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©Copyright JASSS Denton Cockburn, Stefani A. Crabtree, Ziad Kobti, Timothy A. Kohler and R. Kyle Bocinsky (2013) Simulating Social and Economic Specialization in Small-Scale Agricultural Societies Journal of Artificial Societies and Social Simulation 16 (4) 4 <http://jasss.soc.surrey.ac.uk/16/4/4.html> Received: 12-Jan-2012 Accepted: 25-May-2013 Published: 31-Oct-2013 Abstract We introduce a model for agent specialization in small-scale human societies that incorporates planning based on social influence and economic state. Agents allocate their time among available tasks based on exchange, demand, competition from other agents, family needs, and previous experiences. Agents exchange and request goods using barter, balanced reciprocal exchange, and generalized reciprocal exchange. We use a weight-based reinforcement model for the allocation of resources among tasks. The Village Ecodynamics Project (VEP) area acts as our case study, and the work reported here extends previous versions of the VEP agent-based model ("Village"). This model simulates settlement and subsistence practices in Pueblo societies of the central Mesa Verde region between A.D. 600 and 1300. In the base model on which we build here, agents represent households seeking to minimize their caloric costs for obtaining enough calories, protein, fuel, and water from a landscape which is always changing due to both exogenous factors (climate) and human resource use. Compared to the baseline condition of no specialization, specialization in conjunction with barter increases population wealth, global population size, and degree of aggregation. Differences between scenarios for specialization in which agents use only a weight-based model for time allocation among tasks, and one in which they also consider social influence, are more subtle. The networks generated by barter in the latter scenario exhibit higher clustering coefficients, suggesting that social influence allows a few agents to assume particularly influential roles in the global exchange network. Keywords: Specialization, Agent-Based Modeling, Archaeology, Social Networks, Models of Social Influence, Barter Introduction 1.1 Specialization is one way in which agents can increase their productivity (Murciano and Zamora 1997) by cooperating with other individuals (Spencer, Couzin and Franks 1998) to generate increasing returns to scale (population size of social group). The origins of specialization, especially craft specialization, have been linked with increasing sociopolitical complexity since at least the eighteenth century. Adam Smith (1776/1937) chose to begin his Inquiry into the Nature and Causes of the Wealth of Nations by suggesting that "the greatest improvement in the productive powers of labour, and the greater part of the skill, dexterity, and judgment with which it is any where directed, or applied, seem to have been the effects of the division of labour." He connected the origin of specialization with a human propensity to exchange, emphasizing that the interdependence produced by the joint action of specialization and exchange tends to increase overall productivity. Such increased production quite possibly initiated a positive feedback, since, for Childe (1936/1983), surplus production from an effective agriculture underwrote both technical and social divisions of labour, leading eventually in Mesopotamia to the emergence of elites who were able to support full-time craft specialists. Although specialization and production for exchange are often linked to the rise of the state, it is clear that they exist in smaller-scale societies alongside subsistence production (Patterson 2005). 1.2 In this article we develop an agent-based simulation of specialization in resource production, and a system of barter allowing exchange of specialized products, in Pueblo societies existing between AD 600 and 1300 in southwestern Colorado with the ultimate goal of examining their effects in these middle-range Neolithic societies. Since barter can mean rather different things, we specify that by barter we mean "moneyless market exchange" and not the sorts of reciprocal transactions that appear to be universally important in small-scale, non-market societies (Dalton 1982). Our goal here is to present the computational machinery making specialization and barter possible within our existing agent-based model. We are therefore less concerned with the realism of some of the assumptions below, including the amount of storage we allow, and the goods in which agents specialize. For example, specialization in production of ceramics is probably more likely in these societies (Harry 2005) than is specialization in making water available to other households; nor do we really believe that households in these societies were able to store the large quantities of goods we allow below. However, using these sometimes unrealistic assumptions, we hope to, as Epstein (2008: 3-4) says, "illuminate core dynamics" of the systems of barter and exchange and capture "behaviors of overarching interest" within the American Southwest. 1.3 Here we define specialization as the agents' choice to produce quantities of some goods in excess of a level needed for subsistence, while simultaneously underproducing other goods. When agents specialize, if they don't produce all their subsistence requirements, they must acquire these through exchange with other agents (Evans 1978). Specialization as we model it can occur along a spectrum. Agents can be fully specialized, performing one task (here, producing one good) to the exclusion of all others, or they can be partially specialized, performing all tasks to varying degrees. In our system, our agents are expected to be partially specialized, but it is also possible for some agents to become fully specialized. 1.4 As Smith realized, so long as exchange is relatively frictionless, specialization increases the productivity in a market system ( Murciano and Zamora 1997). Productive individuals increase the supply for goods in which they specialize, and they specialize in producing goods in which they have a comparative advantage; at the same time they increase demand for other goods that they need, thereby providing indirect network effects (Young 1928). The level of specialization and output are dependent on several factors, including competition, the characteristics of the exchange networks, and initial conditions (Lavezzi 2003). Cockburn, Kobti and Kohler (2010) created an economic agent specialization model that added features not found in the simpler model produced by Lavezzi (2003), including consumption, production limits, changing populations, and changing trading relationships. The agents in that model were also sensitive to varying supplies of resources. If many agents are already outputting the same resource, the supply for that resource is likely to surpass the demand, thus discouraging additional production of that resource. 1.5 It has been shown that the level of specialization in complex systems, including human societies (Bonner 1993), is affected by the size of the system (Bonner 2004). Research in insect societies by Jeanson, Fewell, Gorelick, and Bertram (2007) indicates that when demand is low and there are many tasks, increased division of labour is an emergent property, suggesting that the level of specialization within insect societies is positively related to the size of colonies. The http://jasss.soc.surrey.ac.uk/16/4/4.html 1 15/10/2015
Transcript of Simulating Social and Economic Specialization in Small ...jasss.soc.surrey.ac.uk/16/4/4/4.pdf ·...
©CopyrightJASSS
DentonCockburn,StefaniA.Crabtree,ZiadKobti,TimothyA.KohlerandR.KyleBocinsky(2013)
SimulatingSocialandEconomicSpecializationinSmall-ScaleAgriculturalSocieties
JournalofArtificialSocietiesandSocialSimulation 16(4)4<http://jasss.soc.surrey.ac.uk/16/4/4.html>
Received:12-Jan-2012Accepted:25-May-2013Published:31-Oct-2013
Abstract
Weintroduceamodelforagentspecializationinsmall-scalehumansocietiesthatincorporatesplanningbasedonsocialinfluenceandeconomicstate.Agentsallocatetheirtimeamongavailabletasksbasedonexchange,demand,competitionfromotheragents,familyneeds,andpreviousexperiences.Agentsexchangeandrequestgoodsusingbarter,balancedreciprocalexchange,andgeneralizedreciprocalexchange.Weuseaweight-basedreinforcementmodelfortheallocationofresourcesamongtasks.TheVillageEcodynamicsProject(VEP)areaactsasourcasestudy,andtheworkreportedhereextendspreviousversionsoftheVEPagent-basedmodel("Village").ThismodelsimulatessettlementandsubsistencepracticesinPueblosocietiesofthecentralMesaVerderegionbetweenA.D.600and1300.Inthebasemodelonwhichwebuildhere,agentsrepresenthouseholdsseekingtominimizetheircaloriccostsforobtainingenoughcalories,protein,fuel,andwaterfromalandscapewhichisalwayschangingduetobothexogenousfactors(climate)andhumanresourceuse.Comparedtothebaselineconditionofnospecialization,specializationinconjunctionwithbarterincreasespopulationwealth,globalpopulationsize,anddegreeofaggregation.Differencesbetweenscenariosforspecializationinwhichagentsuseonlyaweight-basedmodelfortimeallocationamongtasks,andoneinwhichtheyalsoconsidersocialinfluence,aremoresubtle.Thenetworksgeneratedbybarterinthelatterscenarioexhibithigherclusteringcoefficients,suggestingthatsocialinfluenceallowsafewagentstoassumeparticularlyinfluentialrolesintheglobalexchangenetwork.
Keywords:Specialization,Agent-BasedModeling,Archaeology,SocialNetworks,ModelsofSocialInfluence,Barter
Introduction
1.1 Specializationisonewayinwhichagentscanincreasetheirproductivity(MurcianoandZamora1997)bycooperatingwithotherindividuals(Spencer,CouzinandFranks1998)togenerateincreasingreturnstoscale(populationsizeofsocialgroup).Theoriginsofspecialization,especiallycraftspecialization,havebeenlinkedwithincreasingsociopoliticalcomplexitysinceatleasttheeighteenthcentury.AdamSmith(1776/1937)chosetobeginhisInquiryintotheNatureandCausesoftheWealthofNationsbysuggestingthat"thegreatestimprovementintheproductivepowersoflabour,andthegreaterpartoftheskill,dexterity,andjudgmentwithwhichitisanywheredirected,orapplied,seemtohavebeentheeffectsofthedivisionoflabour."Heconnectedtheoriginofspecializationwithahumanpropensitytoexchange,emphasizingthattheinterdependenceproducedbythejointactionofspecializationandexchangetendstoincreaseoverallproductivity.Suchincreasedproductionquitepossiblyinitiatedapositivefeedback,since,forChilde(1936/1983),surplusproductionfromaneffectiveagricultureunderwrotebothtechnicalandsocialdivisionsoflabour,leadingeventuallyinMesopotamiatotheemergenceofeliteswhowereabletosupportfull-timecraftspecialists.Althoughspecializationandproductionforexchangeareoftenlinkedtotheriseofthestate,itisclearthattheyexistinsmaller-scalesocietiesalongsidesubsistenceproduction(Patterson2005).
