Canadian Public Policy

The Canadian National Energy Program and Its Aftermath: A Game-Theoretic Analysis Author(s): Patrick James Reviewed work(s): Source: Canadian Public Policy / Analyse de Politiques, Vol. 16, No. 2 (Jun., 1990), pp. 174-190 Published by: University of Press on behalf of Canadian Public Policy Stable URL: http://www.jstor.org/stable/3550964 . Accessed: 08/10/2012 13:36

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http://www.jstor.org The Canadian National Energy Program and Its Aftermath: A Game-theoreticAnalysis* PATRICK JAMES Department of Political Science McGill University

L'analyse a l'aidde a thoriejeuxee des des politiquesespubliques a t jusqu' maintenant plus de nature prescriptive que descriptive, soulevant ainsi des questions quant a son utilite pratique. Une facon de rectifier ceci est de rendre operationnels les concepts de solution de la theorie des jeux de facon a permettre la comparaisonavec des choix sociaux observes.Ce texte se penche sur une periode interessante en soi de la politique 6nergetique, soit la politique d'energie nationale du Canadaet ses cons6quences durant l'annee qui suit son introduction. Il se divise en cinq parties. Premierement, nous d6crivonsla structure du jeu qui porte sur la confrontationintergouvernementale au sujet de cette politique d'octobre1980 a septembre 1981.Deuxiemement, les solutions th6oriquespertinentes a ce jeu de negociation sont identifiees. Troisiemement,des valeurs mesurables sont deriv6es de ces concepts. Quatriemement, les valeurs obtenues des solutions de la theorie des jeux sont comparees a la distribution des paiements correspondants a l'entente - de septembre 1981. Finalement, les consequences dee ces resultats et les voies de recherchefutures sont examin6es.

Game-theoreticanalysis of public policy has followed a prescriptive rather than descriptive path, thereby raising questions about its practical relevance. One way to rectify this divergence is to operationalize solution concepts from game theory, in order to permit comparison with observed instances of social choice. The purpose of the present study is to examine an intrinsicallyinteresting phase of energy policy, the CanadianNational Energy Program (NEP) and its year-long aftermath, in those terms. There will be five stages to the investigation.ongame-theoretic First, the setting will be described, referring to the phase of intergovernmental confrontationontin Canada over the NEP from October 1980 to September 1981. Second, relevant solution concepts for this bargaining game will be identified. Measurementsare to be derivedfor these concepts in the third stage. In the fourth phase, the values generated by the game-thetheoreticsolutions will be compared to the pay-off distribution correspondingto the Canada-AlbertaAgreement of September 1981. Fifth, and finally, implications of the findings will be explored, along with possibilities for further research.

I think a categorical disavowal of descriptive <,ver the last three decades, game content is implicit in the entire game-theoreti- theorists appear to have followed Rapo- cal approach.Game theory is definitely norma- port's advice. Yet the separation of descrip- tive in spirit and method. Its goal is a pre- tion from prescription has entailed certain scription of how a rational player should behave drawbacks, especially in the context of in a given game situation when the preferences policy analysis. On the one hand, contem- of this player and of all the other players are gi- porary solution concepts in game theory are ven in utility units (Rapoport,1960: 226-7). presented in increasingly rigorous, formal expositions. On the other, these prescrip-

Canadian Public Policy - Analyse de Politiques, XVI:2:174-190 1990 Printed in Canada/Imprim6 au Canada tions about rational behaviour have be- ber and identity of the players, whether the come so far removed from the practical play results in constant-sum pay-offs, and aspects of social choice that, at least in some co-operativeversus non-co-operativecondi- instances, it is reasonable to question their tions. normative relevance.1 Prescriptive viabil- Most fundamental among the questions ity would seem to entail that an ostensible to answer about the energy game are the solution have either some empirical basis number and identity of the players. James or intuitive plausibility. But these aspects (1989) found compelling evidence that the tend to be more descriptive in orientation crisis phase in energy politics at the outset and therefore have received relatively little of the current decade involved two players, attention from game theorists. By contrast, the Canadian federal government and the other scholars usually have studied nego- Government of the Province of Alberta. tiation through the 'descriptiveaccount' of The normal configuration of interest a given interaction (Zartman,1983:6). Thus groups receded during that period, with it is tenable to argue that game theory as bargaining restricted to governments that policy analysis might benefit from efforts engaged in a struggle over substantial and toward practical application, while under- presumablyescalating economicrents from standing of policy-oriented negotiations energy resources. The game of confronta- might be enhanced by a rigorous approach. tion politics between the central govern- Given these concerns, one way to ment and the principal energy-producing proceed is to operationalize solution con- region, Alberta, lasted from the an- cepts from game theory, in order to permit nouncement of the NEP in October1980 to comparison with observed instances of so- the signing of the Canada-AlbertaAgree- cial choice. The purpose of the present ment in September 1981. Given the poten- study is to examine an intrinsically inter- tially vast revenues from taxation of oil and esting phase of energy policy, referring to natural gas at the start of the 1980s, it is the Canadian National Energy Program not surprising that energy politics crystal- (NEP) and its year-long aftermath, in those lized into an intense competition between terms. There will be five stages to the inves- relatively autonomous levels of govern- tigation. First, the game-theoretic setting ment.3 will be identified, referring to the phase of Some description of the NEP's formula- intergovernmental confrontation in tion and implementation, along with the Canada from October 1980 to September politics it inspired, may be useful in demon- 1981. Second, relevant solution concepts for strating that, although societal actors did the game will be identified. Measurements not disappear from the scene, the usual are to be derived for these concepts in the levels of consultation with interest groups third stage. In the fourth phase, the values did not hold true during the phase of con- generated by the game-theoretic solutions frontation. To begin, the NEP consisted of will be comparedto the pay-offdistribution a set of decisions preparedby a small circle corresponding to the Canada-Alberta of policy-makers. These individuals de- Agreement of September1981. Fifth, and fi- signed its provisions within a broad direc- nally, implicationsof the findings will be ex- tion of policy set forth by Energy Minister plored, along with possibilities for further . Thus public officials re- research. sponsible for energy policy, not societal demands, provided the impetus for the The Game-theoretic Setting NEP. Of course, as Doern and Phidd (1983:476) observed, 'the NEP was much Several components must be identified in more a marriage of interests between min- order to proceed effectively with a game- isters and bureaucrats,spawned by intense theoretic framework of analysis: the num- partisan conflict,' as opposed to a 'bureau-

