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    IntroductionHow does the structure of the economyaffect the possibility for societal stability?Rapid economic growth of nearly any sortis routinely prescribed to prevent violentconflict. Collier (Collier 2007a, 2009) hasfamously argued that, for countries emerg-

    ing from conflict with higher chances forconflict relapse, almost any kind of (fast)growth is good growth, since a growing pie2implies that politics will not be a zero-sumgame. This intuition is clearly undergirded bynon-cooperative game theory3 and is gener-ally born out empirically (Collier et al. 2003;Collier & Hoeffler 2000; Collier, Hoeffler, &

    Rohner 2006; Humphreys 2003). Moreo-ver, it has resulted in some creative policyideas, such as Colliers (2007b) suggestionsto minimize bottlenecks that are endemicto post-conflict countries, such as a witheredconstruction sector and a government inca-pable of investing large amounts of money

    quickly in public works. But non-cooperativegame theory is often geared to predictingequilibriums, whether peaceful or not; it isnot designed to predict chaos, when equilib-riums do not exist.

    Chronic instabilitythe absence of eco-nomic and political equilibriumsis of grow-ing interest to policymakers. An increas-ing number of areas around the world arecharacterized by weak states and long-termpolitical volatility. Examples include Somalia,Haiti, Afghanistan, and Burundi. Moreover,the Arab Spring uprisings ushered in a wholenew cohort of challenges for countries whose

    McDougal, T 2013 Stability and the Economy: Cooperative GameTheoretic Implications for Economic Policy in a Dual-Sector Economy.Stability: International Journal of Security & Development, 2(2): 41,pp. 1-19, DOI: http://dx.doi.org/10.5334/sta.ca

    RESEARCH ARTICLE

    Stability and the Economy: CooperativeGame Theoretic Implications for EconomicPolicy in a Dual-Sector Economy

    Topher L. McDougal*

    stability

    * Kroc School of Peace Studies, University of San

    Diego, USA, and the Centre on Conict, Develop-ment & Peacebuilding, Graduate Institute ofInternational & Development Studies, Switzerland,[email protected]

    How does the structure of the economy aect the possibility for societal stability? Thispaper1 employs a cooperative game theory lens to explore possibilities for cooperationand chaos under various growth scenarios and assumptions of distributional equality ina hypothetical 2-sector economy (industrialists and agriculturalists). It suggests thatmaintaining distributional equality amongst agriculturalists is only undesirable under theassumption that the manufacturing sector exhibits positive and decreasing returns toscale; if increasing or negative manufacturing returns are the case, agricultural equal-ity becomes an important policy goal in maintaining stability. In the particular case of ashrinking economy, peace can be preserved given (a) fairly equitable land distribution, and(b) a healthy industrial sector serving agriculture. In terms of aid policy, I suggest that,under decreasing industrial returns, more resources available to an economy can promotecooperative frameworks, but that such boosts will entail a switch to economies structured

    around the industrial sector. I conclude with a suggestion for testing the model.

    http://dx.doi.org/10.5334/sta.camailto:[email protected]:[email protected]://dx.doi.org/10.5334/sta.ca
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    political trajectories experts are struggling topredicteven as they struggle to come upwith convincing explanations for the causesand varying intensities of their revolutionsin the first place (Dupont & Passy 2011; Hol-

    lander & Byun 2012; Momani 2012). Despitea United States foreign policy geared towardthe promotion of stability in the MiddleEast and North Africa, the fall of autocraticregimes revealed not just weak civil socie-ties (Dupont & Passy 2011), but also stabilitythat had been dependent upon external coer-cion. Some of these economies crumbled intotheir constituent pieces. Libya, for instance,might be described as having dissolved into

    a collection of city-states with variously con-tested and overlapping claims on hinterlandsand few economic reasons for national col-laboration (Arvalo de Len 2011). Followingthe cue of Johan Galtung (1969), we mightterm the state of affairs that existed previ-ously in Arab Spring countries to be negativestability, or imposed stability.

    By contrast, this paper seeks to build aneconomic rationale for a positive stability

    one predicated upon economic incentives toform durable coalitions. It seeks to employ acooperative game theory lens to explore pos-sibilities for cooperation and chaos, stabilityand instability, under various growth sce-narios in a hypothetical 2-sector economy.It is important to note that positive stabil-ityakin to the idea of self-reinforcing con-tracts (Weinstein 2005)does not imply theabsence of conflict. Nor does it imply peacein the sense that all parties voluntarily par-

    ticipate in cooperative arrangements thatmaximize their individual payouts. Rather,it merely implies that whatever patterns ofallegiances emerge are stable insofar as noparties have incentives to defect from exist-ing alliances to form new ones. Indeed,stability thus defined may imply a form ofconflict that is simply protracted and intrac-table, whereby one or more parties are per-petually oppressed. Conversely, the absence

    of such stability does not imply the presenceof conflict. Rather, instability in this sense

    implies an economic incentive structurethat lacks equilibrium, where any given setof cooperative arrangements is underminedby another. While economic instability is notsynonymous with conflict, the constantly

    shifting allegiances that it implies may plau-sibly stress institutions tasked with enforc-ing contracts and erode trust, possibly mak-ing recurrent bouts of violent conflict morelikely in the absence of a strong, exogenouscoercive power.

