【BIS】令牌组学和区块链碎片化

BISWorkingPapers

No1335

Tokenomicsandblockchainfragmentation

byHyunSongShin

MonetaryandEconomicDepartment

March2026

JELclassification:D82,E42,G23,L14,O33

Keywords:blockchain,tokenomics,networkeffects,stablecoins,decentralisedconsensus,globalgames,monetarysystem,fragmentation

BISWorkingPapersarewrittenbymembersoftheMonetaryandEconomicDepartmentoftheBankforInternationalSettlements,andfromtimetotimebyothereconomists,andarepublishedbytheBank.Thepapersareonsubjectsoftopicalinterestandaretechnicalincharacter.TheviewsexpressedinthispublicationarethoseoftheauthorsanddonotnecessarilyreflecttheviewsoftheBISoritsmembercentralbanks.

ThispublicationisavailableontheBISwebsite(

).

©BankforInternationalSettlements2026.Allrightsreserved.Briefexcerptsmaybereproducedortranslatedprovidedthesourceisstated.

ISSN1020-0959(print)

ISSN1682-7678(online)

Tokenomicsandblockchainfragmentation*

HyunSongShin

BankforInternationalSettlements

March5,2026

Abstract

Moneyisacoordinationdeviceunderpinnedbystrongnetworke§ects:themoreothersacceptaformofmoney,themoreIwishtoadoptittoo.Thedecentralisationagendaofpublicpermissionlessblockchainsundercutsthesenetworke§ectsandleadstofragmentationofthemonetarylandscape.Validatorswhomaintaintheblockchainneedtoberewardedtoplaytheirrolewiththenecessaryrewardincreasinginthedegreeofdependenceonothervalidatorsíactionstosustainconsensus.Sincetheserewardsmustultimatelybebornebyusersthroughcongestionrents,capacityconstraintsareafea-ture,notabug,especiallyforblockchainswithmorestringentstandardsforconsensus.

Newblockchainswithlessstringentthresholdsforconsensusenterthemarkettoserveuserspricedoutofincumbentchains.Theresultingfragmentationundercutstheverynetworke§ectsthatgivemoneyitssocialvalue.Stablecoinsinheritthisfragmentationfromtheblockchainsonwhichtheyreside.Theanalysishasbroaderimplicationsforthefutureofthemonetarysystem.

JELclassiÖcation:D82,E42,G23,L14,O33

Keywords:blockchain,tokenomics,networke§ects,stablecoins,decentralisedconsen-sus,globalgames,monetarysystem,fragmentation

*TheviewsexpressedherearemyownandnotnecessarilythoseoftheBIS.

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1Introduction

Networke§ectsunderpinthecoordinationroleofmoney.Thekeytoitsroleisthefeedbackloopbetweengreateracceptanceandgreateruse.Themoremerchantsacceptaparticularcurrency,themoreconsumerswishtoholdit;themoreconsumersholdit,themoremerchantswishtoacceptit.Thisvirtuouscircleisthehallmarkofawell-functioningmonetarysystem.

Centralbankshavehistoricallyservedastheinstitutionalanchorforthiscoordination.Byissuingauniformcurrencyandstandingbehinditsvalue,thecentralbankprovidesthefocalpointthatenableseconomicagentstocoordinateonacommonmediumofexchange.Thecommonknowledgeofthecentralbankíscommitmentiswhatunderpinstheself-reinforcingnatureofmonetaryexchange.Justasacommonlanguagefacilitatescommunication,acommoncurrencyfacilitateseconomicexchange(BIS(2023)).

Thepromiseofblockchaintechnologywasthatthiscoordinationfunctioncouldberepli-catedwithoutacentralauthorityñthatthedistributedconsensusofvalidatorscouldsub-stituteforthetrustplacedinacentralbank.Inanequilibriumwithmonetaryexchange,holdingmoneyisarecordofgoodssoldorservicesrenderedinthepast.Inthissense,moneyservesasarecord-keepingdevice.Themottoisthatìmoneyismemoryî(Kocher-lakota(1998)).Inacentralisedsystem,trustedintermediaries(suchasacentralbankoracommercialbank)maintaintheledgerandhavethepowertoupdateit.Inadecentralisedsystem,thisauthorityisdispersedamongvalidatorsñparticipantswhocheckandrecordtransactionsñandthesevalidatorsmustreachagreementonthetruestateoftheledger.Truthiswhateverisdeemedtobesobytheconsensusofnetworkmembers.