The Canadian National Energy Program 175 cratic imposition'. Furthermore, professional associations in- For society-centred models, such as plu- fluence policy in other fields, for example, ralism, groups like the energy industry the legal and medical associations with re- would be expected to have input into the gard to justice and health care, respectively policy-making process. The energy pro- (Doern and Phidd, 1983:80-81). While the gram of the Liberal government, however, oil and gas industries, along with took virtually no notice of the demands of utilities and consumers, looked on with energy producing corporations. The NEP great concern, these groups did not partic- emerged almost entirely from within the ipate directly in the phase of inter- government and bureaucracy. This result governmental bargaining over the NEP.4 is not surprising, given the pre-NEP situa- Both before and after the confrontationpe- tion. It will become apparent - based on a riod, however, such interest groups con- later review of Alberta's July 1980 Pro- tributed to the evolution of energy policy posals - that the Liberal government per- through voting, lobbying and other mecha- ceived the need to respond decisively. The nisms. In sum, the two-player designation Proposals put the Liberal government at a is intended for a specific interval, not the great disadvantage in terms of economic long-term process of making energy policy rent shares and the energy industry would in Canada. have been very unlikely to respond posi- Whether or not the game is constant- tively to a revision favouring Ottawa. The sum is also fundamental to its analysis. A governmenttherefore acted under two con- constant-sum game is one of pure conflict; straints: time and boundaries on the con- one adversary's gain is the other's loss tent of its reply, which had to redistribute (Davis, 1983:75). The alternative to that is rent shares. the variable-sum game, which offers some With regardto the year that followedan- prospect of mutual gain through agree- nouncement of the NEP, the evidence ment.5 clearly favours a two-player game. Collec- By consensus, the bargaining initiated tive action by the oil and gas industries, by the NEP over economicrents is regarded consumers and other groups does not ex- as a variable-sumgame. Simeon (1980:182) plain the subsequent process of bargaining. observed that energy revenues had con- Instead, acting alone, Alberta retaliated tributed over $5 billion to the Alberta Heri- against the federal government almost im- tage Trust Fund, while Courchene and mediately, creating a deadlock that lasted Melvin (1980:192) drew attention to Al- nearly a year. With its program of 'pro- berta's 'rapidlyrising energy revenues'. In vince-building' in disarray, the Lougheed later years, Norrie (1984) and Ruitenbeek government eventually approachedits fed- (1985) also noted the expectation of higher eral rival and entered into bilateral nego- economic rents that had existed during the tiations. As indicated previously, these era of the Program; further evidence re- prominent events entailed action by garding increasing revenues from oil and governments, as opposed to logrolling natural gas at the outset of the decade is among interest groups. plentiful. Since the game is deemed to be None of these observations is intended variable-sum,subsequent analysis focusses to dismiss the impact of interest groups on on interdependent choice, as opposed to the formulation and implementation of security levels and maximizing minimal public policy under normal circumstances. pay-offs in a constant-sum game (Brams, Prominent examples would include the 1975:4-5). Canadian Banking Association's role in Of course, there is a sense in which the shaping evolution of the Bank Act and the game could be considered constant-sum: business lobby's ability to weaken or elim- when the oil firms are included in the bar- inate successive Competition Policy bills. gaining, a fixed amount of recoverable oil

176 Patrick James and gas is assumed and regulation occurs hand, will lean toward the co-operativeend at a single designatedpoint in time. But the of the gaming spectrum. The costs as- price of energy is a variable and the amount sociated with unilateral abrogationserve as of economicallyrecoverable oil is a positive a deterrent, especiallywith regardto break- function of price. At any arbitrarilychosen ing prominent agreements. Although moment the world prices of oil and natural societal actors and other governments gas are fixed, but it is still possible to de- within confederationdid not participate in scribe the game as variable-sum, because the Canada-Albertabargaining game over the aggregate level of economic rents can energy, each of the adversaries had to be change from one scenario to the next. aware of a keenly interested audience com- Another aspect of the game structure posed of future negotiating partners over that must be settled is whether play is co- other issues. With this factor in mind, it is operative or non-co-operative. 'The fun- appropriate to consider the phase of fed- damental distinction between co-operative eral-provincial confrontation over energy and non-co-operativegames,' according to revenues in the context of co-operative Friedman (1986:148), 'is that cooperative game theory.6 games allow binding agreements while Appropriate solution concepts for the noncooperative games do not'. This de- game of federal-provincialbargaining can scription is of more practical value when be identified, given one further piece of in- treated as a continuum rather than a di- formation. The rivalry over energy re- chotomy. It is difficult to imagine any venues belongs to the class of fixed threat agreement in political life that is com- bargaining games. The latter are 'two-per- pletely enforceable; examples to the con- son situations in which the players each ob- trary are easy to cite. Supportfrom interest tain fixed utility levels if they fail to make groups may be transferred from one politi- an agreement' (Friedman,1986:151). These cal party to another; coalitions at nominat- games focus on the distribution of pay-offs ing conventions change allegiance despite between two players, as in the case of the solemn statements to the contrary; and al- conflict over resource-basedeconomic rents liances between nation-states may be dis- between Alberta and the Government of carded if one partner sees an opportunity Canada. to benefit from doing so. However, there are constraints upon Solution Concepts such actions and, in a political system such as that of Canada, blatant disregard by One of the principal shortcomings of game governments for negotiated settlements theory has been the lack of a single, com- will be prohibitively expensive. A reputa- pelling solution concept (Brander, tion for abrogatingagreements - especially 1985:62). This ongoingproblem, which can those of a prominent nature, such as the be traced to the relatively abstract nature 1981Canada-Alberta Agreement - could se- of conventional game theory, is as true for riously impede subsequent efforts to co- fixed threat bargaining games as for any operate with other governments. A record other kind. Solution concepts abound but of capricious dealings also would be unset- share an arbitrarycharacter (Young, 1989): tling for the economy, because important Why should one be considered better than interest groups (like labour and business) another?Since the present focus is more ex- do not look favourablyupon such behaviour planatorythan normative, a natural means from either provincial or federal govern- of judgment is whether a given outcome is ments. in line with the result predictedby a partic- Given these constraints, it is reasonable ular solution concept. to expect that intergovernmental bargain- For example, suppose that a set of solu- ing within Canada, such as the case at tion concepts is derived from various theo-