    This paper is intended to provide a theoret-ical scaffold for efforts to answer questionssuch as: What redistributive or aid policiespromote stability? Can these tools promote

    stability when the economy is shrinking?Are the lessons different for industrial versusagricultural countries? The paper is organ-ized into three remaining sections. In SectionII, a brief background is laid out. In Section III,a model is presented in the tradition of coop-erative game theory. Section IV discusses themodels implications for wealth distribution,firstly between industry and agriculture, andsecondly among agriculturalists. Section IV

    explores the models implications for devel-opment aid policy. Section V concludes witha summary of results, some caveats, and asuggestion for testing the model empirically.

    Competitive & Cooperative TheoriesMost formal models of conflict adopt someversion of non-cooperative game theory astheir basis. This is intuitively understand-able, though it means that cooperative gametheoryuseful in modeling decisions of

    rational actors in choosing whether or not toform coalitions and, if so, of what sizeoftengets overlooked.

    The simplest non-cooperative game theorymodel has just two players, each of whommay choose either to cooperate or not.Depending on the payoffs for each combina-tion of payouts, the game may be character-ized as one of prisoners dilemma, deadlock,chicken, or win-win.4 IfCrepresents the pay-

    out for mutual cooperation, Bthat for back-stabbing, Sthat for getting suckered, and N

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    that for mutual non-cooperation, then thegames can be defined5:

    ( )prisoners di a ,lemmC N SB > > >

    ( )dea lo k ,d cB N C S > > >

    ( )chicken ,B C S N > > >

    with any combination beginning with Crep-resenting a win-win.

    Non-cooperative game theory provides afundamental justification for developmenteconomists emphasis on economic growthas a conflict-prevention measure: when theeconomy is growing quickly, participantsfind themselves in a positive-sum game, inwhich competition is undesirable and coop-eration is rewarded (Collier 2007a, 2009). Inother words, the payout structure has beenaltered so that C> (B, S, N).

    Cooperative game theory provides analternative lens. In it, emphasis is placed onthe core, a set of agents who form a coa-lition such that no defectors or joiners willmake all players better offsimilar to theNash equilibrium requirement that no prof-

    itable deviation exists. However, as Lidow(2008) describes, there are important differ-ences, two of which are central here. First,the Nash equilibrium can be Pareto subop-timal, as illustrated by the game examplesabove, whereas the core consists of onlyPareto-optimal outcomes. Second, the Nashequilibrium only accounts for the possibil-ity of single agents defecting, while the coreallows for the possibility of group defections

    of any size and combination. The latter char-acteristic allows us to ask under what condi-tions we may expect cooperative frameworksto persist.

    A non-empty core is one that is stable.It exists only when the game is balanced(Osborne & Rubinstein 1994)that is, whenthere is a set of coalitions T= {S} with non-negative weights

    sfor each T so that for

    each i

    { }.s T

    Ss

    i

    Moreover, for the core to be non-empty, theabove sum of balanced payouts for all coali-tions must be less than or equal to the all-inclusive group ofNindividuals:

    ( ) ( ).ss T v S v N If that condition is not met, there is the

    possibility (though, it is important to note,not a certainty) of constant unrest unlessenforcement mechanisms can be broughtto bear. Aivazian and Callen (1981) pointout the major implication: when three ormore agents interact in the presence of twoor more externalities, the Coase Theorem

    (1960) may fail and no bargain can be struck.This suggests that in a complex environ-ment, even zero transactions costs are nota sufficient criterion to guarantee stability.Note, however, that stability does not meanthat everyone is included in the society-widecoalition; indeed, exclusion is one stable out-come, so long as the excluded group is eitherhappy with its situation or unable to changeit by offering an attractive alternative coali-

    tion to one or more of the standing coalition.Stability, in other words, might be achievedby marginalizing one or more groups in soci-ety, essentially akin to forming minimumwinning coalitions in non-cooperative gametheory (see, e.g., Hardin 1976; Riker 1962;Riker & Ordeshook 1973). This observationreinforces the idea that stability as definedin a cooperative game theory model impliesneither a positive peace (the presence ofconditions that eliminate the causes of vio-

    lence) nor a negative peace (the absence ofdirect violence) (Galtung 1969). Instead, sta-bility refers here to the formation of coop-erative coalitions.