1.2 Inthisarticlewedevelopanagent-basedsimulationofspecializationinresourceproduction,andasystemofbarterallowingexchangeofspecializedproducts,inPueblosocietiesexistingbetweenAD600and1300insouthwesternColoradowiththeultimategoalofexaminingtheireffectsinthesemiddle-rangeNeolithicsocieties.Sincebartercanmeanratherdifferentthings,wespecifythatbybarterwemean"moneylessmarketexchange"andnotthesortsofreciprocaltransactionsthatappeartobeuniversallyimportantinsmall-scale,non-marketsocieties(Dalton1982).Ourgoalhereistopresentthecomputationalmachinerymakingspecializationandbarterpossiblewithinourexistingagent-basedmodel.Wearethereforelessconcernedwiththerealismofsomeoftheassumptionsbelow,includingtheamountofstorageweallow,andthegoodsinwhichagentsspecialize.Forexample,specializationinproductionofceramicsisprobablymorelikelyinthesesocieties(Harry2005)thanisspecializationinmakingwateravailabletootherhouseholds;nordowereallybelievethathouseholdsinthesesocietieswereabletostorethelargequantitiesofgoodsweallowbelow.However,usingthesesometimesunrealisticassumptions,wehopeto,asEpstein(2008:3-4)says,"illuminatecoredynamics"ofthesystemsofbarterandexchangeandcapture"behaviorsofoverarchinginterest"withintheAmericanSouthwest.
1.3 Herewedefinespecializationastheagents'choicetoproducequantitiesofsomegoodsinexcessofalevelneededforsubsistence,whilesimultaneouslyunderproducingothergoods.Whenagentsspecialize,iftheydon'tproducealltheirsubsistencerequirements,theymustacquirethesethroughexchangewithotheragents(Evans1978).Specializationaswemodelitcanoccuralongaspectrum.Agentscanbefullyspecialized,performingonetask(here,producingonegood)totheexclusionofallothers,ortheycanbepartiallyspecialized,performingalltaskstovaryingdegrees.Inoursystem,ouragentsareexpectedtobepartiallyspecialized,butitisalsopossibleforsomeagentstobecomefullyspecialized.
1.4 AsSmithrealized,solongasexchangeisrelativelyfrictionless,specializationincreasestheproductivityinamarketsystem( MurcianoandZamora1997).Productiveindividualsincreasethesupplyforgoodsinwhichtheyspecialize,andtheyspecializeinproducinggoodsinwhichtheyhaveacomparativeadvantage;atthesametimetheyincreasedemandforothergoodsthattheyneed,therebyprovidingindirectnetworkeffects(Young1928).Thelevelofspecializationandoutputaredependentonseveralfactors,includingcompetition,thecharacteristicsoftheexchangenetworks,andinitialconditions(Lavezzi2003).Cockburn,KobtiandKohler(2010)createdaneconomicagentspecializationmodelthataddedfeaturesnotfoundinthesimplermodelproducedbyLavezzi(2003),includingconsumption,productionlimits,changingpopulations,andchangingtradingrelationships.Theagentsinthatmodelwerealsosensitivetovaryingsuppliesofresources.Ifmanyagentsarealreadyoutputtingthesameresource,thesupplyforthatresourceislikelytosurpassthedemand,thusdiscouragingadditionalproductionofthatresource.
1.5 Ithasbeenshownthatthelevelofspecializationincomplexsystems,includinghumansocieties(Bonner1993),isaffectedbythesizeofthesystem(Bonner2004).ResearchininsectsocietiesbyJeanson,Fewell,Gorelick,andBertram(2007)indicatesthatwhendemandislowandtherearemanytasks,increaseddivisionoflabourisanemergentproperty,suggestingthatthelevelofspecializationwithininsectsocietiesispositivelyrelatedtothesizeofcolonies.The
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behaviourofcognitiveagentscanbemodeledusingmotivationnetworks(Krink,MayohandMichalewicz1999)inwhichagentschoosebetweenmoving,eatingandbreedingbasedonconditionswithintheenvironment.Ouragentsarenotthissophisticated,andonlyusespecializationtodeterminewhatjobstoperformandhowtodividetheirtimeamongthosetasks.
1.6 CockburnandKobti(2009b)andCockburnetal.(2010)claimthatintroducingsocialinfluenceintoasystemwouldincreasethelevelofspecialization.Buildingontheseassertions,herewecreateamodelthatincorporatesbotheconomicstateandsocialinfluence.Agentsareinfluencedbycompetitionfromotheragentsintheirtopographicallybasedsocialnetwork.Itisexpectedthatthereshouldbemoretaskspecializationinthissociallyinfluencedsystemthaninthemodelswithoutsocialinfluence.Wealsoexpectthatthelevelofwealthwillincreaseinthepopulation(MurcianoandZamora1997).Further,specializationandsocialinfluencemayhaveeffectsonpopulationsofagents,andassocialinfluenceinteractswithexchangenetworks,wemayexpectspecializationtochangethestructureofglobalpopulations.Toassessthepresenceandsizeoftheseeffectswecomparesystemsinwhich(1)agentsonlytrytoprocureenoughresourcestomeettheirneeds;(2)wheretheyplanbasedupontheeconomicstateoftheirfamily,possiblyproducingmoreofsomeresourcesforwhichtheyhaveextractiveadvantageduetotheirlocation;andfinally,(3)wheretheyplanbasedupontheireconomicstatewhilealsoconsideringcompetitionfromagentswithintheirsocialnetwork.
1.7 Thereareseveralapproachestomodelingsociallyinfluencedspecialization,includingsocialinhibition,wherebyagentsdiscourageothersfromcompeting(BeshersandFewell2001).Temporalpolyethismisanother,whereagents'specializationisrelatedtotheirage(Ravaryetal.2007).Agentsmightalsolearnfromexperience(MurcianoandZamora1997;Spenceretal.1998;Theraulaz,BonabeauandDeneubourg1998),forexamplebyrandomlyselectingaspecializationattheoutset,andifsuccessful,selectingthatactioninthenextroundwithhigherprobability.
1.8 Forreinforcement-basedsystemstosucceedindynamicenvironments,agentsmustbeabletoovercomepreviouslylearnedbehaviour,especiallywhenfailuretodosoresultsindeath(Beaudreau2003).Agentsmustbewillingtoengageinbehaviourthatpreviouslyhadpoorresultsandalsomustbeabletorespondtoemergencysituations,wherechangemaybedramaticyetnecessary.Moreover,thelevelofsocialinfluencewithinasocietyalsoaffectsthelevelofspecialization.Themoreagentsareaffectedbytheactionsoftheirneighbours,themorespecializedthesocietybecomes(see,forexample,CockburnandKobti2009a;2009b).
CentralizedMulti-agentsystems
1.9 InMulti-AgentSystems(MAS),thestudyofspecializationisoftenmotivatedbyaninterestinhowspecializationcanincreasetheefficiencyofthesysteminreachingitsgoals.AMarkov-chainmodeltodescribetheevolutionarydynamicsoftheemergenceofspecializationinMASispresentedinChai,Chen,Han,DiandFan(2007).Inthatenvironment,agentssearchforandexploitresourceswithincompleteinformationandagoalofmaximizingtheefficiencyoftheentiresystem.TheMASusesacentralizedmodelfordeterminingtaskspecialization,withtaskallocationsemergingasaresultoflong-termsystemevolution.Thus,agents'specializationisdeterminedbytheoverallneedsofthesystemandnotbyindividualconsiderationsalone.Asaresult,anagentcansometimesbecausedtospecializeintasksthataredangeroustoitspersonalinterestswithoutsufficientreward(i.e.,thejobofcleaningupatoxicspill).Agentspecializationinthesesystemswillresultinhighersystemproductivitythaninnon-specializedsystems(Chaietal.2007).
1.10 Usingacentralizedspecializationsystemalsoaddressesanotherproblem:agentsgenerallydonotpossesscompleteinformation,thusanyspecializationdecisionstheymakearelikelytobesuboptimal.CentralizedMASarebetterabletohandlespecializationincomplexandchangingenvironments(Chaietal.2007),partlybecausetheysuppresscomplicationsarisingfromtheself-adaptivestrivingofindividualagents.Centralizedsystemsalsobenefitfromthefactthatresourcesdiscoveredbyindividualscanbemorequicklyexploitedduetotheglobalknowledgeinthesystemandcentralizeddirection.
1.11 CentralizedMAS,however,puttheburdenon"thesystem"tobefullyawareofallrelevantfactorsinthedecision-makingprocessforallagents.Thereisnocompetitionbetweenagentsinthesesystems.Suchsystemsbegthequestionastohowsocietiesofcooperatingagentscanemergefromsocietiesofautonomousagents,sincetheyassumethatanyconflict-of-interestproblemsinwhichcognitiveagentsmightbetemptedtooverridecentralizeddecisionshavebeensuccessfullysolved.Finally,centralizeddirectionissimplyunrealisticforthecaseofthesocietieswemodelhere,inwhichdecision-makingmusthavebeenmoreconsensualandbottom-upthancentralized(VanVugt&Ahuja2011).
CaseStudy:VillageEcodynamicsProject
2.1 TheVillageEcodynamicsProject(VEP)isamulti-disciplinary,multi-institutionproject(Kohleretal.2007).IthasinvolvedindividualsfromWashingtonStateUniversity,CrowCanyonArchaeologicalCenter,WayneStateUniversity,UniversityofWindsor,SantaFeInstitute,ColoradoSchoolofMines,UniversityofNotreDame,andBBL,Inc.Researchersincludecomputerscientists,archaeologists,ecologists,anthropologists,geologistsandeconomists.TheVEPbeganby
describingandmodeling1800km2ofthecentralMesaVerderegionofSouthwestColorado,occupiedbetweenA.D.600and1300byfarmersancestraltocontemporaryPueblopeoples,whichisthesettingforthismodel.Thousandsofhabitationsitesareknownfromthisarea,whichwecanassigntooneormoreof14periodsbasedeitheronexcavationor,inmostcases,theceramicsontheirsurfaces(Varien,Ortman,Kohler,GlowackiandJohnson2007).TheentirenorthernSouthwestwasdepopulatedtowardstheendofthethirteenthcenturyandoneoftheprimarygoalsoftheVEPresearchistounderstandthereasonsthatledtothisdepopulation(Kohler,Varien,WrightandKuckelman2008).Anothergoalistounderstandwhy,duringcertaintimesinprehistory,mostpeoplelivedinlargeandrelativelycompactvillages,whileatothertimes,theydispersedintosmallerhamlets(Crabtree2012).