Ablockchainis,atitscore,asharedledgerñalistoftransactionsthatismaintainednotbyasingleinstitutionbutbyadistributednetworkofvalidators.Transactionsaregroupedintoìblocksîthatarechainedtogetherinsequence,hencethename.Apublicpermissionlessblockchainisonethatanyonecanjoin:thereisnogatekeeperdecidingwhomayparticipateasavalidatororasauser.

Thede

ningfeatureofapublicpermissionlessblockchainisitsconsensusmechanismñthesetofrulesbywhichvalidatorsagreeonwhichtransactionsarelegitimateandinwhatorder

theyarerecorded.Withoutsuchamechanism,validatorscoulddisagreeaboutthestate

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oftheledger,andthesystemcouldnotfunctionasarecord-keepingdevice.TheoriginalconsensusmechanismintroducedbyBitcoinwasproofofwork(PoW),wherevalidators(calledìminersîinthiscontext)competetosolveacomputationallyintensivecryptographicpuzzle.Thewinnerearnstherighttoaddthenextblockoftransactionsandreceivesarewardñnewlymintedtokensplusfeespaidbyusers.Themorerecentandnowmorewidelyadoptedmechanismisproofofstake(PoS),wherevalidatorspledgeaquantityoftheblockchainísnativetokenascollateral(theirìstakeî).Validatorsareselectedtoproposeandverifyblocksinproportiontotheirstake,andmisbehaviourispunishedbyìslashingîñtheconÖscationofstakedtokens.

EthereumístransitionfromPoWtoPoSinSeptember2022(theìMergeî)markedaturningpoint.Itreducedtheblockchainísenergyconsumptionsharplywhileshiftingtheeconomicfoundationsofvalidatorincentivesfromhardwareinvestmenttocapitallock-up.Butthecorecoordinationproblemremained:validatorsmuststillbesu¢cientlyrewardedtocontributetothegovernanceoftheblockchain.Therewardsmustcompensatevalidatorsnotonlyforthedirectcostsofrunninginfrastructurebutalsofortheriskthatthegroupofvalidatorsfailstocoordinate.

Thiscoordinationproblemmanifestsconcretelyingasfeesñthetransactionfeesthatuserspaytohavetheirtransactionsprocessedandrecordedontheblockchain.Thetermìgasîisanaptmetaphor:justasacarneedsfueltorun,everyoperationonablockchainrequirescomputationale§ortbyvalidators,andusersmustpayforthate§ort.Whenmanyuserswanttotransactatthesametime,theybidagainsteachotherforlimitedblockspace,andfeesspikeñmuchastaxifaressurgeduringrushhour.Figure1showshowEthereumgasfeesexhibitedsharpspikesduringperiodsofnetworkcongestion,suchasduringsurgesindecentralisedÖnance(DeFi)activityorspikesinthemintingofnon-fungibletokens(NFTs).Thesespikesarenotmerelyareáectionofexcessdemand;theyarethemechanismthroughwhichtheblockchainextractstherentsneededtosustainvalidatorcoordination.

