.sub.t], [Z.sub.t]).

In this model, non-OPEC producers behave as competitive fringe producers. In addition we assume that non-OPEC production cannot exceed levels consistent with engineering limitations on reserves-to-production ratios, that is, production in a certain period must be equal to or less than a given fraction, [Gamma], of previous year's reserves ([R.sub.[no.sub.t-1]]):

(B3a) [Q.sub.t] [is less than or equal to] [R.sub.[no.sub.t-1]].

In turn, non-OPEC additions to reserves (R[A.sub.no]) depend upon a distributed lag on past real oil prices (P):

(B3b) R[A.sub.[no.sub.t]] = f[P(L)].

By the perpetual inventory formula, reserves at the end of period t are obtained by the identity that they equal initial reserves ([R.sub.[no.sub.t-1]]) plus additions to reserves (R[A.sub.[no.sub.t]]) minus production ([Q.sub.[no.sub.t]]):

(B3c) [R.sub.[no.sub.t]] = [R.sub.[no.sub.t-1]] + R[A.sub.[no.sub.t]] - [Q.sub.[no.sub.t]].

Having determined oil demand in equation (B2), non-communist, non-OPEC production in equation (B3), and given net communist exports ([X.sub.t]), we now turn to the question of how the demand facing OPEC is allocated among its thirteen members. In the non-cheating swing producer scenario, the market shares based on the production quotas announced at the October 1984 OPEC meeting are assumed:

(B4) [Q.sub.[i.sub.t]] = [s.sub.i]([D.sub.t] - [Q.sub.[no.sub.t]] - [X.sub.t]) i = 1,..., 13.

The implied market shares ([s.sub.i]) are as follows: Saudi Arabia (.272), Kuwait (.056), U.A.E. (.059), Libya (.062), Qatar (.018), Iran (.144), Iraq (.075), Indonesia (.074), Algeria (.041), Venezuela (.097), Nigeria (.081), Ecuador (.011), and Gabon (.008).

OPEC GENIE incorporates important aspects of resource scarcity by simulating for a period of seventy years and then valuing any remaining reserves left in the ground. The real discount rate, which is assumed to be 5 percent, can be parametrically varied. Substitute fuel considerations enter directly through the assumption of a backstop fuel price at which synthetic fuels become available and place a ceiling on oil prices. For these simulations, the back-stop fuel price is assumed to be $40 per barrel.

1. For example, Griffin [1985] tested a variety of OPEC behavioral models and showed that with the exception of Iraq (which behaved competitively), OPEC countries appear to follow some variant of a partial market sharing model over the period 1972 to 1983. Interestingly, OPEC countries appear to have been partially sharing markets well before official production quotas were first announced in 1982.

2. Petroleum Intelligence Weekly, 21 March 1983.

3. Netback pricing assured purchasers of Saudi crude a fixed refiners margin enabling the Saudis to dramatically increase crude sales.

4. Both the monthly production and quota data as well as spot price data are taken from Petroleum Intelligence Weekly.

5. Whether there are finite repetitions or infinite repetitions is a matter which is discussed in more detail below.

6. Specifically, let [Z.sup.i]([Q.sup.-i]) denote the best-response function of producer i given the output vector [Q.sup.-i] which describes the output of all other producers. Since the price is determined by

[Q.sup.W](P) = [summation over j[is not equal to]i] [Q.sup.j] + [Z.sup.i]([Q.sup.-i]),

as long as [Z.sup.i] is invertible it is possible to write the best-response mapping as a function of price.

7. The incomplete information folk theorem of Fudenberg and Maskin [1986] extends this result to finitely repeated games.

8. There are three reasons for making this assumption. First, the role of swing producer involves responding to combined world output, not individual output. Second, two-player games are simpler to analyze than games with more than thirteen players, because interactions between the other players can then be ignored. Third, and most importantly, the purpose of this paragraph is to outline an argument which establishes that swing producer behavior can arise in equilibrium. It suffices to show this under this assumption that Saudi Arabia treats the rest of the world as a single player.

9. Appendix A shows that it is possible to find a set of beliefs such that there exists a sequential equilibrium in which for some length of time at the beginning of the game, Saudi Arabia acts as a swing producer and earns profit in excess of the Cournot equilibrium level. The argument relies on the existence of an agreement (such as from OPEC meetings) upon which beliefs can be based.

10. Appendix A presents this argument more formally, and also presents a counterpart for the finitely repeated game case.