2.2 TheoriginalsimulationwasdesignedbyTimKohlerandcolleaguesatWashingtonStateUniversityandtheSantaFeInstitute(Kohler,Kresl,vanWest,CarrandWilshusen2000).Thesimulationcreatesagenthouseholdsthatlive,work,andreproduceinalandscapemodeledonthatofsouthwesternColorado.Muchofthedynamismofthesimulationisprovidedbyannualandspatiallyspecificestimatesofpotentialmaizeproductiononthislandscape,originallydevelopedbyVanWest(1994)andlaterrefinedbyKohler(e.g.,2012).Agentactionsonthislandscapearedesignedtobeasrealisticaspossible,drawingontheconsiderableamountknownaboutthisplaceandtime(Lipe,VarienandWilshusen1999).Agentsareresponsibleforgatheringtheirresources,whilefeedingtheirfamiliesandexchangingwithotheragents.Agentsmustfarmmaize,huntforprotein(cottontailrabbit,jackrabbit,andmuledeer),obtainwaterfromriversandsprings,andgatherfirewoodfromforests.Agentsgetalltheirenergy,asmeasuredincalories,frommaize.Whenproteinisrequired,itcostscaloriestoprocure.Agenthouseholdsmustprovidetheirfamilieswithenoughcaloriestoperformthesetasks,aswellasprovidefortheirbasicmetabolicneeds.Inthecasethatagentscannotobtainalltheresourcestheyneedontheirown,theyareallowedtoexchangewithotheragents.Familiesandfamilymembersaretrackedinthemodel,andweallowdifferentkindsofexchangerelationshipsbetweenkin,andamongnon-kin,drawingonmodelsappropriateforsmall-scalesocieties(Sahlins1972).
2.3 Ifanagentisnotperformingwellatitspresentlocation,itwillmovetoamoresuitablelocationinthestudyarea.Unfortunatelyfortheagents,theyarenotallowedtoexitthestudyarea.Whenconsideringlocationstomoveto,agentsevaluatetheresourceproductivityofprospectiveareas.Thisincludesevaluatingforfarmingproductivity,waterandfuelwoodaccessibility,andhuntingopportunities.Themodelaimstorepresentsoilproductivity,rainfall,animaldensity,forestdensity,andotherfeaturesoftheregionwithafairdegreeofrealism.Eventhevegetationthatfeedstheanimalsinthesimulationisaffectedbyclimaticvariability.
2.4 VEPresearchershaveidentifiedtwopopulationcyclesinthearchaeologicalrecord(Varienetal.2007).Intheearlier,smallercyclethereisrelativelylittleevidenceforspecialization,whereasinthelater,morepopulouscyclethereisevidenceforspecializationinatleastthedomainofpoliticalleadership,andprobablyalsoinprovisionofreligiousservicesandinaspectsofceramicproduction(Bernardini2000).Ortman(2003)providesevidencethathouseholdsrelocatingtothelargestsiteintheVEParea,YellowJacketPueblo,towardstheendofitsoccupationspecializedinceramicproduction.Thisispossiblybecause,aslatearrivals,thenewcomersdidnothaveaccesstohigh-qualityfarmlandandneededtoengageincraftactivitytointegratewiththeeconomy.Theframeworkwecreatehereallowstheemergenceofresource-acquisitionspecialistswithinthesimulation.Ceramicproductionspecificallyisnotmodeledbutcouldlaterbeaddedtothesimulation.
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2.5 KohlerandVarien(2012)presentagreatdealofadditionalinformationaboutthelocalarchaeologicalrecord,thestructureofthesimulation,andourconclusionsderivedfromcomparingthetwo.Theversionofthesimulationreportedinthatvolume—onwhichthispaperbuilds—isavailableathttp://www.openabm.org/model/2518.AlsonotableinthepresentcontextaretheinvestigationsbyKobtietal.ontheroleofexchangeinaggregationanddepopulation,usingculturalalgorithms(Kobti,ReynoldsandKohler2004;Reynolds,KobtiandKohler2004;KobtiandReynolds2005).
Approach
3.1 Amoreformalizeddescriptionofourapproachispresentedintheappendix.Agentsareallowedtodividetheirtimeamongallfourtasksexistingwithinoursimulation(farming,hunting,gatheringwoodandcollectingwater).Thepercentageoftheirtimespentoneachofthesetasksisdependentupontheirneedsfortheresultsofthattask,aswellastheirperceivedabilitytoobtainthoseresourcesmorecheaplyfromcloseneighbours.Ifanagenthas30kglessmaizethanitneeds,itwillseektoincreaseitsmaizeproductionforthefollowingyearby30kg,byadjustingthepercentageofitstimethatshouldpermitthatgoaltobeachieved.Theagentwilltrytodotheoppositeifitisoveritsthresholdforaresource.Itwilloftenhappenthattheagentwillchangemultipleallocations,resultinginatotaloutlaynotequalto100%.Atthispoint,theagentwillnormalizetheseallocations,suchthatitwillspend100%ofitsworkhoursonthesetasks.
3.2 Whenagentshaveexcessstoresofaresource,theywilllettheirneighboursknow.Thoseneighboursthathavehigherproductioncostsfortheseresourceswillpredictthatthisagentwillbeabletohelpthemmeetanyshortfallforthisresourceintheupcomingyear.Theywillbewillingtoreducetheirownproductionaccordingly.Thenetresultofthesefactorsisthatagentswilldynamicallyadjusttheirallocationsbasedonpersonalexperience,aswellascooperationandcompetitionfromothers.
Simulatedenvironment
4.1 TheVEPenvironmentconsistsoffourresources:water,wood,maizeandmeat.Allbutwoodareneededforsurvival.Whileanagentdiesimmediatelyifitdoesnothaveenoughmaizeorifithasbeenshortofmeatproteinforthreeconsecutiveyears,agentsareallowedtosurvivecontinualshortagesofwood(however,theagentsdon'tfactorthisintotheirplanning).Whileagentsareboundbytheseresourcerequirements,theydon'thaveanyunderstandingoftheconsequencesofresourceshortfalls.Thismeansthatanagentdoesnotprioritizewaterormaizeoverwoodorprotein,eventhoughneglectingtheformerincreasesthechancesofdeath.
4.2 Eachresourceisassociatedwithataskthatproducesthatresource.Afarmerproducesmaize,ahunteracquiresprotein,awoodsmangatherswood,andawatercarrierretrieveswater.Eachtaskalsohasconstraintsandrequirementsfortheperformanceofthattask.Farmersrequirelandtoplanttheirmaize.Therearealimitednumberofproductiveplotsonthelandscapeandplotsvaryinproductivity,bothwithinayear(spatially)andfromyeartoyear.Huntingrequiresthepresenceofanimalswithinthepermissiblehuntingrangeof4km.Gatheringwoodrequiresthepresenceofdeadwoodortrees,andcarryingwaterrequiresthattherearewatersourcesthattheagentcantravelto.Forwoodandwater,agentsarenotboundbythedistancetotheseresources;theycantravelasfarasnecessarytoobtainthem.Howeveralltasksrequireenergytoperform,andthusrequiretheagenttohavesufficientcaloriestoperformthetask.Theamountofenergyrequiredforthesetaskswasincorporatedinthesimulationbeforethedevelopmentdescribedherebegan,asexplainedinKohleratal.(2007).
4.3 Agentsmustallocatetheirfamily'stotalcaloriesavailablefortheyearamongthegiventasks.Thenumberofcaloriesrequiredbyeachhouseholdisdeterminedbythenumberofadultsinthehousehold,thenumberofchildreninthehousehold,aswellashowmanyhoursperdayeachisrequired(orwilling)towork.Intheversionofthesimulationreportedhere,thenumberofhourswillingtoworkwassetto6hours/dayforeachindividualinafamilythatisatoraboveworkingage(8yearsold,inoursimulation).Agentsareabletospendanyamountoftheircaloriesonanyspecifictask.Agentsalsohaveasecondarygoal,theaccumulation(storage)ofresourcesthatincreasestheireconomicsecurityfortimeswhentheycannotprocureadditionalresources,suchasduringafamineordrought.Allagentscanonlystoreamaximumof10yearssupplyofanyresource.Ayear'ssupplyistheamountthehousehold(agent)wouldneedforsubsistenceestimatedaccordingtoitscurrentcircumstances.Itshouldbenotedthatwhilethemaximumissetat10,itisrarelythecasethatanagentpossessesthatmuchofaresource.Meat,forexample,israrelyheldinstoragebecauseofthescarcityoftheresourceandthehighrateofdecay.Themaximumstoragewouldtheoreticallyallowahouseholdspecializinginhuntingtostorethemeatfrom10deerwhilewaitingtotradesomeforotherresources.Anyexcessamountabovethemaximumallowedstorage(10years)willbedonatedtonearbyrelatives,ordiscardediftherearenorelativestoacceptthem.Whileagentsmustsustainneedstosurvive,theirfocusisonmaximizingtheirproductivitygiventheirabilities.Allagentshavethesameskilllevel,soabilityisdelineatedbytheproductivityofanagentatperformingatask.Thusanagenthavingmoreproductiveplotswouldgetahigherreturnontheenergyexpendedonthoseplots,andthuscanbeclaimedtobea"better"farmerthananagentwithlessproductiveplots.Topreventagentsfromdyingbeforetheyhavetimetoprocureresources,allhouseholdsaregivenaninitialallocationoftwoyear'ssupplyofmaizeandmeat,astheseresourcescanonlybegatheredinautumnandsummerrespectively.
