Lecture Notes in Operations Research Panos Pardalos · Ilias Kotsireas · Yike Guo · William Knottenbelt Editors Mathematical Research for Blockchain Economy 3rd International Conference MARBLE 2022, Vilamoura, Portugal Lecture Notes in Operations Research EditorialBoard AnaPaulaBarbosa-Povoa,UniversityofLisbon,LISBOA,Portugal AdielTeixeiradeAlmeida ,FederalUniversityofPernambuco,Recife,Brazil NoahGans,TheWhartonSchool,UniversityofPennsylvania,Philadelphia,USA JatinderN.D.Gupta,UniversityofAlabamainHuntsville,Huntsville,USA GregoryR.Heim,MaysBusinessSchool,TexasA&MUniversity,CollegeStation, USA GuoweiHua,BeijingJiaotongUniversity,Beijing,China AlfKimms,UniversityofDuisburg-Essen,Duisburg,Germany XiangLi,BeijingUniversityofChemicalTechnology,Beijing,China HatemMasri,UniversityofBahrain,Sakhir,Bahrain StefanNickel,KarlsruheInstituteofTechnology,Karlsruhe,Germany RobinQiu,PennsylvaniaStateUniversity,Malvern,USA RaviShankar,IndianInstituteofTechnology,NewDelhi,India RomanSlowin´ski,Poznan´ UniversityofTechnology,Poznan,Poland ChristopherS.Tang,AndersonSchool,UniversityofCaliforniaLosAngeles, LosAngeles,USA YuzheWu,ZhejiangUniversity,Hangzhou,China JoeZhu,FoisieBusinessSchool,WorcesterPolytechnicInstitute,Worcester,USA ConstantinZopounidis,TechnicalUniversityofCrete,Chania,Greece Lecture Notes in Operations Research is an interdisciplinary book series which providesaplatformforthecutting-edgeresearchanddevelopmentsinbothopera- tionsresearchandoperationsmanagementfield.Thepurviewofthisseriesisglobal, encompassingallnationsandareasoftheworld. It comprises for instance, mathematical optimization, mathematical modeling, statistical analysis, queueing theory and other stochastic-process models, Markov decisionprocesses,econometricmethods,dataenvelopmentanalysis,decisionanal- ysis,supplychainmanagement,transportationlogistics,processdesign,operations strategy,facilitiesplanning,productionplanningandinventorycontrol. LNORpublisheseditedconferenceproceedings,contributedvolumesthatpresent firsthand information on the latest research results and pioneering innovations as wellasnewperspectivesonclassicalfields.ThetargetaudienceofLNORconsists ofstudents,researchersaswellasindustryprofessionals. · · · Panos Pardalos Ilias Kotsireas Yike Guo William Knottenbelt Editors Mathematical Research for Blockchain Economy 3rd International Conference MARBLE 2022, Vilamoura, Portugal Editors PanosPardalos IliasKotsireas DepartmentofIndustrial CARGOLab andSystemsEngineering WilfridLaurierUniversity UniversityofFlorida Waterloo,ON,Canada Gainesville,FL,USA WilliamKnottenbelt YikeGuo DepartmentofComputing DataScienceInstitute ImperialCollegeLondon ImperialCollegeLondon London,UK London,UK ISSN 2731-040X ISSN 2731-0418 (electronic) LectureNotesinOperationsResearch ISBN 978-3-031-18678-3 ISBN 978-3-031-18679-0 (eBook) https://doi.org/10.1007/978-3-031-18679-0 ©TheEditor(s)(ifapplicable)andTheAuthor(s),underexclusivelicensetoSpringerNature SwitzerlandAG2023 Thisworkissubjecttocopyright.AllrightsaresolelyandexclusivelylicensedbythePublisher,whether thewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuse ofillustrations,recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,and transmissionorinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilar ordissimilarmethodologynowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthors,andtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressedorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional claimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Preface Thisvolumepresentstheproceedingsofthe3rdInternationalConferenceonMath- ematical Research for Blockchain Economy (MARBLE 2022) that was held in Vilamoura,Portugal,fromJuly12to14,2022. Thankfully,thegradualglobalrecoveryfromtheCOVID-19pandemicallowed us to return to a physical format after 2 years and to put together an exciting programmeofresearchpapers,keynotetalksandatutorial,inlinewithMARBLE’s goaltoprovideahigh-profile,cutting-edgeplatformformathematicians,computer scientists and economists to present the latest advances and innovations related to the quantitative and economic aspects of blockchain technology. In this context, the Technical Programme Committee has accepted 14 research papers for publi- cation and presentation on themes including mining incentives, game theory, decentralised finance, central government digital coins and stablecoins, automated market makers, blockchain infrastructure and security. The technical programme also features keynotes by the following distinguished speakers: Michael Zargham (BlockScience and Metagovernance Project), Ioana Surpateanu (Multichain Asset Managers Association), Cathy Mulligan (Instituto Superior Técnico), Rob Hygate (eWATER Services), Arda Akartuna (Elliptic and University College London), Raphaël Mazet (SimpleFi) and Stefania Barbaglio (Cassiopeia