The Canadian National Energy Program 177 U2

0 U1 Figure 1 The Nash and Raiffa-Kalai-Smorodinskysolutions ries of bargaining. Through a series of tests, proposed solution is to settle at the largest at- the respective underlying theories could be tainable payoff point that is proportional to compared with regard to predictive ac- them. curacy; outcomes in specific issue-areas or concerning fixed groups of players might There are five solution concepts to con- tend to support some of the concepts more sider.8 These concepts will be explained in than others. Along those lines, the current two ways. The basic presentation will be di- investigation is intended as a modest begin- agrammatic and non-technical. A mathe- ning in one realm: intergovernmental bar- matical exposition of each solution concept gaining in Canada over economic rents appears in the Appendix. from natural resources. Two of the solution concepts appear in Friedman (1986:160) has summarized diagrammatic form in Figure 1 as points N the nature of the class of solution concepts and u. (From this point onward, solution that is relevant to fixed threat bargaining points will appear in bold print.) These games: points correspond to the Nash and Raiffa- Kalai-Smorodinsky (RKS) solutions, re- The basic intuitive notion is that each player spectively. In the abstract case that will be naturally aspires to the largest payoff available used to bring out the properties of the Nash in the game that is consistent with individual and RKS solutions, Players 1 and 2 exist in rationality. These two individual payoffs are, in a spatial game represented by Figure 1, general, not attainable simultaneously and the with fixed pay-offs in the absence of an

178 Patrick James agreement, and a range of other pay-off Similarto Nash, the RKS solution (u) de- combinations if one is attained.9 pends on the position of the threat point d. Turning to more specific aspects of However, it also is affected by the location Figure 1, the horizontal and vertical axes of point M (M1,M2). More specifically, for represent the utilities derived by Players 1 Player 1, M1plays the role of an 'aspiration and 2, ui and U2,respectively. The set H re- level'; the greater its magnitude, the more fers to all feasible pay-off pairs within this that, a priori, should be be expected from game. Its boundaries are OABO,with O as an eventual outcome. The pay-off M2 ob- the origin and A and B being two other tained at point B is analogous for Player 2. prominent limitations. At point A, Player 1 In other words, a comparisonof ideal states obtains pay-off M1, the highest that is (i.e. M1 versus M2) effectively serves as a possible among all points that are individu- measurement of intensity of expectations ally rational (i.e. those which are at least as regardingthe outcome. Thus the respective good for Player 1 as what could be obtained utilities are rendered comparable for pur- without an agreement), while the pay-off poses of the game, which eventually will be for Player 2 at point A is designated as m2. played for monetary pay-offs. The point B plays the same role for Player Given the constraintimposed by the pro- 2. Thus, at points A and B, the pay-offs for duction possibility frontier, the intersec- Players 1 and 2 are represented by (M1,m2) tion point M = (M1,M2) cannot be achieved. and (ml, M2). The curve AB represents the This is not surprising. The pay-offsM1 and set of efficient outcomes, with a trade-offin M2 are not feasible simultaneously because value for Players 1 and 2. This curve also is each entails a maximal distribution of the referred to as the possibility frontier or marginal pay-offs to just one player. In Pareto set.10It is presented in a mathemati- other words, no efficient allocation of re- cal form in the Appendix. sources could be ideal in a distributional Within the diagram, d = (dl, d2) is the sense for both Players 1 and 2. Thus the threat point. It designates the pay-offs for ideal point, M, is intended for reference Players 1 and 2 in the absence of an agree- only and does not fall within H.12The solu- ment. The point d is inside H, rather than tion u is the point on the possibility fron- along the possibility frontier. In Figure 1, d tier that falls on the line connecting d to M. is located between the origin and the curve There is some value in explaining each composed of efficient outcomes connecting solution concept, beginning with Nash and A and B. The threat point therefore is sub- RKS, in more practical terms. The stand- optimal (as in all cases), because an agree- ard trade-offto consider in a problem of re- ment could produce an outcome preferred venue sharing is distributivejustice versus by both players. efficiency.Since all of the solution points to Most familiar among the five solutions is be considered are on the possibility fron- the Nash bargaining point. The point d de- tier, efficiency can be recast in terms of termines the Nash solution in the following power or advantage;in other words, which manner: The area within H that is above has more impact in deriving a given solu- and to the right of d represents the attain- tion: the balance of positional power within able and individuallyrational points within the game or notions of distributive justice the spatial game. These points are individu- based on other criteria? Various solution ally rational because each is at least as good concepts will tend to balance these con- for both players as what could be obtained cerns somewhat differently. at d, in the absence of an agreement. The With regard to distributive justice and Nash solution is the point that maximizes relative advantage within the game, Davis the product of gains for the players from (1983:122)observes that 'the Nash outcome agreement. The gains, respectively, corre- often appears to be unfair, it tends to make spond to (ul - di) and (u2 - d2). the poor poorer and the rich richer. This is

The Canadian National Energy Program 179 U2

M2/2 M2m2^

0 M1/2 m1 P u1 1 Ml1 Figure 2 The minimal expectations, minimal compromise and middle of the rectangle solutions to be expected, however. A rich player is closer to the ul axis, meaning that the line often in a stronger position than a poor from d to M will intersect the curve AB at one.' For example, if di is substantially a point closer to A, the preferred outcome greater than d2, then ul must be that much for Player 1. With d held constant, the greater relative to U2in order to maximize player with the higher relative expectations the product of gains. The magnitude of a receives a greater revenue share. Thus a product depends upon expansion of each greater magnitude for M1 relative to M2 component - (l - di) and (u2 - d2) - mean- would move the outcome closer to A, while ing that neither relative need nor equality the reverse would produce an outcome in distribution affects the assignment of re- closer to B. The RKS solution focusses on venue shares. each player's advantages and expectations The RKS solution emphasizes relative within the game, rather than relative need power and positional advantage over other or notions of equal sharing. But, in com- criteria for division of revenue. Varying the parative terms, the Nash solution corre- location of point d in Figure 1, with M fixed, sponds even more directly than RKS to the will distribute greater pay-offs to a given balance of power within the game, since player as d approaches that player's axis. aspiration levels are not incorporated. Thus the player with the favouredposition Three other solutions related to that of in the game is rewarded, constituting rec- Nash will also be derived.13These appear ognition of greater power. For example, in in Figure 2. Each requires derivation of a the abstract case displayedby Figure 1, d is reference point, which then can be used to