4.4 Itisnotfeasibletoinitializeanagent'sallocationamongtasksrandomly,sinceanallocationforfarmingthatistoolowwouldlikelyresultinstarvation,withsimilarunfortunateresultsforotherresources.Additionally,theonlywayforanewagenttobeintroducedtothesystemisforahouseholdtosurvivelongenoughtoproduceoffspring.Toaddressthisproblem,wehavehouseholdscalculatehowmuchofeachresourcetheyneedandallocateenoughtimetomeettheseneeds.Thisonlyhappensintheyearinwhichahouseholdiscreated.(Exceptatinitialization,thisisalwaysduetoamarriage.)Weusetheresultingallocationoftimeinthatfirstyeartoseedourweightsforthesecondyear.Ifanagentspends25%ofitsenergyinthefirstyearfarming,thenfarmingwillhavea25%weightinoursystemduringthesecondyear.Afterthis,agentsrelyonaperformanceandfeedbackfunctiontoupdatetheirweightsforsubsequentyears.Ifagentsmaynotbeabletoprovidethemselveswithallthesubsistencegoodstheyneed,theymaytradefororrequestthoseresourcesthroughanexchangenetwork.
4.5 ThesimulationreportedherealsomodifiedtheversionreportedinKohlerandVarien(2012)byallowingagentstopassontheirwealthatdeath.Ifanagenthouseholddies,theresourcesithasstoredwillbedividedequallyamongitschildrenwhoarewithintradingrange,whichissetatthesamedistance(8km)permittedforbalancedreciprocalexchanges(BRN;seebelow).Ifnochildrenarewithinthatrange,thiswealthisdividedequallyamongneighbours,andfinally,ifnootheragentsarewithinrange,theresourcesgotowaste.
4.6 Thegeneraldecision-makingstepsrequiredofeachagentarepresentedinTable1.
Table1:Decision-makingprocessforeachagent(household)
Step Decision/action1 Iffirstyearincurrentlocation,performbasedonfamilyneedsandproceedtostep3.Ifnot,proceedtostep2.2 Ifsecondyearincurrentlocation,useallocationsfrompreviousyeartoinitializeweights.Proceedtostep3.3 Performtasksandexpendenergy.4 Exchangeresourcesifneeded.5 Ifstillalive,updateweights(definedinsection4.4).6 Ifagentlocationnotsustainable,movetonewlocation.7 Returntostep1.
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Agentstates
4.7 Agentshavefourstatesforeachresourcethataffecttheirhealthandwillingnesstotradethatresource.Calculationsforeachstatedependonthesizeandmakeupofeachfamily.Thecalculationsdonotincludeusageoftheresourcesforthepurposesofworkingorperformingothertasks.Thestatesarebasedonhowlongtheagentsestimatetheamountoftheresourcetheypossesswillbeabletomeettheirfamily'sneeds.
TRADING-2yearssupplyormore.SATISFIED-6monthsto2yearssupply.CRITICAL-lessthan6monthssupply(butmorethan0).STARVING-Whenanagentdoesn'thaveanyoftheresource,andneedstoimmediatelyobtainsomeviatradingorbegging.
Exchange
Barter
4.8 Barter—newtothisversionofthesimulation—allowsagentstotradeoneormoreresourcesinexchangeforanotherresource.Previousversionsofthesimulationallowedonlygeneralizedreciprocalexchangeandbalancedreciprocalexchange,andthoseonlyoperatedwithinthedomainsofmeatandmaize,asdiscussedbelowin§4.12and§4.13.Moreover,thebalancedreciprocalexchangesystemonlyallowstime-delayedexchangeswhereasbartersimulatesimmediateexchanges.Wehavedevelopedasimplifiedbartersysteminwhichagentstradegoodsbasedonafairvaluation.Pricesarethereforenotnegotiated.Todeterminevaluesforresources,weusetheagent'scostofproduction.Weacceptthatthisdoesnotresultinthelevelofinequalitythatonewouldexpectinacapitalistbartersystemwherepricesarenegotiated.Forinstance,inasystemwithnegotiation,weexpectthatifanagent(household)hasthesolesupplyofadesiredresource,itcouldinflatethepriceofthatresourcewellbeyonditscostofproduction.Wedidnotincludesuchamechanismasitwouldundulyincreasecomputationalcomplexity.Weusecaloriesasaformofcurrencyinthissimulation.Theinteractionsbetweenthebartersystem,andtheexchangesbasedonreciprocity,areoutlinedbelowin§4.18.Wepostponeforlaterinvestigationwhetherbarterincreasesordecreasesthedegreeofagentinequality(asmeasuredforexamplebytheGinicoefficient)relativetoexchangesbasedonlyongeneralizedandbalancedreciprocity.
Table2:Variablesusedinbarter
Abbreviation MeaningAg AnagentrAG SomeresourceperagenttAG AgentsinthesetofpotentialtradepartnersRWA SetofresourcesanagentiswillingtoacceptREQag AmountofgivenresourcerequiredbyagentAg
4.9 IfforsomeresourcerAG(Table2liststheabbreviationsusedtodescribethebarteralgorithm)anagentisinastateofCRITICALorSTARVING,ittriestoobtainenoughofthatresourcetogetbacktoaSATISFIEDstate.Firstitmustidentifyagentsthatitcanpossiblytradewithfortheresource.Itdoessobythefollowingprocess,whichisrepeatedforeachresource:
1. AskeachagenttAG(withintraderange)ifitiswillingtotradetheneededresourceandwhatitiswillingtoacceptinexchange.2. CallthesetofresourcesthattAGiswillingtoacceptRWA(tAG)3. IftAGhasenoughoftheresourcebeingrequestedbyAG(tAGisinaTRADINGstateforthatresource)and4. IfrAGhasenoughofoneoftheresourcesbeingdemanded(inaSATISFIEDstateorbetter)bytAG,thenaddtAGtoalistoftradepartners,whichwecan
callTList.5. SortTListinorderofpricefortheresourcebeingsought.
4.10 SincethisprocessisrepeatedforeachresourcerAGsought,iftheagentisinneedofmultipleresources,itwillfirstseektoprocureone,thenafterthat(regardlessofsuccess),itwillproceedtothenextresource.Afterfindingoutwhichagentswithinitstraderangearepotentialtradepartners,AGmustthenasktheseagentstotradeinexchangeforwhatitcanofferthem.Thatprocessisasfollows:
4.11 ForeachagenttAGinTList:
a. CalculatehowmuchoftherequiredresourcetAGiswillingtooffer.tAGiswillingtoofferanyamountaslongasitwouldnottakeitbelowitsTRADINGstate.
b. FilterRWA(tAG),removingresourcesrAGnotabovetheCRITICALthresholdforthatresource.TheresultingsetcanbecalledTRADE_SET.c. CalculatehowmuchoftherequiredresourcetAGiswillingtooffer(sothatitdoesn'tfallbelowTRADING);wecancallthissetOFFER.d. LimitOFFERtotheamountrAGdesired.e. CalculateanamountforeachresourceinTRADE_SETthatisequivalentinvaluetoOFFER.rAGisnotallowedtofallbelowSATISFIEDforanyorthese
resources.f. Ifwecanfindacombinationofsuchresources,thentradethatcombinationofresourceswithtAGinexchangefortherequiredresource.g. Ifwecannotfindsuchacombination,thencalculatethemaximumtotalvalueofresourcesthatwearewillingtotradewithtAG.
i. CalculatetheamountoftherequiredresourcethattAGiswillingtogiveforthatvalue.ii. TradetheselectedamountofresourcesinexchangefortheequivalentamountoftherequiredresourcethattAGiswillingtogive.
h. IfrAGisnowinaSATISFIEDstate,thenstop,otherwisemovetothenextagenttAGinTList.
4.12 Asstated,thevalueofaresourceforanofferingagentisdeterminedbythecosttothatagentofacquiringthatresource.Soifitcostsanagent1000caloriestoacquire10kgofprotein,thenthevalueofthatproteinis100calories/kg.Agentsdonotquestionthevalueofresourcesasdeterminedbyotheragents.Agentsarehoweverabletosortthroughthoseprovidingresources.Thereforeanagentknowswhointheirneighbourhoodcanprovidetheresourcemosteconomically.Thisgivestherequestingagentanadvantageintheexchangerelationship,asitcansortsellingagentsbylowestprice,andsellingagentswillacceptthecosttoAGtoproducethegoodsrAGbeinggiveninexchange.
GeneralizedReciprocalExchange
4.13 Evenasweaddbarter,wemaintainreciprocity-basedexchangesinoursystem,sincewecanreadilyobservethatevencontemporarymarketsocietiesretainkinandreputation-basedreciprocalexchangesalongsidemarketexchanges.Werecognizetwodistinctsystemsofreciprocity,whichwemodelseparately.Thefirstisbasedonkinship.Anagenthouseholdknowsthehouseholdsoftheparentsofthehusbandandthewifeaswellasthoseoftheirsiblings(againbilaterally).Thisleadstotheintroductionofthegeneralizedreciprocalnetwork(GRN),whichoperatesoverthisbilateralkinshipnetwork(Kobtietal.2004;Reynoldsetal.2004;KobtiandReynolds2005;Sahlins1972).InGRN,agentsareabletomakerequestsforresourcesfrommembersoftheirclosekin.Thisprovidesasocialsafety
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netwherebyrelatedhouseholdsbandtogethertohelpeachothersurvive.AgentsarenotexpectedtorepaytheresourcesthattheyobtainintheGRN,soifanagentobtainsmaizefromaparent,theyarenotexpectedtorepaythatgift.Thisworksoutinthelongrunforagentsbecauseifthatparentlaterweretoaskthechildforhelp,thechildwouldreciprocate(Crabtree2012;Sahlins1972).DetailsontheinternallogicoftheGRNcanbefoundinthepaperslistedabove.Inadditiontorequests,agentsintheGRNinaTRADINGstatewilldonatesomeoftheirresourcestoamemberoftheirfamily.AlltradinganddonationinGRNinthisinstantiationofthemodelarelimitedtoageographicaldistanceof6km,althoughthisdistanceischangeable.Moreover,kinwillnotputthemselvesbelowtheSATISFIEDstatetohelp,asthismayputtheirownhouseholdatrisk,andimportantly,GRNisonlyimplementedformaizeandmeat.Theorderinwhichthethreetypesofexchangenetworksareactivatedisoutlinedbelow.