11. Only data on OPEC production and prices are available monthly.

12. See for example, Pindyck and Rubinfeld [1991, 461].

13. Instead, with a random walk price changes depend on a random error term and possibly past price changes, which permanently raise or lower prices.

14. Indeed over the period March 1983 to August 1985, the marker price was reduced once from $29 to $28.

15. To confirm empirically that tit-for-tat began in October 1985, the model was fit over different sample periods. The coefficient of determination fell sharply when the sample was extended further back in time. For example, extending the sample back to September 1985, [R.sup.2] = .548. If the sample is extended back to August [R.sup.2] drops to .503. Alternatively, shortening the sample (by assuming that tit-for-tat begins after October 1985) has no apparent effect on [R.sup.2].

16. For example, the Saudi response to an additional barrel of cheating varies as follows at the following different levels of cheating: -.52 barrels at 0 cheating, -.4 barrels at 500,000 B/D, -.27 barrels at 1,000,000 B/D, -.135 barrels at 1,500,000 B/D, -.004 barrels at 2,000,000, +.128 barrels at 2,500,000, +.259 barrels at 3,000,000, +.39 barrels at 3,500,000, and +.52 barrels at 4,000,000 B/D.

17. Instrumental variables include

[P.sub.t-1], ([P.sub.t-1] - [P.sub.t-2]), ([P.sub.t-2] - [P.sub.t-3]), [Mathematical Expression Omitted], [([P.sub.t-1] - [P.sub.t-2]).sup.2], [([P.sub.t-2] - [P.sub.t-3]).sup.2], [Mathematical Expression Omitted].

18. A formal F-test for similar coefficients in both periods showed a value of 3.96, which is well above the critical [F.sub.(.05,3,70)] = 2.74.

19. We restrict our analysis to the class of price paths that grow at constant rates and smoothly approach the backstop fuel price of $40 per barrel, thereby minimizing dynamic inconsistency problems.

20. over the period 1990 to 2010, other OPEC production was assumed to expand annually by one million barrels per day. By 2010, other OPEC producer's reserve-to-production ratio had fallen to 20--a rate consistent with many competitive producers.

21. This price is well below the price observed in most of the 1983-90 period, which provides evidence that OPEC members were not behaving as Cournot players.

22. Resource constraints based on reserve-to-production ratios must be satisfied in the model so that if other OPEC producers' higher market share results in their inability to satisfy their portion of demand, Saudi production is assumed to fill the shortfall subject to the Saudi reserves-to-production constraints.

23. This trigger share is a lower bound for possible trigger shares, since it implicitly assumes that the Cournot period lasts forever once it is reached. This assumption represents a simplification of the more general case of temporary punishment periods, but in the latter case the end of the punishment period must be random to avoid dynamic inconsistency problems.

24. There are reports in Petroleum Intelligence Weekly as early as 24 June 1985, indicating the Saudis were seeking netback pricing contracts for crude sales.

25. Basically, netback pricing guaranteed the refiner/purchaser a fixed margin so that the sale price was computed based on wholesale product prices less the refiner's margin and transport cost. Guaranteed a fixed margin, refiners had incentives to process Saudi crude at the refinery's capacity output.

26. Interestingly, only these interpretations are consistent with our findings. The discussion by Al-Chalabi is particularly interesting, given his position in OPEC as Deputy Secretary General from 1978 to 1989.

27. See The Economist, 15 October 1988.

28. Using only two players requires some justification. In essence, it combines all nations with which Saudi Arabia strategically interacts as a single player. For the swing producer period, OO is all other producers combined. For the tit-for-tat period, OO is the combination of all players whose decisions matter in the Saudi production decision. Combining these players assumes that Saudi Arabia treats them as a group, not individually, and it avoids the complicated problem of how the other producers coordinate their output decisions. From a modelling perspective, the assumption of two players allows the use of Fudenberg and Maskin's [1986] results, which rely on the assumption of two players.

29. For additional details, see Daly, Griffin, and Steele [1982].

30. In these particular simulations, world GDP is assumed to grow at 2.75 percent annually.

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JAMES M. GRIFFIN and WILLIAM S. NEILSON, Professor, Texas A&M University, and Associate Professor, Texas A&M University. We wish to thank Michael Baye, John Van Huyck, Steven Wiggins, Rodney Smith, and the referees for helpful comments. Larry Vielhaber and Weiwen Xiong provided excellent research assistance.

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