Therelationshipbetweengasfeesandvalidatorincentivesrevealsafundamentaltension.Whendemandforblockspaceishigh,feesriseandvalidatorsarewellcompensated.Buthighfeesdeterusers,especiallythosemakingsmallorroutinetransactions.Theseusersare

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Figure1:Ethereumgasfees.TheÖgureshowstheevolutionofaveragegasfeesontheEthereumnetwork.Spikesingasfeescoincidewithperiodsofpeaknetworkactivity,suchassurgesinDeFiactivityandNFTminting.Thesefeespikesreáectthecongestionrentsthatarenecessarytosustaintheincentivesofvalidatorswhocontributetogovernance.Thehigh-feeepisodesarealsotheperiodsthatsawthegreatestoutáowofuserstocompetingblockchainssuchasSolanaandBNBChain.Sources:Etherscan;BIScalculations.

theÖrsttomigratetocompetingblockchainsthato§erlowerfeesñblockchainsthatcano§erlowerfeespreciselybecausetheyhavelowercoordinationthresholds(andhencelesssecurity).Theuserswhoremainonthemoresecureblockchainarethosewiththehighestwillingnesstopay:institutions,largeDeFiprotocols,andtransactionswheresecurityandcensorshipresistanceareparamount.Thissortingofusersacrossblockchainsistheessenceoffragmentation.

Figure2illustratesthecrucialdistinction.Thenewuserintheleft-handpanelchoosesthemorecrowdedvenueduetothenetworke§ects:greateruseleadstogreateracceptance,whichreinforcesfurtheruse.Theright-handpanelshowshowcapacityconstraintsononeblockchainpushuserstocompetingplatforms,sothatthenetworke§ectsthatunderpinmoneyareundermined.Insteadofconvergencetowardasinglemediumofexchange,theresultisfragmentation.

Thefragmentationoftheblockchainuniversearisesfromthefactthatcapacitycon-straintsarenecessarytoincentivisevalidatorstoperformtheirgovernancetasks,makingtheconsensusmechanismself-sustaining.WhenEthereumísgasfeesspikedduringperiodsof

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Figure2:Networke§ectsandstrategicsubstitutabilityinmoney.Theleft-handpanelillustratesthevirtuouscircleofnetworke§ects:greateracceptanceleadstogreateruse,whichreinforcesacceptance.Theright-handpanelillustratesstrategicsubstitutability:whencapacityconstraintsononeblockchainpushuserstocompetingplatforms,thenetworke§ectsthatunderpinmoneyareundermined.Insteadofconvergencetowardasinglemediumofexchange,theresultisfragmentation.

heavyuseñpeakingatlevelsthatmadeevenroutinetransactionsprohibitivelyexpensiveformanyusersñtheresponsewastheemergenceofalternativeblockchains.Solanaattracteduserswithlowfeesandhighthroughput.Tronbecametheworkhorseforcross-bordersta-blecointransfersinemergingmarkets.BNBChain,Avalanche,anddozensmorecarvedouttheirownniches.By2025,Solana,Tron,andEthereumwereeachgeneratingfeerevenueofbroadlycomparablemagnitude,1reáectingalandscapeinwhichnosinglechaindominatesallusecases.Thisfragmentationisnotanaccidentormarketfailure;itistheconsequenceofthetokeneconomics(ìtokenomicsî)ofdecentralisedconsensus.

Congestionindecentralisedledgersundercutsthenetworke§ectsofmoney.Whentrans-actionfeesbecometoohighononeblockchain,usersmigratetoalternatives.Newblockchainsemergetocatertotheseusers,andtheuserbasesplintersacrossmultipleplatforms.Ratherthanthevirtuouscircleofgreateracceptanceandgreateruse,thereisafragmentationofthemonetarylandscape.

Theblockchainuniversehasdisplayedpreciselysuchfragmentation.Figure3showstheevolutionofthelayer1blockchainlandscape.Alayer1(orìL1î)blockchainisabase-levelnetworkthatprocessesandÖnalisestransactionsonitsownledgerñEthereum,Solana,andTronarealllayer1chains.Thetermdistinguishesthesefoundationalnetworksfromlayer2

1Annualisedfeerevenueforeachchainwasintherangeof$500ñ600millionbylate2025.Source:TokenTerminal(

).

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Figure3:Layer1blockchainfragmentation.TheÖgureillustratestheproliferationoflayer1blockchainsandthedispersionofactivityacrossplatforms.Ratherthancoalescingaroundasingledominantplatform,theecosystemhasbecomeincreasinglyfragmented,withnewblockchainscapturinguserswhoaredeterredbyhighfeesonincumbentchains.Sources:CoinMetrics;DeFiLlama;BIScalculations.