BalancedReciprocalExchange
4.14 Thebalancedreciprocalexchangenetwork(BRN)isareputation-basedborrowing/loaningnetworkthatenablesagentstoexchangemaizeormeatwithneighbourswhoarenotkinintheexpectationthattheywillberepaidthesameamountofthesameresourceatalaterdate.Thisisprobabilistic,soagentswillnotautomaticallyloantosomeonerequesting,evenifthathouseholdhasagoodorneutralreputation(inthismodel,weallowa75%chanceofsayingyestotheseindividuals).Ifanagentloansaresourcetoaneighbour(heredefinedasahouseholdwithinBRNtradingdistanceof8km,butlikeGRNthisdistancecanbemodified),itexpectstoreceivethatresourcebackwhenitasksforit.Agentswillasktoberepaidonceperyear,attheendoftheharvest,orimmediatelyiftheagentisindireneed(inaSTARVINGstate;however,agents,asintheGRN,willnotexchangeiftheyarebelowauser-specifiedstateforriskofdeathbystarvation).Iftheneighbourrepayswhenasked,thenitsreputationremainsintact.Iftheneighbourisunabletorepaytheloan,thiswilldamageitsreputation.Reputationsareonlydyadic(betweentwoagents),soanagentcouldhaveanegativereputationwithoneagentwhilebeingheldinhighesteembyanother(Crabtree2012).
4.15 Agentsareabletoimprovetheirreputationsbyloaningresources.Ifaneighbourloansanagentaresource,itsreputationwiththatagentgoesup.Thismeansthatlaterifthisneighbourisinneedofanotherresourcethatitspartnerinapreviousexchangecanprovide,thispartnerismorelikelydoso.ResourcetransactionintheBRNislike-for-like.Thismeansthatifanagentisloanedsomemaize,thedebtisrepaidinmaize.AsforGRN,BRNisonlyimplementedformaizeandmeat.
4.16 Neighbours(thoseagentsinaBRN)aremuchlessgenerousthankin(agentsinaGRN).AnagenthastobeinaTRADINGstatebeforeitwillconsidermakingaBRNexchange.Thenthereputationoftheaskingagentisconsidered.Theaskingagentneedsapositiveorneutralreputationbeforetheneighbourwillproceed.Ifthesetworequirementsaremet,theagentwillconsiderwhetheritisina"loaningmood"(asdeterminedbytheprobabilitynotedabove).AnagentwillnotallowitselftofallbelowaTRADINGstateinloaningaresourcetoaneighbour.
4.17 BRNpromotesastrong"community"bondamongagents,thoughthesebondsareonlyexpresseddyadically.Whileagentsdonotaccountforthis(ineithertheirmovementalgorithm,orbyseekingtoenhancetheirreputationsasagoal)largercommunitieswithmorepositivelinkagesprovidemoreopportunitiesfortradeandassistance.Ofcoursethisisbalancedbycompetitionforresources;iflocalpopulationsbecometoolarge,resourcesmaybecomelimiting.Thiscanresultinagentshavingtoleavetheircommunitytofindamoreproductivelocation,evenatthecostoflosingtheircurrenttradepartners.Notethatwhileweusethewordcommunity,thisisnotaphysicalconstructwithinthesimulation.Hereweregardacommunitysimplyasanetworkofagentswithinacertainradius,tiedtogetherbytheirexchangepractices.
Sequenceofexchangesinthemodel
4.18 Agentsfirstseektoobtaintheneededamountofaresourceviathebarternetwork.Iftheagentstillhasnotobtainedenoughoftheresourceitneedsfromitstradingpartnersandit'sinaSTARVINGstate,itattemptstouseoneofthereciprocitynetworks.FirsttheagentusestheGRNtoaskupto4kin(thisnumberisachangeableparameterinthesimulation)togiveittheamountit'sshort.Ifitcannotobtainenoughviathismethod,itthentriestoborrowusingtheBRN.Ifafterallthis,rAGisstilldeficient,thenAGdiesiftheresourceismandatory(water,maize)orsuffersmalnutrition(protein),whichmayalsoleadtodeathafter3years.Sincebalancedandgeneralizedreciprocityexchangesonlypertaintoproteinandmaize,agentscanobtainwaterandwoodonlyviabarterorbydirectprocurement.
SocialInfluence
4.19 Agents'behavioursmaybeinfluencedbythebehavioursofthosearoundthem(Waibel,Floreano,MagnenatandKeller2006).Givenachoicebetweenmultiplespecializations,wefactorinwhatanagent'sneighboursaredoingandallowthattoinfluencetheagent'sdecision.AnagentNisdefinedasaneighbourofanagentAgifNandAgaredirectlyconnectedwithinasocialnetwork(foroursimulationthisnetworkislimitedtothetraderadiusofBRN).Ithasbeenshownthatsocialinfluenceoftencanincreasethelevelofagentspecializationwhencomparedtosystemswithnosocialinfluence(CockburnandKobti2009a).CockburnandKobti(2011)showedthataweight-allocatedsocialpressuresystemwouldbecapableofstimulatingtheemergenceofahighlevelofspecializationwithinapopulation.Webaseourcurrentmodelonthatmethod.
4.20 ForeachagentAg,thereshouldexistacompositefunctionSoc(t)foreachtasktinEC.Soc(t)wouldbeafunctionrepresentingthesocialinfluencetowardsperformingtaskt.Anexampleofsuchafunctionwouldbepeerpressuretowardsperformingatask.Inaneconomicnetwork,thesocialinfluencemaybeareflectionofthedemandforaproduct.Insuchasituation,itisalsopossibletocreatethesocialinfluencefunctionsuchthattherealsoexistsnegativeinfluence.Anexampleofthiswouldbenegativeinfluenceinthecaseofapotentialsalethat'slostbecauseacompetitorcanprovideabetterproduct.ThehandlingoftheresultofSoc(t)isdependentupontheagentandthedomain.Giventhesameexampleofanagentsellingaproductandthesamedemand-influencefunction,anagentmayreduceproductionorreducethepriceofitsproduct.
4.21 Forourcase,wefirstdesignater(t)astheresourceproducedbytaskt.Eachagentrequestingaresourcer(t)exertsproductionpressureonitspossibletradepartnersinthefollowingmanner:
1. Locateallagentswithintraderange,placingtheminalistwecallPOSS2. DetermineaninfluencerateIR=1/thesizeofPOSS3. LetrAmount=amountofresourcer(t)thatAgisseekingtoprocure4. ForagenttAGinPOSS
a. exertupwardproductionpressureontAGfortasktintheamountofrAmount×IR(fortAG:Soc(t)=Soc(t)+rAmount×IR)b. LettAmount=amountofresourcer(t)thattAGhasavailable,ORrAmount,whicheverislowerc. exertdownwardproductionpressureontAGfortasktintheamountof2×tAmount×IR(fortAG:Soc(t)=Soc(t)+amountTraded×IR)d. IftAGandAgcompletedatradeforr(t)
i. ThenamountTraded=theamountofr(t)tradedbetweenAgandtAGii. ExertupwardproductionpressureontAGfortasktintheamountofamountTraded×IR(fortAG:Soc(t)=Soc(t)+amountTraded×IR)
(Interpretationsofquantities:4aindicatestoeachagentthatmayprovidetheresourcethatthisagenthasademandfortheresource;4c:Thispressureaccordswithanagent'sexpectationofcompletingatradefortheamountpossible(tAmount).Iftheagentcompletesthetrade,thepressurewillbereversedbasedontheamountofresourcetraded.Iftheagentisunabletosell,thenthisiseitherbecausethereexistsanotheragentthatwasabettertradepartnerfortherequestingagent,ortherequestingagentdidnothavetheresourcesthatthesellingagentwasdemandinginexchangefortheresource.4dii:Thisrewardstheexpectationofsale.Theneteffectisthatifanagentisaskedforaresourceandisabletoprovideit,thenthatmeanstheircurrentlevelofproductionissufficienttomeetdemand.)
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4.22 AsellingagentAg,havingexcessresourcesavailableattheendofaproductionperiod(inaTRADINGstate)alsoexertspressureonitscompetitorsinthefollowingmanner:
1. Locateallagentswithintraderange,placingtheminalistwecallPOSS2. DetermineaninfluencerateIR=1/thesizeofPOSS3. LetrAmount=amountofresourcer(t)thatAghasthatitisstillwillingtotrade4. ForagenttAGinPOSS
a. Ifproductioncostofr(t)ishigherfortAGthanforAgi. ExertdownwardproductionpressureontAGintheamountofrAmount×IR(stateddifferently:Soc(t)=Soc(t)-rAmount×IRfortAG)
4.23 Thereforeanagentwillattempttoindicatetocompetitorswithhigherproductioncoststhatitisabettersourceoftheresourceandthatitwouldbemorecapableofprovidingthatresourcetothem.Thisdealswithagentswhoarewithinrangeofeachother,butarebothself-sufficientwithregardstoaresource.Exertingcompetitivepressureencouragesthelessefficientagentstolowertheirproductionandrelyonthemoreefficientonesfortheresource.
4.24 Anagentthatispressuredsociallydoesnothavetochangeitsbehaviour.Sometimes,ifanagentisalreadyinaTRADINGstateforaresource,theywillignorepressuretoincreaseproduction.Thereasonbehindthisbehaviouristhattheagentdeterminesthatitalreadyhadsurplus,butnoonewasabletoexchangeforit(possiblybecausenoagenthasanythingtoofferthattheagentiswillingtoaccept).Inthatcase,increasingproductionwillnotleadtoanincreaseintrade.AgentsalsowillnotdecreaseproductioniftheyarebelowaSATISFIEDstate.Thisoccursiftheagentdeterminesitcouldnotprocuremoreoftheresourcebecauseitdidnothaveanythingtotradetothesellingagents.Thereforereducingtheirproductionwillnotresultinthemobtainingmoreneededgoodsandwouldthereforebeantitheticaltotheirsurvival.