    An example may help to illustrate thesepoints. Lets say that a particular economyconsists only of three parties: two farmersand one industrialist. One farmer owns a lotof land, so we will call him the landowner.Working alone, the farmer and the indus-

    trialist each earn US$500, while the land-owner earns US$1,000. Moreover, each party

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    can form a coalition with another to reapeconomies of scalein other words, ben-efits that would not accrue to any party act-ing independently. The farmer may providecheap labor to the industrialists, for a total

    of US$1,400 (in which case, the landownerwould still earn US$1,000). Alternatively, thefarmer may provide cheap labor to the land-owner, for a total of US$1,900 (leaving theindustrialist to earn his usual US$500). Thenagain, the industrialist could team up withthe landowner to produce US$1,900 (leav-ing the farmer to earn his usual US$500).Finally, an all-inclusive coalition would pro-duce US$2,500.

    Note first that the all-inclusive coalitionrepresents the optimal solution. That is,economy-wide cooperation produces morerevenue than any other possible configura-tion of coalitions. And yet, it is unstable: saythe landowner is paying just over US$500 inwages to each of his partners. In that case,the farmer and the industrialist will chooseto defect, earning up to US$700 apiece. Butsubsequently, the landowner (earning just

    US$1,000 now) will offer a coalition to one ofthem, peeling them off to earn, say US$800,and boosting his own revenues to US$1,100.It turns out that there may be no stableequilibrium when the payout of economy-wide cooperation is low enough, even if it isthe optimal solution for that society. In theabsence of external coercion, the coalitionswill perpetually disintegrate, reform, and dis-integrate again.

    The ModelWe now formalize these ideas using a 2-sectoreconomy in which there is one industrialist,M, and two farmers, F

    1and F

    2. The choice to

    model a 2-sector economy is not only conveni-ent for this models structure because returnsto scale in each sector provide the necessarytwo externalities mentioned above. It is alsoimportant insofar as the switch from an agri-cultural to an industrial economy has figured

    in the development economics literature asthe single most important historical process

    in generating high-paying jobs on a society-wide scale. This can be seen in the work ofLewis (1954), in the analyses of DependencyTheorists and Import Substitution Indus-trialization proponents (Arndt 1987; Bacha

    1978; Frank 1978; Prebisch 1950, 1959), inExport-Oriented Industrialization, and in thethinking of heterodox economists (Amsden2001; Chang 2002).

    Individually, the industrialist can producemanufactured goods based on raw materi-als found in the land, while the farmers canfarm their land. Raw materials are evenly dis-tributed across all lands. If one or both farm-ers choose, they may form a coalition with

    the industrialist such that their lands rawmaterials feed the industrialists processes.Alternatively, the two farmers may form acoalition and farm their lands collectively.The production functions of each sector aresuch that manufacturing has a productiv-ity coefficient, C, and farming, L. Returnsto scale vary by sector, with representingmanufacturing and farming. Moreover,the farmers land, R, is split between the

    farmers such that F1s allotment is pR andF2s is (1 p) R, wherep [0,1]. The indus-

    trialist has his own additional allocation ofland at his disposal, aR.

    We are now ready to put the piecestogether. The values of the singleton coali-tions are then:

    { } ( )1V F L pR

    =

    (1a)

    { } ( )( )2 1V F L p R

    =

    (1b)

    { } ( )V M C aR

    =

    (1c)

    The values of the three 2-party coalitions are:

    { } ( ) ( )( )1,V M F C aR pR C R a p

    = + = +

    (2a)

    { } ( )( )

    ( )( )

    2, 1

    1

    V M F C aR p R

    C R a p

    = +

    +=

    (2b)

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    { } ( )1 2,V F F L R

    =

    (2c)

    Note that we have assumed that a farmer-industrialist coalition will operate with thetechnological coefficient and return to scaleof the industrial sector. This implies, wronglyin some hypothetical cases, that C(R(a + 1p) ) > L (R(a+ 1 p) ). The assumption isherein justified solely on the grounds that itsimplifies the analysis.

    The all-inclusive coalition must be gearedeither toward farming or toward manufactur-ing, taking on the higher of the two values:

    { }( )

    ( )( )( )

    1 2

    1, , max

    1

    C R aV F F M

    L R a

    +

    = +

    (3)

    Recalling the requirement for a non-emptycore, and if we denote payouts to the twofarmers and the industrialist under the grantcoalition asf

    1,f

    2, and mrespectively, then we

    may state that such payouts must meet orexceed the payouts for singleton coalitions,such that

    { }1 1 ,f V F

    (4)

    { }2 2 , andf V F

    (5)

    { } .m V M

    (6)

    Moreover, the payout for any two actors underthe grand coalition must meet or exceed theirpayout as a couplet coalition, such that

    { }1 1 .f V F

    (7)

    We can now say that the possibility for insta-bility will exist if

    { } { } { }(

    ( ) { }

    { } { }

    )

    1 2 1 2

    1

    2 1 2

    1, ,

    3

    ,

    , , .