(ìL2î)blockchains,whicharesecondarynetworksbuiltontopofanL1chaintohandletransactionsmorecheaply,periodicallysettlingbacktothebaselayerforsecurity.(Layer2solutionsarediscussedfurtherinSection3.)Ethereum,oncethedominantplatformfordecentralisedapplications,hasseenitsshareofactivityerodedbyahostofcompetitors.Solanahasattractedusersseekinglow-cost,high-speedtransactions.Tronhasbecomethebackboneforstablecointransfersinemergingmarkets,particularlyinAsia,theMiddleEast,andAfrica.BNBChain,Avalanche,Sui,Base,andmanyothershaveeachcarvedouttheirownniches.Atthetimeofwriting,dozensofblockchainecosystemshadattractedmeaningfulactivity,withthebulkoftransactionsconcentratedonthelargestchains.2

Thefragmentationisalsoevidentinthestablecoinlandscape.Ratherthanconvergingonasingleplatform,stablecoinactivityisscatteredacrossmanychains(Figure4).Asoflate2025,EthereumheldthemajorityoftotalstablecoinsupplybutwasfacingcompetitionfromTronandSolana,eachofwhichhadattractedtensofbillionsofdollarsinstablecoinbalances.3Eachchainservesdi§erentgeographiesandusecases:Ethereumforinstitutional

2DeFiLlamatrackedover60activeblockchainsasoflate2025.See

/chains

.

3DeFiLlamastablecoindashboard,

/stablecoins.AsofDecember2025

,Ethereumheldroughly55percentofaggregatestablecoinsupply,Tronapproximately$79billion,andSolana

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Figure4:Stablecoinfragmentationacrossblockchains.TheÖgureshowsthedistributionofstablecoinsupplyandactivityacrossmultipleblockchains.Ethereumremainsthelargestsingleplatform,butagrowingshareofstablecoinactivityhasmigratedtocompetingchainssuchasTronandSolana.Thefragmentationofstablecoinsacrosschainsunderminesthefungibilityandinteroperabilitythatapaymentinstrumentrequires.Sources:CoinMetrics;DeFiLlama;BIScalculations.

settlement,Tronforlow-costremittances,SolanaforretailpaymentsandDeFiactivity.

Crucially,stablecoinsondi§erentblockchainsarenotinteroperable(Figure5).AUSDCtokenonEthereumisnotthesameasaUSDCtokenonSolanañtheyexistonseparateledgersthathavenonativewayofcommunicatingwitheachother.Transferringbetweenchainsrequirestheuseofbridges:specialisedsoftwareprotocolsthatlocktokensononechainandissueequivalenttokensonanother.Thesebridgesintroduceadditionalrisks,includingvulnerabilitiesinthesmartcontractcodeñbridgeexploitshaveaccountedforbillionsofdollarsincumulativelosses4ñandtheyimposecostsanddelaysthatunderminetheseamlesstransferabilitythatisthehallmarkofmoney.Theresultisalandscapeinwhichstablecoinsfromthesameissuerexistinmultiple,non-fungibleformsacrossdi§erentblockchains,fragmentingliquidityandundercuttingthenetworke§ectsthatshouldbethestrengthofawidelyadoptedpaymentinstrument.

Theeconomicsofvalidatorincentives,asdevelopedbelow,providesanexplanationofsuch

over$16billion.

4Chainalysisestimatedcumulativebridgehacklossesatover$2.5billionbetween2021and2024.SeeChainalysis,CryptoCrimeReport(2024).