Updatefunction
4.25 Weuseauniformupdatefunctionforeachtaskinourweightsystem.Thisupdatefunctionisappliedattheendofeachyear,anddetermineshowtheagentwillallocatetimefortheupcomingyear.Giventasktthatprovidesresourcerandxamountofresourcer:
1. IftheagentisinaTRADINGstate,thenassumey=x-thethresholdforTRADING.Theagentwillthenreducetheweightoftasktproportionallysoitshouldresultintheagentproducingylessofrthanitproducedthisyear.Inotherwords,iftheagenthas200kgtoomuchmaize,thenitwillreducetheweightitappliestofarmingsothattheagentexpectstoproduce200kglessmaizenextyear.Toavoidanagentmakingtoodrasticacut,basedperhapsonanabnormalamountofaresourcebecauseoftrading,werestricttheamountanagentisallowedtoreduceaweightto50%ofthecurrentvalue.
2. IfanagentisinaCRITICALorSTARVINGstate,thentheagentwillattempttoincreasetheweightforthetasktsothatitexpectstoproduceenoughadditionalresourcesinthefollowingyeartogetittoaSATISFIEDstate.Again,toavoidovercompensating,werestrictthemaximumincreaseto300%.
3. Applyanysocialpressureasdeterminedpreviously.
Results
5.1 Toevaluatetheimpactsoftheseadditionstothebasesimulation,weranthesimulationthreetimes,oncewithagentsallocatingeffortbasedonlyonfamilyneeds(Scenario1),whichissimilartotheoriginalsimulationbutwithadditionssuchasthebarternetworkandresourceinheritance.Wedonotexpectthisscenariotoresultinmuchspecialization.Wethenranthesimulationwithagentsallocatingeffortbasedonlyontheircurrenteconomicstate(Scenario2).Inthatcase,agentssettheirweightsfortasksbasedontheamountofaresourcetheyhaveremaining.Iftheyhavemorethantheyneedbasedontheirreservethreshold(TRADINGstate),thentheyreduceproduction.Theyincreaseproductioniftheyarebelowthislevel.Thecalculationforthisupdatewasexplainedpreviously.Finallyweranthesimulationwithbotheconomicstateconsiderationsandsocialinfluenceenabled(Scenario3).Withtheadditionofsocialinfluence,agentswillreducetheirproductionofaresourceiftheyareinaTRADINGstateandthereisanagentavailablethatcanprovidetheresourcemorecheaplythantheagent'scostofproduction.
5.2 Wecomparethedifferentmethodsusingseveralmeasures.Onesuchmeasureistheleveloftaskspecialization(asexplainedbelow),whichisapplicableonlytothesecondandthirdscenarios.Wealsocomparetheproportionofthepopulationineachofthree"settlementtypes"differentiatedbythenumberofhouseholdscohabitingspecificcellsinthemodel.Wealsonotethechangeinthevolumeofexchangewhenagentsallocatebasedonlyonneeds,andwhentheyattempttospecialize.Additionally,wemeasuretheaccumulatedwealth(measuredasdefinedbelow)ofthepopulationunderthesethreescenarios.
5.3 Finally,wecomparethestructureoftheexchangenetworksthatforminScenario2,andinScenario3,usinganapproachdesignedtorevealthedegreeofcompartmentalizationinthenetworks.Theexchangenetworkprovidesanothermeansofcharacterizingtheoverallstructureofthesystem;forexample,howdoesthedegreeofspecializationaffectthestructureoftheseexchangenetworks?Innetworkanalysisoneanalyzesthefrequencyofnodes(theagents)andthefrequencyofedges(here,theexchangesbetweenagents)(Newman2010).Byunderstandinghowtheconnectance(theproportionofpossiblelinksbetweenagentsthatarerealized)ofeachagentchanges,andvariabilityinthenumberofedges,wecanbetterunderstandphenomenaofinterestinthereferencesystemsuchastheresilienceofthenetworktoperturbationortheefficiencyofthenetworkindistributinggoodsorinformation.Wepresumethatdifferentnetworkstructureshavedifferentoutcomesfortransmissionofinfluence,innovations,andsociallyinfluencedbehavioursingeneral.Belowwecontrastyearsofhighandlowpopulationwithinandbetweenscenarios.
5.4 Tomeasurethedegreeoftaskspecialization,weuseamethoddevelopedinGorelick,Bertram,KilleenandFewell(2004)tocalculatetheleveloftaskspecializationwithinthesystem.Weusetheweightgiventoeachtasktocalculatetheleveloftaskspecializationattheendofeachstepinthesimulation.Theweightsofallagentsarethenstoredinann-x-mmatrix,wherenisthenumberofagentsandmisthenumberoftasks.Thereforeeachrowinthematrixrepresentsanagent'stimeallocationamongalltasks.Thematrixisthennormalizedsuchthatthetotalofallvaluesinthematrixis1.ThemutualinformationandShannonentropyindex(Shannon1948)arethencalculatedforthedistributionofagentsacrosstasks.TheShannonentropyisthendividedbythemutualinformationscore,resultinginavaluebetween0and1.Avalueof1indicatesthatallagentsspendalltheirtimeononetask(notofcourseinthesametask),whileascoreof0meansthatthereisnotaskspecialization,aswouldbethecasewheneachagentdividesitstimeequallyamongtasks.SeeGorelicketal.(2004)forafullexplanationofthismethod.
EffectsonPopulationSizeandDegreeofSpecialization
5.5 AscanbeseeninFigure1,andasexpected,thereisamarkedincreaseinpopulationsizewhenspecializationisadded(Scenario2vs.1).Somewhatsurprisingisthatpopulationlevelsareslightlylowerwhensocialinfluenceisaddedtoeconomicspecialization,thoughpopulationsconvergelateinthesimulation(Scenario3vs.2).Perhapstheadditionofsocialinfluencecanmakeagentstooreliantonthesuccessofothersfortheirownsuccess,somewhatanalogoustoHegmon'sdemonstrationthatsharingtoobroadlycanbedetrimentaltocommunitysurvival(Hegmon1989).Anotherpotentialexplanationmaybethatsinceagentsheredonotconsidersocialnetworkswhenmoving,theymaybeabletomoveoutsideoftheirsocialnetwork,populatinganareawheretheyhavenoexchangepartners.Thisincreasesthelikelihoodthatagentswillnotbeabletoexchangeuntiltheyareabletorebuildanexchangenetwork(Crabtree2012).
5.6 Wealsofoundthatthedegreeofproductionspecializationincreasedsignificantlyasweaddedsocialinfluencetothefactorsthatagentsconsider(Figure2,Scenario3vs.2).ThisfurtherconfirmsthefindingsofCockburnandKobti(2009a;2009b).Inallfigures,AD600correspondswiththeinitialcolonizationoftheVEPareabyfarmers.However,thisareawasinfactdepopulatedaroundAD1280,afactnotreplicatedinthesesimulations.Instead,weseeaspikeinthelevelsofspecializationaroundthistimeinoursimulation.
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5.7 Therearefactorstobenotedintheperformanceoftheunderlyingspecializationmechanismthatwewerenotabletofullyexplorehere.Namely,thenumberofyearsofstoragewealloweachagentisveryimportant.Aswehavenomonetarycurrency(outsideofcaloriccosts)anddonotallowexchangesofgoodsforlabour,storedresourcesaretheonlysourceofwealthandassetsforexchange.Investigationsnotpresentedhereshowthatthelevelofspecializationincreasesasweincreasethenumberofyearsofstorageallowed.Wecanconcludethataddingsocialinfluencetoourreferencesystemwitheconomicspecializationleadstoapopulationthatisnotnecessarilylargerinsize,butonethatismorespecialized.
Figure1.Populationlevelsforeachofthethreescenarios;Scenario1needsonly;Scenario2economicstate;Scenario3basedonbotheconomicstateandsocialinfluence.Tonoteishowmuchhigherpopulationsarewhentheyarenotbasedonneedsonly.
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Figure2.ThedegreeofproductionspecializationbetweenScenario2foreconomicstateandScenario3foreconomicstateandsocialinfluence.
EffectsonDegreeofAggregation
5.8 Asnoted,agentswillmoveiftheyarenotthrivingattheircurrentlocation.Whenchoosingadestination,agentsdonotfactorinthepresenceofpotentialexchangepartners,oranyexchangenetworksthatmayexistamongthosehouseholds,unlikeinCrabtree(2012).Ourresultsshowthatagentsaremorelikelytocohabitthesamecellwhentheyspecialize,asseeninFigure3.Withoutspecialization,agentsprimarilyliveinsmallhamletsof1-2households,andfewincommunitycenters(of9ormorehouseholds).Wefoundthatwithjusteconomicstateinfluencingplanning(Scenario2vs.1),agentsaremorelikelytoliveinbighamlets(3-8households),surpassingtheproportionlivinginsmallerhamletsafteraboutAD750intherunspresentedhere.Theproportionofagentslivingincommunitycentersisalsogreaterineitherscenario2or3thanin1.Thismaysuggestthatagentsmovelessasaresultofspecialization,oritmaysuggestthattheyarebetterabletotoleratetheeffectsofscramblecompetitionforresourceswhentheirresourceneedsarecomplementaryratherthanredundant.Moregenerallytheseresultssuggestthatanincreaseinspecializationmightoftenleadtoincreasesinsizesofthelargestsites,andinthedegreeofaggregation,inthearchaeologicalrecord.
5.9 Interestingly,whencomparingScenario3vs.2,weseethatagentstakingintoaccountonlyeconomicstate(Scenario2)aremorelikelytoliveincommunitycenters(>8households)formostofthesimulation.AgentsinScenario3aremorelikelytoliveinbighamlets(of3-8households)thanaretheScenario2agents.Thesedifferencesarerelativelyslight,however,andmightdisappearifweweretorepeatthisexerciseusingmultiplerealizationsofeachoftheseeconomicscenariosusingdifferentrandomnumberseedsanddifferentparametersettingsforbasicagentoperation.ThestrongersignalisthecleardifferencebetweenthegreateraggregationexpectedunderScenarios2or3relativetoScenario1.
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Figure3.Proportionofhouseholdsineachtypeofsettlement,hamlets,bighamletsandcommunitycentersforScenario1needs,Scenario2economicstateandScenario3economicstateandsocialinfluence.