    V F F M V F V F

    C aR V F M

    V F M V F F

    < + +

    + +

    +

    (8)

    The condition for an empty core is then:

    ( )( ) ( )( )

    ( )( ) ( )( )( ) ( )( )

    11

    3

    1 ,

    , andgiven 1 1

    C R a C R a p

    C R a p L R

    C R a L R a

    + < + +

    + +

    + > +

    (9a)

    ( )( ) ( )( )

    ( )( ) ( )

    ( )( ) ( )( )

    11

    3

    1 ,

    given .1 1

    L R a C R a p

    C R a p L R

    L R a C R a

    + < + +

    + +

    + > +

    (9b)

    Graphically, the condition is representedbelow by three functions: (a) the manufac-turing payout (blue), (b) the agricultural pay-out (green), and (c) the empty core bench-mark (red, given by the right hand side ofEquations (9a) and (9b). The empty core willobtain whenever the red line exceeds both

    the blue and the green.

    ImplicationsThis section is broken into four parts, inwhich the models predictions for instabilityare analyzed given: (1) rising technologicalefficiency in the industrial sector; (2) risinglevels of industrial asset ownership; (3) avarying distribution of assets between farm-ers; and, (4) increasing societal resources.The latter might be interpreted, for instance,

    as raising the amount of international aid acountry receives. Each of these dynamics willbe examined under three assumptions: (A)increasing returns to scale for industry, andpositive decreasing returns to agriculture(i.e., > 1 > )6; (B) decreasing returns toboth industry and agriculture (the standardmicroeconomic assumption), and (C) nega-tive returns to scale for both industry andagriculture7. For the sake of comparability, it

    is assumed in all cases that > (except inFigure 3C).

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    Rising Industrial Efciency

    In the case of positive mixed returns to scale(increasing for industry, decreasing for agri-culture), rising industrial efficiency is pre-dicted to produce a switch from an economy

    dominated by agriculturalists to one domi-nated by industrialists. Moreover, there is a

    brief period in the transition during whichtime no stable equilibrium exists, and thepossibility for societal chaos looms (see Fig-ure 1). In the more typical case of decreasingreturns to scale in both sectors, that period

    of possible instability is more protracted,stretching out longer (see Figure 2). Finally,

    Figure 1: Stable and unstable economies as a function of rising industrial efficiency undermixed (increasing for industry, decreasing for agriculture) returns to scale. L = 1, R= 2,a= 0.5,p= 0.5, = 1.1, = 0.2.

    Figure 2: Stable and unstable economies as a function of rising industrial efficiency underdecreasing returns to scale. L = 1, R= 2, a= 0.5,p= 0.5, = 0.9, = 0.1.

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    in the case of negative returns to scale inboth sectors, the period is infinite, with theindustrial economy never coming to the res-cue, and stability only assured at low levelsof industrial technology in an agricultural

    society (see Figure 3).As these hypothetical histories are highly

    stylized, it is foolish to attempt to map realhistorical episodes, with all of their atten-dant complexities, onto them. But the ideathat an increase in productive efficiencywould lead to instability, even in countrieswith strong national governments, doesfind some historical corroboration. The pro-totypical increase in production efficiency

    occurred during the English Industrial Revo-lution, generally dated from around 1760 toaround 1832. This period coincided almostperfectly with the peak of the enclosuremovement, which precipitated dramaticdeclines in peasant livelihoods and the con-sequent urbanization that fed industriallabor pools (see, e.g., Polanyi 2001 [1945]).Prior to the beginning of the Industrial Revo-lution, English Prime Ministers since at least1721, and going back even to 1715 when

    the post of Lord High Treasurer was perma-nently created, came exclusively from the

    Whig party, broadly associated with constitu-tional monarchy, classical liberalism, trade,and industry. The enclosure movement andInclosure Acts, however, saw a slow rea-lignment of economic interests, such that

    the landed gentry and increasingly power-ful bourgeoisie were induced to cooperate,simultaneously boosting the productivityof arable land and manning factories. Thepolitics of England gave way to a period ofuncertainty, dominated by a factionalizingTory party and characterized increasingly bydiscontent of the agriculturalist classes. Thistrend manifested itself both in the Toriesreluctant support under the 2nd Earl of Liv-

    erpools Prime Ministry for the Corn Laws of1815, as well as in the Luddite uprising andspates of machine breaking. The statesharsh crackdown on the latter came to domi-nate public opinion of the Tory party, whichwas dissolved in 1834 (Morgan 2010, Ch. 7,8).This historical period is fraught with warsand other historical complications, makingany direct causal link between increasedproductive capacity and political instabilityimpossible to establish. Moreover, previous

    periods in English history are not immunefrom turmoil, either. However, the proposi-

    Figure 3: Stable and unstable economies as a function of rising industrial efficiency undernegative returns to scale. L = 1, R= 5, a= 0.5,p= 0.5, = 0.75, = 0.05.