180 Patrick James designate a specific solution point on the pectations. Its reference point incorporates possibility frontier. As in the case of N, the the worst- and best-case scenarios for each respective solutions maximize the product player under conditions of agreement. In a of gains to the players from bargaining,but more general sense, like m, P is a function the point of reference is not d. of aspirations within the game, as opposed The reference point of minimal expecta- to relative power, because a player's fate tions, m, is based on what each player can under non-agreement is not considered in expect to receive when the adversary ob- dividing the pay-offs. tains the ideal pay-off. Thus, Player 1 gets Third and last among the Nash-oriented mi at B, the ideal outcome for Player 2, solutions is the middle of the rectangle. while the latter obtains m2 at A, the best This refers to the center of the smallest rec- point for Player 1. The solution is the point tangle containing H as a referencepoint for on the possibility frontier that maximizes the solution. With zero as the origin, and A the product of gains for each player ((ul - and B determining the dimensions of the mi) and (u2 - m2), respectively) relative to rectangle, the relevant point is R = (M1/2, m. The resulting point m resembles the M2/2). The solution R is the point on the other two that will be derived because each possibility frontier that maximizes the pro- 'depends on the shape of H, but has no de- duct of the players' gains relative to R. pendence on the threat point d' (Friedman, Middle of the rectangle is the solution 1986:168).14In other words,members of the that most directly measures relative aspira- class of solutions linked to Nash are based tions within the game. Although RKS and on various properties of the set of feasible minimal compromise also depend upon results, as opposedto the nature of the out- each player's pay-off at its ideal outcome, come without an agreement. the middle of the rectangle is influenced Under the regime of minimal expecta- only by the respective best points. As in the tions, each player is in a position to gain cases of minimal compromiseand minimal relative to a 'minimax' outcome. Thus the expectations, gains relative to the reference solution m is not power-basedin the sense point are independent of the balance of of Nash (or even RKS) because the non- power between Players 1 and 2. Of course, agreement point (d) does not influence its like these solutions, relative need is not a division of pay-offs. Instead, a distribution matter of concern for R, either. is derived by comparing levels of minimal This completes the presentation of solu- aspiration under conditions of agreement. tion concepts. In a comparative sense, the Two other Nash-oriented solutions re- five points fall along a continuum with re- main to be identified. The reference point spect to the trade-offbetween power within of minimal compromise is an average of the game and other distributive criteria. what the player expects in the ideal and The Nash solution depends strictly on posi- worst-case scenarios along the curve AB. tional advantage at the threat point, while (For example, Player 1 would be expecting the three Nash-oriented solutions - mini- M1 and mi at each respective location. This mal expectations, minimal compromiseand results in Pi = (M1 + ml)/2.) The values middle of the rectangle - emphasize criteria generated for the reference point, P = (P1, derived from the players' aspirations P2), reflect the initial boundaries for H within the game. Finally, the RKS solution created by A and B. Thus the solution will rests somewhere in the middle, depending depend directly on properties of H. The so- on both ideal and threat points. lution P is the point on the possibility fron- In order to obtain values for the five so- tier that maximizes the product of the lutions in the context of the energy game, players' gains relative to P. at this stage it is necessary to operational- Minimal compromise is a more compre- ize the respective reference points. hensive solution concept than minimal ex-

The Canadian National Energy Program 181 Table 1 Expected economic rent shares and aggregate values from non-frontier oil and gas for 1982* Provincial governments Federal government Oil and gas producers and consumers

Scenario Share of Aggregate Share of Aggregate Share of Aggregate rents rent value rents rent value rents rent value

Alberta's July 1980 proposals 0.37 10.804 0.08 2.336 0.55 16.060 Unrevised NEP, 28 October 1980 0.30 8.670 0.21 6.069 0.49 14.161 Stalemate, with Alberta's retaliation 0.32 8.448 0.22 5.808 0.46 12.144 Canada-Alberta Agreement 0.34 9.996 0.19 5.586 0.47 13.818 *The aggregate rent values are expressed in billions of dollars. SOURCE:Adapted from Helliwell and McRae (1982:17).

Measuring Points of Reference and liability. To begin, the data generated by Deriving Solutions the macroeconomic model have 'face' valid- ity. The scenarios are based on assumptions Several points in Figure 1 require oper- built into the actual policies put forward by ationalization: the origin, d, A and B. Once the governments. Thus the revenues listed values exist for these points, it will be in Table 1 reflect the expectations of the possible to generate the five solutions. players during the game. For example, the Given the nature of the game, the origin four scenarios build in a 2 per cent annual in Figure 1 is identified as the conventional increase in the world oil price, as antici- point (0,0). Pay-offs lower than zero are pated by all parties in 1980-1981 (Helliwell impossible for both players. The utilities and McRae, 1982:14).16 are economic rents for two governments Another question related to validity con- from oil and gas production; these mone- cerns the use of data on revenues projected tary pay-offs obviously reach a minimum of for 1982 (which appear in Table 1), as op- zero for each player when there is no pro- posed to 1986, which Helliwell and McRae duction. also estimated. Given the usual time hori- Table 1 displays data on expected eco- zons associated with elected governments, nomic rents from oil and gas for the rele- it is reasonable to assume that short-term vant levels of government and other considerations carried more weight. Use of recipients in 1982.15 All of the aggregate the data for 1986, the final year of the rent values are expressed in billions of dol- Canada-Alberta Agreement, also would re- lars. The table has been constructed on the quire measurement of discount parame- basis of data from Helliwell and McRae ters. Estimating the immediate value of (1982). Using a macroeconomic model of future revenues would be, at best, a prob- the non-frontier oil and gas industry, they lematic task. estimated the provincial and federal shares Considerations of validity appear to of energy revenues under various condi- favour the 1982-oriented data from Hel- tions. Four of these scenarios, listed in liwell and McRae; reliability points in the Table 1, are directly relevant to the task at same direction. The modelling procedures hand. described in great detail by Helliwell and Before describing the scenarios, it is ap- McRae (1981) do not appear to have pro- propriate to discuss the data from Helliwell voked criticism. Thus the scenarios listed and McRae in the context of validity and re- in Table 1 deserve to be treated as repro-