EffectsonVolumeofExchange
5.10 Alongwithanincreaseintheproportionofhouseholdslivinginlargercommunities,weobservedasignificantincreaseinbarterundereitherofthescenariospromotingspecialization,comparedtotheconditionwhereagentsallocateeffortsbasedontheirprivatesubsistencerequirements(Scenario1).Thisisdueinparttoworkersworkingmorehoursonaverage,andthustryingtoproducemorethantheyneedtomeettheirfamily'sneeds.Theexcesssupplyofresourcesresultsinmoreagentsinshortagebeingabletofindsomeonewillingtomeetthatdemand.WeseeinFigure4thatthereisverylittletradinginsomeresourcessuchaswoodinthe"needsonly"scenario(whereasmuchisrequested,butalmostnoneisexchanged).Withagentsjusttryingtoproduceenoughfortheirownfamily,it'sunlikelythattheywilloverproduce,andsotheyaccumulatenoexchangeablesurplus.Thereforethereisnobarter,despitethefactthattherestillisahighlevelofdemandforwood.Withthechangeinallocationstrategymoreofthedemandforsuchresourcescanbemetbecausethereismoreoverproductionofresources.Althoughthelevelofdemandisnotfullymetunderspecialization,theunmetdemandismuchlessthaninthe"needsonly"scenario.
Figure4.Volumeofexchangeofwoodperscenario;solidlinedepictsrequestedwood,whiledottedlinerequestsexchangedwood.NotehowinScenario1theneedsonlyscenariowoodisrequestedfrequentlybutseldomexchanged.
EffectsonVolumeofStorage
5.11 Figure5revealsthatwhenagentsallocatetheirlabourbasedonlyonneeds(Scenario1),wefoundthattheystorelessthaninthespecializationscenarios(2and3),despitethefactthattheirstoragerestrictionsareidentical.Thisisasexpectedsinceagentsprocuringonlywhattheyneedrarelyoverproduce.Overproductioninthatcaseisdueeithertotheinabilityofanagenttoaccuratelyestimatetheneedsofitsfamily,orinabilitytoprocureexactlytheamountrequired(forexampleit'snotpossibletoonlykillhalfadeer).Ontheotherhand,whenallocatinglabourbasedoneconomicandsocialfactors,agentsaremuchmoreproductive.Theresourcestheyoverproducearemaintainedinthesystem(thesociety),resultinginhigheraverageagentwealth.Wecanseethatthereisstillalowstorageamountformeat.Thisisduebothtothehighdecayrateforthisresourceinstorage,aswellasthelandscape-widedepressionofthemostimportantmeatsource,deer(bothinourmodels,andintheworldtheyreference).Averagestoragelevelsdonotchangenoticeablywhensocialinfluenceisaddedtoeconomicspecialization,eventhoughthatadditionresultsinasmallincreaseofspecialization,aswesawinsection5.1.
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Figure5.Storagebasedoneachscenario.Notethatintheneedsbasedscenario,Scenario1,agentsstoremuchlessthanintheothertwoscenarios.
EffectsonSocialNetworks
5.12 Asseenabove,exchangeincreaseswheneconomicstateandsocialinfluencearetakenintoaccount,asshowninFigure4forwood.Additionally,storageofmostresourcesisgreaterwhenagentsspecializethanwhentheyonlytakeintoaccounttheirneeds,asseeninFigure5.Finally,whenagentsspecialize,populationsincrease(seeFigure4forexample).Thesethreeresultsleadustoexpectthatthesocialnetworksthatformfrombarteringofeachoftheseresourceswillbemarkedlydifferentamongthethreescenarios:whenagentstakeintoaccountonlytheirneeds(Scenario1)andwhentheyspecialize(Scenarios2and3).Performinganetworkanalysisonthedyadicexchangesbetweenagentsprovidesameansforcomparingthestructureofthesystememergingfromtheseinteractions.
5.13 Forthisanalysisweidentifiedfourpointsintime(asreportedinTable3)fromScenarios2and3.Table4reportsthenumberofexchangesthroughtimeinthebarternetworkforScenario2.Table5reportsthecorrespondingfigureswhenallocationofeffortisbasedoneconomicstateandsocialinfluence(Scenario3).
5.14 Notsurprisingly,whenthesimulationbeginsexchangeishigh.Whentheagentsareinitiallyseeded,randomly,onthelandscape,manyareplacedinareaswithpoorproduction.Consequentlytheagentstrytomakeupfordeficienciesofresourcesbybarteringwithoneanother.Withrespecttothenumberofedgespernode,bothScenario2and3arerathersimilar,anddeclineslightlythroughtime.However,exceptinthefirstyearofthesimulation,Scenario3alwaysgeneratesmoreexchangingagents—nodes—andmoreexchanges—edges—thandoesScenario2.
5.15 Anotherinterestingcontrastbetweenthetwoscenariosliesisinthedifferingdegreeoftheclusteringcoefficientthateachnetworkgenerates.Thenetwork'sclusteringcoefficientisthemeasurementofthenumberofedgesbetweentheneighboursofanodendividedbythemaximumnumberofedgesthatcouldexistbetweentheneighboursofnoden,asdescribedinAssenov,Ramirez,Schelhorn,LengauerandAlbrecht(2008).Theclusteringcoefficientofanodenis:
Cn=en/(kn(kn-1))
"whereknisthenumberofneighborsn,andenisthenumberofconnectedpairsbetweenallneighborsofn"(Assenovetal.2008NetworkAnalyzerSupplementalMaterials).Theclusteringcoefficientofanodeisalwaysscaledbetween0and1,whichallowsforcomparability(Assenovetal.2008;Donchevaetal.2012).Inthiscontext,ahigherclusteringcoefficientmeansthattheentiresystemofexchangesexhibitsmoreclusteringintocondensedcomponents.Alowerclusteringcoefficientmeansthatthesystemofexchangesismoredispersedoverall.Notethatthisis"aspatial"inthattheclusteringofexchangesisnotnecessarilyrelatedtothelocationofagentsonthelandscape.Here,wecalculatetheclusteringcoefficientasaveragedacrossallofthenodestogiveaclusteringcoefficientfortheentirenetwork.Clusteringcoefficientsarecalculateddifferentlydependinguponwhetherthenetworkisdirectedorundirected.Networksofexchangearedirected,sinceonehouseholdisprovidingresourcesforanother,soanalysesarebasedondirectionality;eventhoughexchangeisreciprocal,eachexchangeitselfis
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directional.Forthisanalysistheclusteringcoefficientiscomputedfordirectednetworks.TheseresultsarereportedbelowinFigure6.
5.16 ComparingScenarios2and3,weseeinFigure6andTable5thatthesociallyinfluencednetworkgenerallyexhibitsahigherclusteringcoefficientevenastheoverallconnectivityoftheagentsisdeclining.Thissuggeststhatthesociallyinfluencednetwork(Scenario3)ismorereliantonafewnodestosupplytherestofthenetwork.Bascompte(2010)characterizestherelianceonfewnodestosupplythenetworkasa"compartmentalization"or"thetendencyofacomplexnetworktobecomeorganizedin'compartments'characterizedbyagroupofspeciesinteractingmorestronglyamongthemselves"(Bascompte2010:765).
5.17 ThoughBascomptereferstobiologicalnetworks,compartmentalizationissimilarlyusefulhere.Insteadofdifferentspeciesinteracting,thecompartmentsareformedofgroupsofagentswhotogethercanbeconceptualizedascommunities.Forexample,inyear1100ofScenario3(Figure7c)theoverallnetworkhasbeendividedintomultiplegroups;someofthesegroupsareconnectedthroughjustafewindividuals.Therearealsooutlyinggroupsthatarecompletelycutofffromtheflowofgoodsinthemainnetworkandothersubnetworks.Thesenetworksappeartobemorecompartmentalized,asalsoindicatedbytheslightlyhigherclusteringcoefficientinTable5,thanthenetworksgeneratedunderScenario2.
5.18 IfonewantedtodisrupttheflowoftheScenario3networkstherearecertainnodesthatwouldbeinstrumentaltodestroy.InScenario2year1100(Figure6c),ontheotherhand,thereisamoreequaldistributionofnodeinteractions;ifonerandomnodeweretoberemoved,itwouldbelessdisruptivetotheoverallflowofthenetworksincenode-to-edgedistributionisfairlyequal.InScenario3ifoneweretoremovearandomnodetherewouldbeahighprobabilityofremovinganon-essentialnode.However,if,perchance,oneofthe"hub"nodes(thenodewiththemostconnections)wereremoved,itsentirenetworkwouldcollapse.Thehubnodesprovidethebulkoftheinteractions,andonceremovedmorecompartmentalizationwouldoccur—portionsofthenetworkwouldnolongerbeconnectedtoeachother(seeReynolds,Kobti,KohlerandYap2005).
Table3:Characteristicsofpopulationatyearswhennetworksareassessed
Year Characteristicofpopulation600 Startofsimulation1000 Populationpeak1100 Populationtrough1200 Populationpeak1300 Populationtrough
5.19 Wehavenotyetinvestigatedwhetherthe"hubnodes"ofScenario3arealsorelativelywealthy,thoughitislikelythattheyhavebothlargefamilies,andmorestoragethanaverage;wedoknowtheyarerelatively"rich"inthenumberofconnectionstheyhave.Wealsohypothesizethattheyareadvantageouslyplacedonthelandscapebothwithrespecttolandscapeproductivityandwithrespecttotheirabilitytoactasintermediariesbetweentwonetworksegmentsbecauseoftheirlocation.Clearlytheyareinstrumentaltothedistributionofthegoods.
5.20 Uponvisualinspectionofthefigureswecanseethatexchangeslookverysimilarinyear600forbothstrategies(Figures7aand8a).Foryear1100,inthenetworkcreatedbyScenario2agentstherearefewexchanges,anditappearsthateachexchangingagentisequallyconnected.However,inyear1100underScenario3weseethatexchangeismorefrequent.Possiblythesocialinfluencethathelpstocreate"hub"nodesalsofacilitateexchangeamonglargernumbersofagentsthanispossiblethrougheconomicstatealone.