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    tion that industrial productivity gains arealways stabilizing does not seem to find sup-port in this particular episode.

    Growing Industrial Asset Ownership

    Let us now turn our attention now to thetotal assets owned by the industrialist. Underpositive, mixed returns to scale (increasing forindustry, decreasing for agriculturesee Fig-ure 4), society transitions smoothly from anagricultural to an industrial economic basewithout any intervening period of insta-bility. In the case of universally decreasingreturns, however, lower levels of industrialasset ownership are the only stable option

    (see Figure 5). Interestingly, this holds trueboth in the case in which the agriculturalsector is more efficient than industry (inwhich an agricultural economy is favored),and in the reverse case, when an industrialeconomy is preferred. The same can be saidof a shrinking economy, though in that case,agriculture must, of necessity, be the moreefficient of the two sectors, while industri-alists benefit from restricted ownership (see

    Figure 6). If either one or the other of thosetwo requirements goes unmet, there is nostable societal coalition.

    Varying Asset Distribution between

    Farmers

    The relationship between inequality and eco-nomic growth has been the subject of intensescrutiny in economic and development lit-

    erature since the classic article by Kuznets(1955). That piece famously suggested thatincome inequality could be expected to risein the early stages of industrial development,declining again as the economy matured.More recently, many scholars have focusedon the causal reverse of that relationshipassessing the effect of inequality, and partic-ularly land and asset inequality, on economicgrowth. Fort and Ruben (2006) used panel

    data with land Gini coefficients to show thatland inequality negatively impacts growth,both directly and, interestingly, by degradingthe positive effects of educational programs.

    Another body of literature has focusedon the link between inequality and conflict.Cramer (2005) summarizes the bewilderingarray of arguments for and against such a link,including proponents of both linear (Mul-ler, Seligson, & Fu 1989; Nafziger & Auvinen2002) and nonlinear relationships. In termsof nonlinear theories, it is pertinent to ourdiscussion that there are proponents for both

    Figure 4: Stable and unstable economies as a function of growing industrial assets undermixed (increasing for industry, decreasing for agriculture) returns to scale. C= 1, L = 2,R= 3,p= 0.5, = 1.25, = 0.75.

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    U-shaped and inverted-U-shaped relationshipsbetween the two phenomena. Cramer placesHirschman (1981) in the U-shaped camp, ashe describes a tolerance for inequality: wheninequality rises, the majority of people cease

    to feel solidarity with the economic elite, andmay attempt to usurp their wealth by violentmeans; when it drops, many cease to believe

    that socioeconomic mobility is a possibility,and unrest grows. Cramer places in the sec-ond camp those who believe that radical ine-quality so disempowers the poorest that theyare prevented from agitating, but that perfect

    equality removes any incentive for predatoryviolence (e.g., Nagel 1974). In the middle,then, a region for potential unrest exists.

    Figure 5: Stable and unstable economies as a function of growing industrial assets underdecreasing, and returns to scale. C= 1.5, L = 1, R= 2,p= 0.5, = 0.6, = 0.3.

    Figure 6: Stable and unstable economies as a function of growing industrial assets undernegative returns to scale. C= 0.5, L = 1, R= 5,p= 0.5, = 0.75, = .05.

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    None of these studies has sought toplace land or asset inequality in conversa-tion with economic growth to predict con-flict or instability. In this section, we show

    that inequality can be associated with bothincreased anddecreased likelihoods of insta-bility, depending upon the returns to scaleexhibited by our two economic sectors. Tothat end, we now turn to the distributionof assets between the two farmers,p, wherep = 0.5 signifies perfect equality and p = 0andp= 1 signify perfect inequality.

    Under mixed returns to scale (increas-ing for industry, decreasing for agriculture),

    the benchmark level for instability (i.e., theempty core) is a convex function of the distri-bution of agricultural assets (see Figure 7). Itmay intersect the payout functions for stableindustrial or agricultural coalitions. In fact,the convexity of the function is increasedwith greater returns to industry. This seemsto imply that, when industryor cities, if wewish to interpret the sector as an essentiallyurban oneis experiencing rapid economicgrowth, the importance of maintaining rela-tive distributional equality in rural areas isheightened. (If one unrealistically assumesthat both sectors exhibit increasing returns,

    there is no possibility for instability; a univer-sally accelerating economy appears, in thismodel, to be an inherently stable one.)

    By contrast, in the scenario of decreasing

    returns to scale in both sectors, the bench-mark curve for an empty core becomes con-vex (see Figure 8). Accordingly, the likeli-hood for societal instability becomes greatestwhen rural inequality is lowest. The intuitionbehind this is simply that, in the absence of anall-inclusive economy yielding high enoughrewards to guarantee self-enforcement of con-tracts among its participants, neither farmeris able to offer the other farmer or the indus-

    trialist a deal that effectively marginalizes theexcluded party.As predicted in Section III, the curvature

    of the empty core benchmark with respectto rural land distribution changes againwhen the returns to scale dip into negativeterritory: it becomes convex (see Figure9). This finding suggests that, in a shrink-ing economy, maintaining rural land equal-ity is crucial. This conclusion accords withAndr and Platteaus (1998) assessment ofthe salience land inequality in the contextof stagnant agricultural productivity and agrowing population.