182 Patrick James ducible evidence about expected economic confederation through the Heritage Fund. rents, pending reasons to the contrary. Thus Mi = 10.804 and m2 = 2.336, based Another aspect of reliability concerns on Table 1. the comparabilityof statistics. The crucial With regard to the unrevised NEP of 28 points within the spatial game, such M and October 1980, it is easy to see a federal d, along with pay-offs for the Agreement, orientation. Helliwell and McRae (1981:15) are generated by the same model. Other outline the components of the Program sources, such as Gorbet (1980) or that are relevant to the macroeconomic Copithorneet al. (1985),do not providedata model: on the complete set of reference points. Taken together, considerations of validity (i) the federally-setwellhead prices for crude oil and reliability are positive for the data pre- and natural gas ...; sented by Helliwell and McRae (1982). (ii) the petroleumcompensation charge levied Turning to the scenarios listed in Table on all usersof oil products; 1, the first is based on proposals made by (iii) the transferof 50%of the revenuesof the Alberta's government in July 1980. The oil exporttax to the producingprovinces; proposals covered conventional oil and gas (iv) the new naturalgas and liquidstax, start- pricing, oil sands development, revenue ing at $.30/mcfand rising to $.75/mcfby 1983; sharing, interprovincial loans and taxa- (v) the 8%petroleum and gas revenue tax; and 18 tion.1 Premier proposed (vi) the phasing out of depletion allowances and to raise conventional oil prices over the the introductionof incentive grants. course of three years to 75 per cent of the Chicagoprice with no increase in provincial These policies, collectively speaking, ag- royalty rates for either conventional oil or grandized the power and influence of Ot- gas. Development of the oil sands would be tawa at the expense of the Government of accelerated, including a $7 billion invest- Alberta. The Federal Government used its ment directly in the sands and provision of powers of taxation to generate revenues for an infrastructure for the workforceby the the central treasury and thereby counter- Province of Alberta. The federal share of act the trend toward a decentralized con- royalties from the oil sands would increase federation. The pay-off for Ottawa under also. With respect to natural gas, the price this scenario therefore is considered to be would be fixed at 85 per cent of the oil price, that of its perceived ideal point, B, so mi = with producers paying costs of transporta- 8.670 and M2 = 6.069. tion of new gas to eastern Canadian Lougheed retaliated against the NEP on markets. New mineral leases would be sub- 30 October 1980, with the principal action ject to federal taxation and Alberta would being a proposed three-stage reduction of provide funding for various interprovincial conventional oil shipments to eastern projects and loans. In return, Lougheed Canada. Over the course of a nine-month asked that Ottawa refrain from imposing a period, the cutbacks eventually would wellhead tax on either oil or natural gas and reach 15 per cent of the prior production also not tax natural gas exports. level of 1.2 million barrels per day (Globe Since these proposalscame directly from and Mail, 1 November 1980:14). Alberta the Government of Alberta, the economic also issued a court challenge to the NEP rents under this scenario are taken to ap- and suspended high-profile megaprojects. proximate those of point A in Figure 1, with In pursuing these responses, Lougheed had Alberta as Player 1. For Alberta, the result- obvious motivations: the courting of inter- ing distribution of revenues would corre- est groups to promote electoral success and spond to the perceived ideal outcome. The protection of constitutional rights under province would retain control over re- Section 109. sources and advance its interests within Combined with the NEP, Alberta's

The Canadian National Energy Program 183 Table 2 Points of reference for the provincial and federal governments in the spatial game Pay-off for player 1, Pay-off for player 2, Solution or Scenario provincial government* federal government*

Segment A Segment B Segment A Segment B Nash (N) 9.194 8.976** 8.810 5.999** RKS(u) 9.900 9.253** 5.971 5.899** Minimal expectation (m) 9.737 13.910 6.627 4.222 Minimal compromise (P) 10.039** 11.850 5.413** 4.964 Middle of rectangle (R) 8.016 11.306 13.546 5.160 Canada-Alberta agreement 9.996 5.586

*Each payoff is expressed in billions of dollars. **These payoffs fall within the acceptable range of values.

Table 3 Squared differences for solutions relative to the Canada-Alberta agreement Squared difference Squared difference Sum of squared Solution for player 1* for player 2* differences Segment A Segment B Segment A Segment B Segment A Segment B Nash 0.643 1.040** 10.394 0.171** 11.037 1.211** RKS 0.009 0.552** 0.148 0.098** 0.157 0.650** Minimal expectations 0.067 15.319 1.084 1.860 1.161 17.179 Minimal compromise 0.002** 3.437 0.030** 0.387 0.032** 3.824 Middle of rectangle 3.897 1.716 63.362 0.181 67.362 1.897

*Each difference is expressed in billions of dollars squared. **These squared differences are based on solution points which fall within the feasible set. riposte initiated a phase of confrontation measurements for the origin, d and M that lasted almost a year. This era therefore (based on A and B), can now be identified. can be treated as one of non-agreement. In In sum, the points A, B and the Agree- the context of the spatial game, the re- ment all are considered to be on the fron- venues generated for and Ot- tier. The first two points are perceived to be tawa by the macroeconomic model would ideal for Alberta and the Government of approximate those in the absence of an Canada, respectively, in distributional agreement, therefore di = 8.448 and d2 = terms, while the Agreement is the scenario 5.808. identified by Helliwell and McRae as the Finally, there is the Canada-Alberta highest in overall revenues among those Agreement to consider. The pay-offs here simulated. The mathematical derivation of do not correspond to those at any pre- the connections between these points (e.g., viously specified point in the spatial game. points A and B and the Agreement) appears These pay-offs, according to Helliwell and in the Appendix. McRae (1982:16) are higher (in aggregate) than those 'in any of the other cases'. Thus Comparing Solutions the Agreement, allowing for economic and political constraints, should be regarded as Table 2 displays the pay-offs derived for a point approximately on the possibility every solution, with the aggregate values frontier. At a later stage, this point will be for the Canada-Alberta Agreement in- compared to the five solutions which, given cluded to facilitate comparison. (The rele-

184 Patrick James vant calculations are performedin the Ap- Conclusion pendix.) Each solution has been calculated twice, relative to (1) the segment of the One of the standard complaints against frontier connecting point A to the Agree- game theory is that it lacks practical rele- ment (Segment A) and (2) the segment of vance. While game theory has a self-pro- the frontier connecting the Agreement to nounced focus on normative issues, that point B (Segment B). The Nash solution, for orientation becomes problematic when example, is (9.194, 8.810) along Segment A viewed in the context of policy analysis. The and (8.976, 5.999) along Segment B. present study has attempted to use game However, all but three of the potential so- theory in a more descriptive and, poten- lution points are inadmissablebecause they tially, socially relevant manner. The phase lie beyond the boundaries set by the con- of confrontation initiated by the NEP has necting segments. For example, to obtain a been modeledas a two-party,variable-sum, maximum for the Nash reference point co-operative game. Statistics on govern- relative to Segment A, it is necessary to mental revenues from energy have been move the players to (9.194, 8.810), a point used to estimate pay-offs for game- that lies beyond the upper boundaryof Seg- theoretic solution concepts, with the latter ment A. The three feasible solution points being compared to the values from the are Nash and RKS relative to Segment B Canada-AlbertaAgreement. Several obser- and minimal compromise relative to Seg- vations can be made about this process of ment A. evaluation. Table 3 compares the solutions to the First, it is interesting that one of the Canada-Alberta Agreement in terms of Nash-oriented solutions, minimal com- overall descriptive accuracy.For each solu- promise, corresponds very closely to the tion, the difference in pay-offs for the two Canada-Alberta Agreement. This solu- players is calculated relative to the Agree- tion's point of reference depends on each ment and then squared. These squared player's expectations based on its ideal and values then are added together, in order to worst cases. In the federal-provincial estimate how similar each solution point is energy game, rational choice therefore to the actual agreement achieved by Al- seemed to focus on 'averaging' ideal and berta and the federal government.19Squar- minimal pay-offs. Perhaps that is true of ing the differences has the advantage of other bargaining games within confedera- emphasizing large discrepancies;a solution tion. If so, that would identify a 'form of concept that makes a relatively small error rationality' (Laver, 1986:33) specific to the in estimating each pay-off is considered Canadianpolitical process. more accurate in an overall sense than one Second, there is a normative point to which is more exact for one player but far consider. Costs of transaction from bar- off target for the other. The differenceswill gaining could be reduced by using minimal be estimated for all of the points, although compromise as a principle. Assuming that it is understoodthat the margin of error for governmentalplayers think in those terms, those outside the boundariesof the frontier they might tend to see the explicit compari- would be difficult to interpret. As it turns son and integration of ideal and minimal out, one of the feasible solution points has expectations as fair, or at least tolerable. the smallest margin of error: The solution More productive intergovernmental bar- generated by minimal compromise, P, is gaining, along with relatively stable out- quite close to the point correspondingto the comes, could result from the use of minimal Agreement. Returning to Table 2, the per- compromise to stimulate negotiations in centage differences for the provincial and good faith. federal governments are 0.43 and 3.10, re- A third point focusses more specifically spectively. on the federal government's outlook on the