Services) as well asatutorialonDecentralisedFinancepresentedbyLewisGudgeon,DanielPerez, SamWernerandDragosIlie(ImperialCollegeLondon). We thank all authors who submitted their innovative work to MARBLE 2020. In addition, we thank all members of the Technical Programme Committee and other reviewers, everyone who submitted a paper for consideration; the General Chairs, Prof. William Knottenbelt, Prof. Yike Guo and Prof. Panos Pardalos; the Organisation Chair, Jas Gill; the Web Chair, Kai Sun; the Publication Chair, Ilias Kotsireas;theFinanceChair,DianaO’Malley;thePublicityChair,SamWerner;and othermembersoftheCentreforCryptocurrencyResearchandEngineeringwhohave v vi Preface contributedinmanydifferentwaystotheorganisationeffort,particularlyKaterina Koutsouri.Finally,wearegratefultoourprimarysponsor,theBrevanHowardCentre forFinancialAnalysis,fortheirgenerousandongoingsupport. Vilamoura,Portugal PanosPardalos July2022 IliasKotsireas YikeGuo WilliamKnottenbelt Contents TowardsEquityinProof-of-WorkMiningRewards ................... 1 RamiA.KhalilandNarankerDulay MarketEquilibriaandRiskDiversificationinBlockchainMining Economies ........................................................ 23 YunKuenCheung, StefanosLeonardos, ShyamSridhar, andGeorgiosPiliouras OntheImpactofVoteDelegation ................................... 47 HansGersbach,AkakiMamageishvili,andManvirSchneider Decentralized Governance of Stablecoins with Closed Form Valuation ......................................................... 59 LucyHuo, AriahKlages-Mundt, AndreeaMinca, FrederikChristianMünter,andMadsRudeWind GriefingFactorsandEvolutionaryIn-StabilitiesinBlockchain MiningGames .................................................... 75 StefanosLeonardos, ShyamSridhar, YunKuenCheung, andGeorgiosPiliouras Data-DrivenAnalysisofCentralBankDigitalCurrency(CBDC) ProjectsDrivers ................................................... 95 ToshikoMatsuiandDanielPerez DissimilarRedundancyinDeFi ..................................... 109 DanielPerezandLewisGudgeon DeFiSurvivalAnalysis:InsightsintoRisksandUserBehaviors ........ 127 AaronGreen, ChristopherCammilleri, JohnS.Erickson, OshaniSeneviratne,andKristinP.Bennett vii viii Contents Gas Gauge: A Security Analysis Tool for Smart Contract Out-of-GasVulnerabilities ......................................... 143 BehkishNassirzadeh, HuaiyingSun, SebastianBanescu, andVijayGanesh TweakableS :ANovelS ConstructionBasedonTweakable leeve leeve HashFunctions ................................................... 169 DavidChaum,MarioLarangeira,andMarioYaksetig InterheadHydra:TwoHeadsareBetterthanOne .................... 187 MaximJourenko,MarioLarangeira,andKeisukeTanaka PredictionMarkets,AutomatedMarketMakers,andDecentralized Finance(DeFi) .................................................... 213 YonggeWang Wombat—AnEfficientStableswapAlgorithm ........................ 233 JenHoungLie,TonyW.H.Wong,andAlexYin-tingLee Multi-TierReputationforDataCooperatives ........................ 253 AbiolaSalau, RamDantu, KirillMorozov, KritagyaUpadhyay, andSyedBadruddoja Towards Equity in Proof-of-Work Mining Rewards RamiA.KhalilandNarankerDulay Abstract This work targets unfairness in Nakamoto, Bitcoin’s distinguished per- missionlessconsensusprotocol,towardsminerswithrelativelysmallcomputational powers,andminerswhichparticipateduringrelativelyunrewardingminingperiods. Weproposeasetofcomputationally-groundedmetricsformeasuringminerexpen- ditures, miner compensation, and coin value. Using our metrics, we quantitatively bring to light the sources of inequity in Nakamoto using Bitcoin as a real-world example.Furthermore,weproposeasetofrewardissuanceconstraintsformining incentive mechanisms to achieve equitable rewards, and argue for the efficacy of applyingourconstraints. · · Keywords Proof-of-Work Cryptocurrency Rewards 1 Introduction ThemostprominentProof-of-Work(PoW)miningcryptocurrency,Bitcoin[6],does nottreatallofitsminersfairly.Specifically,minerswithrelativelysmallcomputa- tionalpowers,andminerswhichparticipateintheprotocolduringrelativelyunre- warding late periods, are forced to expend more time and resources than others to createthesameamountofcoins.ThislackoffairnessisinherenttoBitcoin’sprotocol design. OneoftheprimarytenantsofBitcoinistoremainpermissionless,allowingany- onetoattainacopyoftheentireledger,andinserttransactionsintoitwhileremaining inagreementwithallotherminersonitsexactcontents.Thispermissionlessagree- ment between all Bitcoin ledger replicas is enabled by the Nakamoto consensus B R.A.Khalil( )·N.Dulay ImperialCollegeLondon,London,UnitedKingdom e-mail:[email protected] N.Dulay e-mail:[email protected] ©TheAuthor(s),underexclusivelicensetoSpringerNatureSwitzerlandAG2023 1 P.Pardalosetal.(eds.),MathematicalResearchforBlockchainEconomy,LectureNotes inOperationsResearch,https://doi.org/10.1007/978-3-031-18679-0_1