    Figure 7: Stable and unstable economies as a function of farmer inequality under mixed(increasing for industry, decreasing for agriculture) returns to scale. Perfect equality isdenoted byp= 0.5. C= 1, L = 2.5, R= 2, a= 0.5, = 2, = 0.5.

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    How can we make sense of the importanceof rural equality in rapidly industrializingnations? One possibility is to consider theimport-substitution industrialization (ISI)policies adopted in many Asian and LatinAmerican countries during the 1960s and1970s. Davis (2004) argues that rural land

    equality in the former enabled the farmingclasses to cohere as a political force, therebypressuring the government to hold industrialfirms accountable to production standardsand paving the way for export-led industri-alization and enhanced political stability inthe 1980s and 1990s. In Latin America, by

    Figure 8: Stable and unstable economies as a function of farmer inequality under decreasingreturns to scale. Perfect equality is denoted byp= 0.5. C= 3, L = 2, R= 3, a= 0.1, = 0.5,= 0.4.

    Figure 9: Stable and unstable economies as a function of farmer inequality under negativereturns to scale. Perfect equality is denoted byp = 0.5. C = 1, L = 3, R = 0.1, a = 0.5,= 0.25, = 0.75.

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    contrast, Davis argues that radical land ine-qualities disenfranchised rural peasants vis--vis rural landholders, setting the stage forthe failure of 2nd-stage ISI, the proliferationof debt crises, and generally contested and

    unstable political regimes continuing to thepresent day.

    Increasing Societal Resources

    Can cooperative game theory shed any lighton aid policy, in addition to distributionalpolicy? Simplistically, this question suggestsvarying the resources available to the econ-omy under various returns to scale. I skip thecase of increasing returns to industry, as we

    have determined that it is always defined bya non-empty core. In the scenarios of mixedincreasing / decreasing returns for industryand agriculture respectively, and of univer-sally decreasing returns, however, an inter-esting picture emerges: at low resource lev-els, a cooperative societal framework coheresaround agriculture, and at high levels, aroundmanufacturing. At middling resources levels,however, an empty coreand thus the possi-

    bility for instabilityemerges (see Figure 10and Figure 11).

    One very imperfect historical analog tothis pattern is that of the 19th century UnitedStates, when the country was based around alargely agricultural economy. The 13 originalcolonies experienced a rapid rise in per capita

    real product from around US$68 in 1800, toUS$111 in 1840, to US$170 in 1860 (Lindert& Williamson), at which point the AmericanCivil War commenced. This example is prob-lematic for a number of reasons, includingthe fact that agricultural and industrial tech-nology was advancing in the lead-up to theCivil War, and that these endogenous dynam-ics likely represent a large part of the causeof the rise in societal resource levels in the

    first place. To that extent, then, the exam-ple may more aptly exemplify the patternof stability as the level ofCrises, as detailedin a previous subsection. In either case, theCivil War did seem to mark a definitive shiftfrom a largely agricultural economy to alargely industrial one in which machinery(albeit largely animal-powered at the time)increasingly played a large role in boostingagricultural production (Rasmussen 1965).

    The model suggests more broadly that aidpolicy might theoretically then be used to

    Figure 10: Stable and unstable economies as a function of resource levels (R) under mixed(increasing for industry, decreasing for agriculture) returns to scale. Perfect equality isdenoted byp= 0.5. C= 1, L = 3, a= 0.5,p= 0.5, = 1.5, = 0.25.

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    hasten the transition from an agricultural to

    an industrial economy in these situations.Assuming all negative returns to scale,

    however a more intuitive picturethat of

    the classic poverty trap (Collier et al. 2003)

    forms (see Figure 12). Low resource lev-els are associated with an empty core andthus heightened likelihood of instability. At

    Figure 11: Stable and unstable economies as a function of resource levels (R) under decreasingreturns to scale. Perfect equality is denoted byp= 0.5. C= 2, L = 2, a= 0.1,p= 0.3, = 0.9,= 0.3.

    Figure 12: Stable and unstable economies as a function of resource levels (R) under negativereturns to scale. Perfect equality is denoted byp = 0.5. C = 1, L = 3, a = 0.5, p = 0.5,= 0.75, = 0.25.

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    higher resource levels, cooperation becomespossible for an agricultural society, but inter-estingly, this is not possible for an indus-trial society under negative returns. This isbecause the industrialist, as a monopolist in

    this model, must cooperate with at least oneagriculturalist, which subordinates the pay-out of an industrial society to the empty corebenchmarka phenomenon that does notaffect agriculturalists. Of course, the fact ofnegative returns to scale implies that societalresources will, in the long run, be declining,eventually precipitating a return of stability.