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Figure5:Stablecoinsarenotinteroperableacrossblockchains.TheÖgureillustrateshowthesamestablecoin(e.g.USDC)existsinseparate,non-fungibleformsondi§erentblockchains.Transferringsta-blecoinsacrosschainsrequirestheuseofbridges,whichintroducerisks,costs,anddelays.Thislackofinteroperabilityfragmentsliquidityandunderminesthenetworke§ectsofasinglepaymentinstrument.Sources:BIS.

fragmentation.Decentralisedinfrastructurescomewithabuilt-intendencytowardfragmen-tationthatworksagainsttheverynetworke§ectsthatgivemoneyitssocialvalue.Thefragmentationargumentistheáipsideofblockchainísìscalabilitytrilemma,îasdescribedbyVitalikButerin(Buterin(2021)),whoposedtheproblemastheimpossibilityofattain-ing,simultaneously,aledgerthatisdecentralised,secure,andscalable.Thecontributionofthispaperistoprovideaformaleconomicmechanismthatunderpinsthistrilemmaandtodrawoutitsimplicationsforthemonetarysystem.Thetheoreticalframeworkdrawsontheglobalgamesliterature(MorrisandShin(1998,2003)),andtheformalanalysisextendstheapproachinAuer,Monnet,andShin(2025).

1.1Relatedliterature

Theliteratureonthenetworke§ectsofmoneyhasdeeproots.Menger(1892)Örstarticulatedtheideathatmoneyemergesasthemostmarketablecommoditythroughaself-reinforcingprocess:themorewidelyacommodityisaccepted,themoreotherswishtoholdit,untilonecommodityemergesasthedominantmediumofexchange.Jevons(1875)identiÖedthe

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ìdoublecoincidenceofwantsîasthecorefrictionthatmoneyresolves.Theseclassicalin-sightswereformalisedbyKiyotakiandWright(1989,1993),whosesearch-theoreticmodelsshowhowmoneycanariseasacoordinationequilibriumamongagentswhowouldother-wisestruggletotrade.Acentrallessonofthesemodelsisthatthemonetaryequilibriumexhibitspowerfulstrategiccomplementarities:themoreagentsacceptaparticulartoken,thegreatereachagentísincentivetoacceptit.Matsuyama(1993)extendsthislogictoshowthatthewelfaregainsfrommonetaryexchangeareincreasinginthebreadthofthenetwork,sothatfragmentation-thecoexistenceofmultiple,weaklyconnectedmonetarynetworks-isinherentlycostly.

Thecoordinationperspectiveonmoneyconnectstoabroaderliteratureonincreasingreturnsandnetworke§ectsintheadoptionofstandardsandtechnologies(Arthur(1989),KatzandShapiro(1985)).Justasthevalueofatelephonenetworkincreaseswiththenumberofsubscribers,thevalueofacurrencyincreaseswiththenumberofusers.Butunlikeatelephonenetwork,whereinteroperabilitystandardscanlinkcompetingplatforms,theinteroperabilityofcompetingmonetarynetworksismuchhardertoachieve-especiallywhenthenetworksarebuiltonincompatibledecentralisedledgers.

Theeconomicsofblockchainconsensushasattractedgrowingattention.Huberman,Leshno,andMoallemi(2021)provideanearlyeconomicanalysisoftransactionfeesinBitcoin.Easley,OíHara,andBasu(2019)studytheevolutionofBitcointransactionfeesandtheimplicationsformarketdesign.Pagnotta(2022)linksBitcoinpricestothesecuritypropertiesoftheblockchain.Cong,He,andLi(2021)analysethetensionbetweendecentralisedminingandthecentralisationofminingpools-atensionthatforeshadowsthecoordinationproblemstudiedhere.Onstablecoins,GortonandZhang(2023)drawaparallelwiththeìwildcatbankingîerawhenprivatelyissuedbanknotesproliferatedwithoutauniformcurrency,andMakarovandSchoar(2022)provideanoverviewofdecentralisedÖnanceanditsstructuralchallenges.

Thebroaderliteratureonmoneyandinstitutionaldesignprovidesfurtherconceptualfoundations.Kocherlakota(1998)establishestheformalequivalencebetweenmoneyandmemory.BrunnermeierandNiepelt(2019)analysetheconditionsunderwhichprivateand

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publicmoneyareequivalent.Onthedesignofdistributedledgers,Townsend(2020)providesacomprehensivetreatment,whileCataliniandGans(2020)discussthesimpleeconomicsofblockchain.ChiuandKoeppl(2019)studyblockchain-basedsettlement.