The Canadian National Energy Program 185 energy game. Since the Canada-Alberta port under grant 410-87-0403. Ottawa less than the stale- 1 For example, all but a very few articles in the In- Agreement gave ternationalJournal Game are inacces- mate d) in terms of Theory (point strictly monetary sible to those without advanced training in (see Table 1), it could be that Ottawa placed mathematics. Furthermore, a survey of that jour- a positive value on resolving the conflict nal over the last decade revealed only three ar- with Alberta, at least temporarily. This ob- ticles (Saaty, 1979; Straffin and Heaney, 1981; servation is consistent with an Grotte and Brooks, 1983) that linked game theory interpreta- to tion of federal which public policy. priorities emphasizes 2 For a highly readable introduction to game theory, Ottawa's desire to build support for consult Davis (1983); a more general treatment of centralization through constitutional rational choice as a mode of analysis appears in measures. McLean (1987). An introduction to rational choice as to resources is in Fourth, and finally, the present study applied natural available For an excellent an initial effort toward Sproule-Jones (1982). application represents only ap- to US and Canadian energy politics, see Uslaner plication of game theory to Canadian pub- (1989). lic policy. Among many potential avenues 3 Doern and Toner (1985) and James and Michelin for research, it is possible to mention only (1989) provide a wide range of evidence that as model of a few. Further sources of quantitative data favours state autonomy a formulation and of energy policy during the could be consulted, in order to assess the re- implementation period in question, leading to a conclusion in liability of the measurements derived from favour of a two-party, intergovernmental bargain- Helliwell and McRae (1982).20 In addition, ing game. Both the NEP and its subsequent interviews with participants in the bargain- revision reflected competition between govern- as to a over the ing over energy revenues could produce ments, opposed class struggle means of or interest useful information production logrolling among supplementary regard- groups. These latter two scenarios correspond to ing intensity of preferences over the out- Marxism and pluralism, respectively, the usual comes. competition for state autonomy in the explanation Another approach would be to model the of the policy process. confrontation phase in energy politics as an 4 For example, Jenkins (1986:157-8) described the provincial government and multinational cor- iterated (i.e. multiple stage) game, in order porations as allies but also implied that the coali- to confront these and other questions: tion had a clear hierarchy during the phase of What are the roles played by incomplete in- confrontation: 'Alberta provided considerable formation and perceptions of power? Does bargaining leverage to the MNC's opposition to risk propensity affect the strategies the NEP simply because it was a political actor whose views could not be ignored by a federal pursued in rent-seeking? More specifically, government trying desperately to fight western could the Canada-Alberta Agreement have alienation within the confederation.' been achieved without prior institution of 5 For a comparative analysis of strategic choice in a policy like the NEP? constant-sum and variable-sum games, see Davis More generally, there are other games (1983). In the literature of game theory, the and often within confederation to consider. Further respective terms constant- variable-sum are used interchangeably with the designations application of game theory to Canadian zero- and non-zero-sum. politics could reveal patterns that other- 6 It could be argued that a co-operative game would wise might not be discerned. never include a year of stalemate, such as that seen in the case of the Federal-Alberta game over Notes energy revenues. However, describing a game as co-operative implies that binding agreements may occur; it does not require that a deal must be made * I am to Andre John A. grateful Blais, Galbraith, at any given time. Thus the year of deadlock fol- Michael Hudson Christopher Green, Lusztig, lowing Alberta's retaliation against the NEP does Vaillancourt and an Meadwell, Frangois not fall outside the boundaries of a co-operative referee for critical and to anonymous commentary game or rational choice. For a treatment of the Maria Marcheschi and for word Kathryn Ippolito phase of confrontation as an iterated game, con- processing. I also thank the Social Sciences and sult James (1989). Humanities Research Council of Canada for sup-