    Conclusion

    In the distributional policy analysis, I sug-gested that maintaining equitable assetsamongst agriculturalists is only undesirableunder the assumption that the manufactur-ing sector exhibits positive and decreasingreturns to scale. If increasing8 or negativereturns are the case with the manufacturingsector, however, agricultural equality thenbecomes an important policy goal in ensur-ing stability in the cooperative model. In the

    particular case of a shrinking economy, sta-bility can be preserved given (a) fairly equita-ble land distribution, and (b) a healthy indus-trial sector serving agriculture.

    In terms of aid policy, I suggested that,under decreasing industrial returns, moreresources available to an economy can pro-mote cooperative frameworks, but that suchboosts will entail a switch to economiesstructured around the industrial sector. Thisis an important point because, while many

    of development success stories have linkedagricultural production to urban industry(Brazil, India, and China, for instance) anda large body of literature views such rural-urban linkages favorably (see, e.g., ESCAP/UN-Habitat 2002; Evans 1992, 2001; Kam-meier 2002; Momen 2006; Tacoli 1998), aidpolicy in general has tended to shy away fromthe active promotion of industrialization.9I also discussed how, under negative indus-

    trial returns, an increase in resources wouldpromote a cooperative framework based

    around agriculture. Taken together, then,the model suggests that aid policy should beinformed by an empirical assessment of sec-toral returns to scale when peacebuilding isa critical goal.

    The cooperative model comes with severalimportant caveats. For one, as previouslynoted, while a non-empty core ensures coop-eration, the reverse is not true: an empty coredoes not guarantee instability. For another,the model in no way attempts to describe theeffects of state enforcement in the form, forinstance, of police. In fact, the state does notfigure at all here. In this respect, the modelis perhaps most applicable to countries or

    areas in which state governments are weakand ineffective, or in which state interestsare highly tied to one of the sectors modeled.For the current purposes, however, these fail-ings may not matter much, as we are moreconcerned with guaranteeing stability thanpredicting instability.

    More pertinent to the field of Peace Stud-ies, though, is the consideration that themodel describes stability, and not negative

    or positive peace.

    10

    That is, a stable arrange-ment may exist in which no profitable devia-tions exist, but which is not objectively toler-able, or humanely desirable, for one or moreof the participants. Underlying this model,then, is a rational-choice view of stability thatclashes with grievance-based views, suchthe idea that peasants rebel not when thereis a better deal to be gained, but whentheir subsistence livelihoods are threatenedwith destruction (e.g., Scott 1976). Moreover,

    it does not necessarily follow that a modeldesigned to predict the actions of individualsis applicable on a macroeconomic basis.

    A final caveat is that the diagrams pre-sented herein are simply exercises in com-parative statics. There is no ineluctable logicthat would draw the level of, say, societalresources, up. And as the example of 19thcentury America highlighted, these factorsare not independent of one another. Moreo-

    ver, there may easily be circular causation atwork, insofar as instability may decrease lev-

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    els of resources, technological coefficients,or returns to scale, in ways that are not mod-eled here.

    However, there is value in the considera-tion of these sorts of models. At the most

    basic level, they draw out implications of aspecific definition of economic stability. Thisdefinition differs markedly from the stand-ard implicit one, which diagnoses instabil-ity symptomatically by way of reference torecurrent conflict. By contrast, the definitionadopted here posits that conflict may, itself,be economically stable, even while providingone possible mechanism that could weakensocial and political institutions to the point

    where recurrent conflict is more likely. Insome ways, this definition of stability reso-nates with the current discursive context inwhich conflict management is preferred tokeeping or building peace (Mac Ginty 2012:2325). Moreover, this type of model is highlyadaptable, and may easily be refined in waysthat improve believability (see, e.g., McDou-gal & Ferguson 2012).

    In closing, I note that the model is possibly

    testable. One strategy for doing so involvesthe somewhat neglected dataset by Crego,Larson, Butzer, and Mundlak (1998), whichenables dual-sector estimation of productioncoefficients and returns to scale across 41developing and developed countries for theperiod 19621992. Paired with the Uppsala(2009) conflict dataset and additional dataon land distribution and control variablesas yet unidentified, the Crego et al. datasetmight allow for a test of association between

    an empty core and political volatility. Rear-ranging Equations (9a) and (9b), we mightconstruct a dependent variable x

    itmeasur-

    ing the difference between the empty corebenchmark and the all-inclusive coalitions:

    ( )( ) ( )( )

    ( ) ( )( )

    ( )( ) ( )( )

    1( 1

    2

    ) 1 ,

    given 1 1 , and

    itx C R a p C R a p

    L R C R a

    C R a L R a

    + + + +

    +

    + > +

    (10a)

    ( )( ) ( )( )

    ( ) ( )( )

    ( )( ) ( )( )

    1( 1

    2

    ) 1 ,

    given 1 1 ,

    itx C R a p C R a p

    L R L R a

    L R a C R a

    + + + +

    +

    + > + (10b)

    for inclusion in a standard fixed time effectslogistic regression equation.