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Figure6.NetworkclusteringcoefficientforeachofScenario2economicstateandScenario3economicstateplussocialinfluenceforyear600,1000,1100,1200and1300.CoefficientsarereportedinTable4andTable5.
Table4:Connectivitywhenallocatingonlybasedoneconomicstate(Scenario2)
Year Nodes Edges NetworkClusteringCoefficient Numberedges/node600 181 478 0.130 2.641000 595 1592 0.013 2.681100 443 1194 0.014 2.701200 271 678 0.011 2.501300 317 749 0.016 2.36
Table5:Connectivitywhenallocatingbasedoneconomicstateandsocialinfluence(Scenario3)
Year Nodes Edges NetworkClusteringCoefficient Numberedges/node600 180 468 0.091 2.601000 625 1746 0.026 2.791100 495 1320 0.020 2.671200 455 1160 0.023 2.551300 470 1185 0.016 2.52
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Figure7.Exampleexchangenetworks,scenario2.Pinkdotsrepresenthouseholdsandbluelinesrepresentexchanges.Multiplelinesrepresentmultipleexchangesforthosehouseholds.a.year600,b.year1000,c.year1100,d.year1200,e.year1300.Graphsareformedbasedonconnectance,notonphysicalspace.Nodes
towardtheedgesaretheleastconnected,whilenodestowardthecenterarethemostconnected.
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Figure8.Exampleexchangenetworks,scenario3.Pinkdotsrepresenthouseholdsandbluelinesrepresentanexchange.Multiplelinesrepresentmultipleexchangesforthosehouseholds.a.year600,b.year1000,c.year1100,d.year1200,e.year1300
Conclusions
6.1 Inthispaperwecreatedaweight-basedsystemforagenttimeallocation,resultinginspecializationofproduction.Thisinturnrequiredustodevelopasystemofbartersothatagentscouldexchangethegoodstheyvariablyproduced.Weexploredtwoscenariosforsuchspecialization.Inone,agentsareallowedtodeterminethedegreeofspecializationbasedonlyontheireconomicstate.Inthesecond,theytakeintoaccountboththeireconomicstateandasocialinfluencefromtheirneighbours.Asexpected,householdsbecamemorespecializedwhentheywere"allowed"todoso.Agentsalsobecameincreasinglyco-resident(thatis,morehouseholdsco-residewithinspecific200m×200mcellsinthesimulation),exchangedmoregoodswitheachother,andachievedhigherglobalpopulationlevelsineitherofthespecializationscenariosthaninScenario1.
6.2 Thesocialnetworksformedfromthetwotypesofspecializationdisplayedsomewhatdifferentcharacteristics.Whilebothdisplayedincreasingcompartmentalizationthroughtime,Scenario3displayedagenerallyhigherclusteringcoefficient.Thesocialinfluenceofagentsinthissimulationisimportanttofacilitatetheflowofgoodsthroughoutthesystem.Futureresearchintothe"wealth"ofthehubnodeswillhelpelucidatehowthesenodessupplythenetwork.
6.3 Aswebegintoexplorethisnewmodelusingparameterizationsmorereasonableforourreferencecase—theBasketmakerIIIthroughPuebloIIIperiodsinthecentralMesaVerderegion—wewillinvestigateseveralquestionsraisedbytheanalysishere.Whatarethespatialcharacteristicsofthenetworksformedbythecombinationofspecializationandbarter?Howdothesizesandlocationsofthecommunitiesdiscoverableinthemodelcomparewiththoseknownfromourstudyarea?Doesthecombinationofbarterandspecializationincreasethesizesofthecommunitiesinthemodel,relativetocommunitiesdiscoverablefromthenetworksgeneratedbyreciprocityamongagentswithlargelyredundantproduction?
6.4 Kohler,HerrandRoot(2004)suggestedthatmanyofthedifferencesbetweenpre-AD1280inSouthwestColoradoandthepost-AD1375PueblosocietiesinthenorthernRioGrandecanbeattributedtotheadditionofproto-marketforcestoeconomiespreviouslystructuredbyeconomiesbasedmostlyonreciprocity.Abbottetal.(2007)suggestedthatintheHohokamareainthedesertsofsouthernArizona,periodicmarketplacesandbarteringoodssuchasearthenwarecontainersmaybeimportantstructuringforcesevenearlier,byaroundAD1000.Furtherworkwiththismodelwillhelpusunderstandtheextenttowhichdifferencesinsiteandcommunitysizesandlocationscanbelegitimatelyattributedtotheadditionofbarterandspecializationtoeconomiespreviouslybasedonreciprocity.
6.5 Inthemodelspresentedhereweareengagingincounter-factualexplorations,sinceitappearsunlikelytousthatthehighdegreesofspecializationandlargeamountsofbarterthattypifyourScenarios2and3infactcharacterizedtheeconomiesofsocietiesinsouthwesternColoradobetweenAD600and1300,whentheareawemodelwasdepopulatedinacollapsethataffectedtheentirenorthernSouthwest.Assumingthatthisdepopulationwasnotjustduetoalargeexternalshock(whichmayinfacthavebeenthecase)wecanusethesemodelstoguideourintuitionsastowhetherthepre-1300societiesinsouthwesternColoradowouldhavebeenmore(orless)resistanttothiscollapseiftheyhadinfactdevelopedmorespecializationandbarter.
6.6 Intheirrecentreviewofthestructuralcharacteristicsofsystemsapproachingandundergoingcriticaltransitions,Schefferetal.(2012)proposethat,ingeneral,modularityandheterogeneitycreatemorerobust(lessfragile)systemsthandoconnectivityandhomogeneity.Inourmodelsystems,itistruethatspecializationandbarterleadtomoreconnectivityamonghouseholds,aspointedoutinsection5.5,butontheotherhand,thosehouseholdsaremoreheterogeneousthanintheScenario1case,whereallhouseholdsengageinthesamesuiteofactivitiestoapproximatelythesameextent.So,whiletheirhighconnectivitymaymakeScenario2-and3-typesystemsmorepronetoundergoingacriticaltransitionsuchascollapse,theirheterogeneitymayprovidesomeprotectionagainstthatpossibility.Thatthepost-1300PueblosocietiesinthenorthernRioGrandeseemtohavebeenhighlystableinspiteoftheir(presumed)highdegreeofconnectivitymaysignalthatheterogenetityismorefundamentaltostabilitythanisdegreeofconnectivity.ItisalsopossiblethattheagriculturalsystemsdevelopedinthenorthernRioGrande—basedonwatermanagementratherthanrainfall—weresomuchmorestablethatanydeleteriousconsequencesforhighconnectivitywereneverexpressed.
6.7 ThenextphaseinthisstrandofVEPresearchwillinvolveenlargingourstudyareatoincludebothsouthwesternColoradoandthenorthernRioGrande.ThiswillprovideuswithanopportunitytoseetheextenttowhichthestructureoftheenvironmentinthenorthernRioGrandeitselfencouragestheformationofspecializationandbarter,orwhetherthepossibilityofengaginginasinglespecialization(suchasgrowingcotton,whichwasnotpossiblethroughoutthatarea,orinsouthwesternColorado)canprovokeacascadeofotherspecializationsinthemodelhouseholds.
Acknowledgements
ThisresearchwasmadepossiblebygrantDEB-0816400toKohler,CraigAllen,ZiadKobti,andMarkVarien.CrabtreealsoacknowledgessupportfromgrantDGE-080667.CrabtreeandKohlerthanktheLaboratoireChrono-Environnement(UMR-6249)oftheMaisondesSciencesdel'Hommeetdel'EnvironnementC.N.LedouxandtheUniversitéofFranche-ComtéofBesançonforsupportwhilecompletingfinaleditstothismanuscript.
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Appendix-FormalProblemDescriptionandApproach
ProblemDescription
GivenagentAg,thesettAGandaresourcerAG,howdoesanagentallocateitsrAGamongeachtasktintAG?
So:Σxi=S(RAg)whereiiseachtaskintAG,S(rAG)referstotheamountoftheresourcerAGavailable,andxireferstoafractionofS(rAG).
Theproblemalsoinvolvesthefollowingconditions:TheproblemiscontinuousoveraperiodofiterationsS(rAG)changesbetweeniterationsxiisallowedtochangeoveriterationsEachagentAgalsohasasetREQ(Ag),suchthataresourcerinREQ(Ag)needssomeamountofrforsubsistencebetweeniterations.
Weight-basedmodelfortimeallocationamongtasks
Weusedaweight-basedapproachforagents'timeallocationbasedonCockburnandKobti'sstudy(2011).Aquicksummaryofthatapproach(namedWASPS)ispresentedhere.
ForeachagentAg,weproposeasetEC,whereeiinEC.ThereisataskiintAGandeirepresentstheweightoftaski.
TaskweightsinECarerelative,thereforeforthegivenataskiandaresourcetobeallocatedrAG,theamountofrAGtobeallocatedtotaskiis:ei/S(EC)×S(rAG)whereS(EC)isthesumofallelementsinEC.WemakenoassumptionsabouttheinitializationoftheweightsinEC.Theycanberandomlyassigned,orinitializedbysomeothermethod.Ataskhavingaweightof0willresultinthetaskbeingallocatednoneofrAG.AgmustpossesssomeevaluationfunctionP(t)foreachtasktinEC.P(t)isassumedtobeacompositefunction,assumedtobeaneconomicperformancefunction.P(t)isappliedtoeachtaskinECaftertheperformanceofthattask,thereforerepresentingtheresultofperformingthetask.IfP(t)>0,thetaskisassumedtohavehadapositiveresult,inwhichcaseetisincreasedbysomefactor,whichisdomaindependent.InthecaseofP(t)<0,etissimilarlydecreasedbysomefactor.TheresultofthisprocessistheupdatingoftheweightsinEC,whichinturndeterminehoweachagentallocatestheresourceinquestion.MoredetailsonthemethodologycanbefoundinCockburnandKobti(2011)
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