186 Patrick James 7 A less draconian version of this critique would economists. As Jump (1981:35) has noted, in focus on the lack of a relativelysmall subsetof con- reviewing a different model, simulation results vincing solution concepts. Each memberof such a are 'specificto the modelbeing used, and while the subset would predict well in specific settings. author may be familiar with its inner structure, 8 The following description of solution concepts is the audiencegenerally is not'. Thus the statistics based primarilyupon Friedman (1986:160-2,167- conveyedby Table 1 should be regardedwith cau- 70). tion, despite the advantagesalready noted. 9 The point identifiedas d in Figure 1 sets the boun- 18 The followingdescription of the Albertaproposals daries for individual rationality in this game. It is based on Scarfe (1981:11). designates the pay-off that each player would 19 For example,in the case of the RKSsolution, rela- receive in the absence of an agreement.Individual tive to SegmentA, the pay-offdifference for Alber- rationality requires that neither player accept a ta - compared to the Agreement - is 9.900 - 9.996 pay-offless than that obtainedat d, assumingthat = -0.096. The squareddifference is 0.009. For the monetary pay-offs are all that matter to the federalgovernment, the differenceis 5.971- 5.586 player. = 0.385 and the squaredvalue is 0.148. The sum 10 A pay-off allocation satisfies Pareto optimality if of squares thereforeis 0.009 + 0.148 = 0.157. there does not exist another distributionat which 20 In that regard, the recently published study by all playersare at least as well off and one playeris Helliwell et al. (1989) would be one possibility. better off than before. In Figure 1, each point Among other subjects, it covers regulation of alongAB is Pareto optimalbecause none of the su- crudeoil and natural gas, taxation and the impact perior points can be attained. of alternativepolicies on revenues and rents. 11 The Nash bargaining solution satisfies a set of rigorously specified conditions from Friedman References (1986:155-6),including individualrationality and invarianceunder positive utility transformations. Steven J. Game and 12 The points along the lines AM1and BM2 cannot Brams, (1975) Theory be attained in this game. Thus, aside from the Politics (New York: The Free Press). curve AB, the possibility frontier consists of cur- Brander, James A. (1985) 'Economic Policy For- ves from the origin to A and B, respectively.The mation in a Federal State: A Game Theoretic exact shapes of the latter two curves (OAand OB) Approach.' In Richard Simeon (ed.), Inter- cannot be estimated from availabledata. governmental Relations (Toronto: Univer- 13 Perles and Maschler(1981) have analyseda 2-per- sity of Toronto Press). son, Nash bargaininggame in a dynamiccontext, Copithorne, Lawrence, Alan MacFadyen and a solution that builds in deriving concept poten- Bruce Bell (1985) 'Revenue Sharing and the tial in the feasible set. the changes However, Efficient Valuation of Natural Resources,' is an exercise in statics present study comparative Canadian Public - de Politi- and assumes that H is fixed over the courseof bar- Policy Analyse ques, XI:465-78. gaining. Thomas J. and James P. Melvin 14 Friedman(1986:161-2,167-8) refers to a proofthat Courchene, Revenues: many solutions can be generated by combining (1980) 'Energy Consequences for basic derivations from Nash, such as those con- the Rest of Canada,' Canadian Public Policy sidered here, with d. However, these solutions - Analyse de Politiques, VI:192-204. lack an intuitive basis and are interestingmore for Davis, Morton D. (1983) Game Theory: A Non- their mathematical properties than for practical technical Introduction, rev. ed. (New York: application. Basic Books). 15 The pay-offs for the provincialgovernments are Doern, G. Bruce and Richard W. Phidd (1983) taken to approximatethose of Alberta,which held Canadian Public Policy: Ideals, Structure, the overwhelmingproportion of oil and gas reser- Process (Toronto: Methuen). ves the among provinces. Doern, G. Bruce and Glen Toner (1985) The 16 It is to that morerecent data would easy argue give Politics The and Im- more accurate estimates of revenues that the of Energy: Development the NEP (Toronto: players could have expected to obtain under each plementation of Methuen). scenario.However, theperceived, as opposedto ac- James W. tual, expectations from the game are more Friedman, (1986) Game Theory with relevant to measurement of the ideal and threat Applications to Economics (New York and points. Oxford: Oxford University Press). 17 Another aspect of measurement, which lies Globe and Mail, National Edition. beyond the scope of this analysis, is the internal Gorbet, F.W. (1980) 'Energy Self-Sufficiency: A validity of the macroeconomicmodel as viewed by Realistic and Desirable Goal?' Canadian

The Canadian National Energy Program 187 Public Policy - Analyse de Politiques,VI:472- Analytic Hierarchy Process,' International 80. Journal of Game Theory,8:225-34. Grotte, Jeffrey H. and Peter S. Brooks. (1983) Scarfe, Brian L. (1981)'The Federal Budget and 'Measuring Naval Presence Using Blotto Energy Program, October 28th, 1980: A Games,' International Journal of Game Review,'Canadian Public Policy- Analyse de Theory,12:225-36. Politiques, VII:1-14. Helliwell, John F. and Robert N. McRae (1981) Simeon, Richard (1980) 'Natural Resource 'The National Energy Conflict,' Canadian Revenues and :A Sur- Public Policy - Analyse de Politiques, vey of the Issues,' Canadian Public Policy - VII:15-23. Analyse de Politiques, VI:182-91. -- (1982) 'Resolving the Energy Conflict: Sproule-Jones, Mark (1982) 'Public Choice From the National Energy Program to the Theory and Natural Resources:Methodologi- Energy Agreements,' Canadian Public cal Explication and Critique,' American Policy - Analyse de Politiques, VIII:14-23. Political Science Review, 76:790-804. Helliwell, John F., Mary E. MacGregor,Robert Straffin, Philip D. and James P. Heaney (1981) N. McRaeand Andre Plourde, (1989)Oil and 'Game Theory and the Tennessee Valley Gas in Canada: The Effects of Domestic Authority,' International Journal of Game Policies and World Events (Toronto: Theory, 10:35-43. CanadianTax Foundation). Uslaner, Eric M. (1989) Shale Barrel Politics: James, Patrick (1989) 'Energy Politics in Energy and Legislative Leadership (Stan- Canada,1980-81: Threat Power in a Sequen- ford, CA:Stanford University Press). tial Game,' unpublished manuscript. Young, Oran R. (1989) 'Bargaining, James, Patrick and RobertMichelin (1989) 'The Entrepreneurship, and International Poli- Canadian National Energy Program and Its tics: Escaping the Dead Hand of Nash and Aftermath: Perspectives on an Era of Con- Zeuthen.' Paper presented at the Annual frontation,' American Review of Canadian Meeting of the InternationalStudies Associa- Studies, 19:59-81. tion. Jenkins, Barbara (1986) 'Reassessing the "Ob- Zartman,I. William (ed.) (1983) The 50%Solu- solescing Bargain":A Study of Canada'sNa- tion (New Haven: Yale University Press). tional Energy Program,' International Organization,40:139-65. Appendix Jump, Gregory V. (1981) 'On Interpreting Simulations with a Macroeconomic Model,' With respect to estimating the possibility fron- Canadian Public - de Politi- Policy Analyse tier, Figure 1 shows a curve connecting A to B VII:35-38. ques, which is concave to the origin. In other words, a Laver, Michael (1986) Social Choiceand Public continuous trade-off is assumed for ul and u2. (Oxford and New York: Basil Black- Policy However, lacking further data on the precise well). shape of the curve, a straight line will be used Iain Public Choice:An Introduc- McLean, (1987) as an approximation.Since the ultimate concern tion and New York:Basil Blackwell). (Oxford is with proximity of points along the line seg- Kenneth Canadian Norrie, (1984) 'Energy, ment AB to each other, this approximationdoes Federalismand the 14:79-91. West,' Publius, not create any practical difficulties. Equation 1 M.A.and M. Maschler 'The Perles, (1981) Super- expresses u2 as a linear function of ul and two Additive Solution for the Nash Bargaining constants, intended to represent the line seg- Game,' International Journal of Game ment AB: Theory,10:163-93. (1) u2 = klul + k2 Rapoport, Anatol (1960) Fights, Games, and where Debates (Ann Arbor: of University Michigan kl = slope of line from A to B. Press). k2 = intercept of line along u2 axis. Jack 'Economics of In-Situ Ruitenbeek, (1985) Substitution of A(M1, m2) and B(mi, M2) in Oilsands Production: Some for Implications Equation 1 yields the following expression: Public Canadian Public - Ana- Policy,' Policy (1') U2 = (M2 - m2)ul + M2 - (M2 - m2)ml de lyse Politiques, XI:407-14. (mi - M1) Thomas L. 'The U.S.-OPECEner- (mi -M1) Saaty, (1979) Having derived an expression for the possi- The gy Conflict: Payoff Matrix by the bility frontier, each of the five solution points