    Notes 1 I gratefully acknowledge the insights of

    Nicholai Lidow, who first brought thisidea to my attention, as well as the sig-

    nificant suggestions of two anonymousreviewers. I am also grateful to Neil T.Ferguson for his work subsequent to thewriting of this piece, which renders thebasic model elaborated herein more real-istic and sophisticated.

    2 A growing pie is an economists meta-phor for a growing set of shared resourc-es. If one wants to increase the size of herpiece of the pie, the two fundamental

    ways of doing this are to make otherspieces smaller (i.e., redistribute the re-sources in ones favor) or to grow theshared resources such that ones propor-tion of the total remains constant butnow implies a larger amount.

    3 Hirshleifers (1988) seminal conflict mod-el essentially implied a very endorsementof economic growth.

    4 The eponymous example of a prisonersdilemma is that of two would-be crimi-

    nal accomplices who have committeda serious crime. The two have been im-prisoned and the police have evidence toconvict each of them on lesser charges(say, breaking and entering), but not theprincipal charge. The accomplices are in-terrogated separately and have no way ofcommunicating. The police attempt toentice each into inculpating the other bycommuting their sentence. Thus, if both

    accomplices cooperate by not snitching,each will do a small amount of time in

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    jail. If one snitches, he will get out im-mediately, while the other will be heldfor life. And if both snitch, they will bothbe held for a long time. An example ofdeadlock might be the Israel-Palestine

    conflict. As in the prisoners dilemma,the best outcome for either player (takento be Israels Likud political party and thePalestinian Liberation Organisation inthis case) would be for the other side toaccommodate its demands. Unlike in theprisonners dilemma, though, the nextbest option is not to cooperate, but rath-er mutual non-cooperation, since accom-modation by either party in that context

    could be seen as a sign of weakness lead-ing to the partys ouster from power. Anexample of chicken might be that of theCold War. As in the prisoners dilemma,the best outcome for either player wouldbe for the other side to cooperate (say,by unilaterally disarming) and therebyallow for its domination. However, un-like in the prisoners dilemma, the con-sequence of mutual non-cooperation

    (both sides arming, possibly resulting innuclear war) is far worse than being theone suckered, making it rational to coop-erate if the other side seems committedto non-cooperation.

    5 See, e.g., Tsebelis (1990). 6 While it is unusual to assume increasing

    returns to scale in an economic model, abody of economic literature has demon-strated that industrial cities can and doexhibit increasing returns (Arthur 1989;

    Fujita, Krugman, & Venables 1999; Krug-man 1991a, 1991b, 1998).

    7 Again, it is unusual to assume negativereturns to scale in economic models, asrational actors are assumed not to in-vest at all when returns to them are lessthan what they invest. However, it mightbe postulated that, for whatever reason,non-investment is not possible, precipi-tating a poverty trap (Duflo & Banerjee

    2011). Negative returns to industry maybe somewhat similar to what Hoselitz(1955) termed a parasitic cityone

    which destroys wealth, or at least sucks itout of the country in question.

    8 Romer (1994), Arthur (1989) and Krug-man (1991b) were among the first tomodel increasing returns to scale in ur-

    ban industrial areas. Increasing returnsto scale can be explained solely as a func-tion of pecuniary agglomeration econo-mies resulting from the presence of spe-cialized intermediary industries in thepresence of transportation costs (see, e.g.,Fujita et al. 1999; Krugman 1998), butmay also arise due to pecuniary recruit-ment economies in the labor market, aswell as non-pecuniary economies associ-

    ated with technological innovationallmechanisms originally discussed by Al-fred Marshall (1920 [1890], Ch. 10).

    9 For example, while the World Bank hasa dizzying array of agricultural exten-sion, crop, forestry, animal husbandry,irrigation, and fishery projects acrossthe developing world, few projects dealwith the promotion of industry in sucha hands on way. Rather, World Bank in-

    dustry projects tend to promote good in-vestment climates through public sectorreform, infrastructure provision, and in-stitutional capacity-building. Historically,critiques have been leveled against theWorld Bank to the effect that it systemati-cally misrepresents the needs of develop-ing countries to push rural developmentagendas (see, e.g., Ferguson 1994 [1990]).Amsden (2001, 2007, 2012 (manuscript))alleges that the aid industry as a whole

    has managed to ignore the fact that in-dustrialization is the only economicprocess that has historically managed toprovide high-paying jobs (and therefore ameans of pulling oneself out of poverty)to large portions of society.

    10 For the seminal discussion of positive ver-sus negative peace, see Galtung (1969).

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