TheglobalgamesmethodologythatunderpinsthetheoreticalanalysisoriginateswithCarlssonandvanDamme(1993)andwasdevelopedbyMorrisandShin(1998,2003).Theapproachhasbeenappliedtobankruns(GoldsteinandPauzner(2005),RochetandVives(2004))andtodebtmarkets(MorrisandShin(2004)).Auer,Monnet,andShin(2021,2025)applytheglobalgamesframeworktothegovernanceofdistributedledgers,providingthedirectantecedentforthepresentpaper.

Therestofthispaperisorganisedasfollows.Section2developsthetheory.ItÖrstdescribesthevarietyofconsensusmechanismsacrossblockchains,thensetsuptheformalglobalgamemodelandderivesthekeyresultsonvalidatorrewardsandblockchaincapacity.Section3drawsoutÖvekeylessonsfromtheanalysis.Section4o§ersconcludingremarks.

2Elementsofatheory

Fordecentralisationtowork,individualvalidatorshavetobeincentivisedtoplaytheirpartintheconsensusmechanism.Theconsensusmechanismsusedbypublicpermission-lessblockchainsvaryintermsoftheirpreciserules.

2.1Consensusmechanisms

Table1liststheconsensusmechanismsofÖveprominentblockchains.Althoughthemecha-nismsdi§erintheirdetails,theysharecommonfeaturesthatcanbedistilledintoageneralframework.

Bitcoinísproofofworkmechanism(Nakamoto(2008))requiresminerstoexpendcom-putationalresourcestosolveacryptographicpuzzle.Thehighenergycostservesasacom-mitmentdevicethatraisesthecostofsubvertingtheledger.However,thiscomesatthepriceoflowthroughputandhighenergyconsumption,whichlimitsBitcoiníscapacityasapaymentsystem(Huberman,Leshno,andMoallemi(2021)).Ethereumísproofofstake

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Table1:Consensusmechanismsofmajorblockchains.ThetableliststheconsensusmechanismsofÖveprominentblockchainsandhoweachmechanismworks.Thedetailsdi§er,butallmechanismssharethecommonfeatureofrequiringcoordinationamongvalidatorstomaintaintheintegrityoftheledger.

Chain

Consensusmechanism

Howitworks

Bitcoin

Proofofwork

Minerssolvehashpuzzles

Ethereum

Proofofstake

ValidatorsstakeETH;slashingpunishesmisbehaviour

BNBChain

Proofofstakedauthority

ValidatorselectedbyBNBstake;rotateblocks

Solana

Proofofhistory/BFTvoting

Stake-weightedleaderproposes;validatorsvote

Tron

Delegatedproofofstake

TRXholderselect27superrepresentatives

replacesenergyexpenditurewithcapitallock-up,dramaticallyreducingenvironmentalcostswhileretainingtheeconomiclogicofincentivecompatibility.BNBSmartChainandTronbothadoptvariantsofdelegatedproofofstake,inwhichasmallersetofvalidatorsiselectedbytokenholders.Thisreducesthecoordinationburdenñfewervalidatorsneedtoagreeñbutatthecostofgreatercentralisation.SolanaísproofofhistorysupplementsitsBFTvot-ingprocesswithacryptographicclockthatorderstransactionsbeforeconsensusisreached,enablinghighthroughputwithsub-secondÖnality.

Thekeyobservationacrossallthesemechanismsisthatthereisatrade-o§betweenthestringencyofthecoordinationrequirementandthecostofachievingconsensus.Mechanismsthatrequirebroaderparticipation(morevalidators,higherconsensusthresholds)providegreatersecurityandcensorshipresistancebutrequirehigherrewardsforvalidatorstomain-tainincentives(asexplainedinmoredetailbelow).Mechanismswithnarrowerparticipation(fewerelectedvalidators,lowerthresholds)cano§erlowerfeesandhigherthroughput,butatthecostofreduceddecentralisation.Thistrade-o§motivatesthegeneralframeworkthatfollows.