188 Patrick James can be expressedin mathematicalterms. For the Agreement,with the latter also being connected Nash solution, the functionfrepresents the pro- to point B. Equations 1* and 1**represent these duct of the utility gains for Players 1 and 2: respective line segments: (2)f = (ul- di) (u2- d2) (1*) U2 = -4.02ul + 45.77 The point at whichfreaches its maximumcorre- (1**) u2 = -0.36ul + 9.23 sponds to the Nash solution, N. (After substitu- Nash's bargainingsolution maximizes Equa- tion for either ul or u2, the second derivative of tion 2, subject to the constraints imposed by the function f has a negative value. It therefore membership in H. Substitution of values for d is certain that the point identified as N repre- and u2 in Equation2 yields the followingexpres- sents the maximum of the function f(ul, u2). sion: This also is true of the other functions:g, k and (2')f = (ui - 8.448)((-4.02ui + 45.77)-5.808) q.) The substitution for u2 is taken from Equation With regard to the RKS solution, the line 1*.The maximumoff also can be calculatedrela- from d to M is conveyed by Equation 3: tive to the other line segment, from the point of (3) U2 = aul + b Agreement to point B. Each result will be re- where ported for every solution, although only the cal- a = slope of line from d to M. culations based on Equation 1* will be shown. b = intercept along u2 axis. To continue, the maximum of f is derived by The point u must satisfy both Equations 3 and taking its first derivative and setting that ex- 1'; the former connects d to M while the latter pression to zero. The value obtained for ul is guarantees Pareto optimality. Equation 3 9.194. Substitution for ul in Equation 1* yields means that the RKS solution links the expecta- N = (9.194, 8.810) as the Nash solution. Based tions of the players to both the non-co-operative on Equation1**, the maximumis (8.976, 5.999). and ideal outcomes. The first of these results is out of the range set For the point of minimal expectations,the so- by the line segments, while the second is accept- lution m corresponds to the maximum of the able. As will become apparent, most of the solu- function g: tion points fall beyondthe boundariesset by the (4) g = (ul - ml)(u2 - m2) connected line segments. The reference point for minimal compromise To derive the RKS point (u), the first step is is generated by the following equations: to identify the straight line connecting d = (5) P = Mi + ml (8.448, 5.808) and M = (10.804, 6.069). Substi- 2 tution of the M and d values in Equation3 yields (6) P2 = M2 + m2 the following result: 2 (3') u2 = O.lll + 4.872 where The line given by Equation3' intersects with the P1 = pay-off to Player 1. possibility frontier to produce u. Equation 1* P2 = pay-off to Player 2. then can be used to substitute for u2 in Equa- For minimal compromise,the solution P maxi- tion 3'. mizes the function k: (3")-4.02ui + 45.77 = 0.111lll + 4.872 (7)k = (ul- Pl) (u2- P2) Thus ul = 9.900; substitution in Equation 3' es- Finally, the solution point R for the middle tablishes u2 = 5.971. The RKS solution turns of the rectangle is the point on the possibility out to be u = (9.900, 5.971). Based on Equation frontier that maximizes the function q: 1**, the solution is (9.253, 5.899). Only the lat- (8) q = (u - R1) (u2 - R2) ter falls within the acceptable range. where With respect to the point of minimal expec- R1 = Mi/2 tations, the solution is derivedby combiningAl- R2 = M2/2 berta's pay-off under the unrevised NEP with Using the data from Table 1, it is possible to the federal pay-off derived from Alberta's July estimate the possibilityfrontier, although Equa- proposals and maximizing the product of gains tion 1' must be modifiedin order to achieve that relative to this point. The reference point is m goal. Alberta's July Proposals (point A), the = (8.670, 2.336); substitution in Equation 4 Canada/AlbertaAgreement, and the Unrevised yields the following expression: NEP (point B) all occupy positions on the fron- (4') g = (ui - 8.670)(u2 - 2.336) tier. Thus there are two line segments to be esti- Substitution for u2 in Equation 4', using Equa- mated. One will connect point A to the tion 1*, generates the following expression:

The Canadian National Energy Program 189 (4") g = (ul - 8.670)((-4.02ul + 45.77) - 2.336) the solution is (11.850,4.964). The latter of the This equation reaches its maximum when ul = two solution points falls outside of the feasible 9.737. Substitution in Equation 1* yields m = range. (9.737, 6.627). Based on Equation 1**, the solu- As for the last solution, the middle of the rec- tion is (13.910,4.222). Each solution falls outside tangle, that is based on adjusted values for Mi of the feasible range. and M2. The reference point is R = (5.402, Substitution of values for M and m in Equa- 3.035). Substitution in Equation 8 yields tions 5 and 6 yields the reference point for min- (8') q = (ui - 5.402)(u2 - 3.035) imal compromise: Substituting for U2gives (5') P1 = 10.804 + 8.670 (8") q = (ul - 5.402)((-4.02ui + 45.77)-3.035) 2 The maximumofq occurswhen ul = 8.017. Sub- (6') P2 = 6.069 + 2.336 stitution in Equation 1* gives R = (8.016, 2 13.546) as the solution. Based on Equation 1**, The result is P = (9.737, 4.203). Substitution in the solution is (11.306, 5.160). Each solution is Equation 7 yields the following expression: out of the feasible set. (7') k = (ul - 9.737)(u2 - 4.203) Having performedall of the relevant calcula- Once again, substitution for U2is appropriate: tions, only three of the solution points fall (7") k = (ui - 9.737)((-4.02ul + 45.77)-4.203) within an acceptablerange: Nash and RKS,rela- The maximum of k occurs when ul = 10.039. tive to the line segment connecting point B to Substitution in Equation 1* yields P = (10.039, the Agreement, and minimal compromise,rela- 5.413) as the solution. Based on Equation 1**, tive to the segment linking the Agreement to A.

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190 Patrick James