Allthesemechanismssharethecommonfeaturethattheymustbeself-sustaininginthesensethatwhenothervalidatorsfollowtherulesasprescribedbytheconsensusmechanism,itisintheinterestsofaparticularvalidatoralsotofollowtherules.Inthelanguageofgame

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theory,theprotocoldescribedintheconsensusmechanismmustconstituteanequilibriumofagame.

Forthemaintheoreticaldiscussion,itisusefultoworkwithageneralapproachtocon-sensusmechanismssothatwecanextractthekeyeconomiclessons.

Forthispurposeweworkwithageneralcoordinationproblemwiththefollowingfeatures.Supposethereisalargenumberofvalidators,whereeachvalidatorhasabinarychoicebetweencontributingtothegovernanceoftheblockchain(bearingasmallcost),oroptingoutandfree-ridingontheothervalidators.Althoughcontributingtogovernanceentailsacost,providedthatenoughoftheothervalidatorscontributetogovernance,anindividualvalidatorpreferstocontribute.Thecrucialelementiswhatdeterminesìenough.îAunanimityrulewouldbeaverystringentcriterionforwhatconstitutesìenough.îAlessstringentrulewouldbeasupermajoritywherethethresholdforsuccessfulcoordinationislower-say,atwo-thirdssupermajority.

Themorestringentisthethreshold,themoresecureistheblockchain.However,thegreatersecuritycomeswithacost.ThehigherthresholdforsuccessfulcoordinationraisesthestakesfortheindividualvalidatorwhoisweighingupthebeneÖtsandcosts.Incurringthecostofgovernancecontributionneedstobeweighedagainstthefalloutfromafailureofthevalidatorgrouptocoordinateonthegoodequilibrium.

Forthisreason,moresecureblockchainswithahigherthresholdforsuccessfulcoordina-tionhavetoprovidehigherrewardstothevalidatorstocompensatethemfortherisksthatarisefrompotentialmiscoordination.Thehigherthethresholdforsuccessfulcoordination,thehighermustbethereward.Inthelimitingcasewhereunanimityisrequiredtoupdatetheledger,itturnsoutthattherequiredrewardstothevalidatorstendtoinÖnity.Inotherwords,ablockchainthatneedsunanimityamongself-interestedvalidatorscannotfunctionwithÖniterewards.

Theupshotisthattheviabilityofablockchaindependsontherewardsthatcanbepaidtothevalidators.Themorestringentistherequiredsupermajoritytoachieveconsensus,thehighermustbethereward.Sinceusersoftheblockchainmustultimatelypayfortherewardsthatgotothevalidators,themoretheusersarewillingtopayfortheprivilege

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ofusingtheblockchain,thegreateristhestringencyofthesupermajoritythresholdthatdeterminessuccessfulcoordinationofgovernance.However,theuserbaseofaparticularblockchainislimitedbythewillingnesstopayofitsusers.Theblockchainextractsthesurplusfromthegroupofusers.Thecapacityoftheblockchainissetfromtheoutsetsoastoensurethatasu¢cientlyhighstreamofrentsaccruestotheparticipatingvalidators.Inthissense,congestionoftheblockchainisafeature,notabug.Thecongestionisnecessarytoensurethatuserspaysu¢cientlyhighgasfeestorewardthevalidators.

2.2Globalgame

Weproceedtoformalisethestylisedconsensusmechanismintroducedabove.Thereisacontinuumofvalidatorsindexedbytheunitinterval[0;1].Eachvalidatorchoosesbetweentwoactions-eithertocontributetogovernance,ortooptout.Contributingtogovernanceentailsacost,andthesecostsvaryacrossvalidators.Forvalidatori∈[0;1],thecostofcontributingtogovernanceisci>0.

TheblockchainfunctionswellprovidedthatenoughvalidatorsworktofulÖlgovernanceduties,whereìenoughîisdeÖnedintermsofathreshold.Providedthatproportionormoreofthevalidatorscontributetogovernance,theblo