Economic design in cryptoeconomics_game theory_mechanism design_market design_v.1.0

Economic Design in Cryptoeconomics
- Focus on Game Theory, Mechanism Design, Market Design
Jongseung Kim
SK telecom Blockchain Business Development Unit
2018. 9. 8

Institutional Technology
Information Technology
+
Two Characteristics of Blockchain Technology

Making Sense of ‘Cryptoeconomics’
“Crytoeconomicsis the practical science of using economic mechanisms
to build distributed systems,
where important properties of that system are guaranteed by financial incentives,
and where the economic mechanisms are guaranteed by cryptography.”(JoshuaStark)*
Cryptography Economics
+
<Source:https://medium.com/l4-media/making-sense-of-cryptoeconomics-5edea77e4e8d>
Signatures
Hash Functions
Zero-Knowledge Proofs
…
Game Theory
IncentiveDesigns
InstitutionalDesigns
…

Information and Incentives
•Economicsystem structured to dealwith the twinproblems ofinformationand incentives
•How can wecoordinateaction — make exchanges, buildrelationshipsand communities — inaworld of
incompleteinformationandpotential rentseeking?
•Wherecryptographers havefoundtheir solutionsinpublickeycryptography and proofof work
mechanisms, economists have foundsolutionsinmarkets, regulation,andinstitutions.
<Source:https://medium.com/cryptoeconomics-australia/byzantine-political-economy-de25bf8f047e>
Byzantine
Fault
Tolerance
Robust
Political
Economy
Algorithmic Questions ßàConstitutional Questions

What is ‘Economic Design’?
ü Game theory provides a structured language that helps in analyzing interactive
situations; when several individuals have to make decisions, and the outcome depends
on each person’s choice.*
ü The generalpurpose of mechanism design is to design games in order to achieve
specific outcomes.
ü Market Design :Auctions and matching or assignment problemsare in fact special cases
of mechanism design.
<Source:GuillaumeHaeringer, <Market Design :Auction andMatching>TheMITPress,2018>
Game theory,behavioral economics,and market design all allow us to look at rules, and
howpeople interact with them, understand them, circumventthem, and change them.

Game Theory – Mechanism Design –Market Design
Game Theory
The study ofmathematical
models ofstrategic interaction
betweenrational decision-makers
Mechanism Design
How to design
the ‘ruleofthe game’?
Market Design
A kind ofeconomicengineering,
utilizinggametheory, algorithms,
simulations, and more
’94 : JohnHarsanyi,JohnF. Nash,Reinhard Selten
’05 :ThomasC. Schelling,Robert J.Aumann
’96 : William Vickrey,JamesMirrlees
’07 : LeonidHurwicz,Eric S.Maskin,RogerB. Myerson
’14 : JeanTirole
’12 : LloydS.Shapley,Alvin E. Roth
Reverse
Applied
Behavior
Psychology
Behavior
Economics
Complexity
Economics
Influenced

What is ‘Nash equilibrium’?
<Source:http://studycas.com/component/k2/revisiting-nash-equilibrium-in-prisoner-s-dilemma>
If each player has chosen a strategy and no player can benefit by changing strategies
while the other players keep theirs unchanged, then the current set ofstrategy choices
and the corresponding payoffsconstitutes a Nash equilibrium.
Prisoner's Dilemma – Payoff Matrix

What is ‘Schelling point’?
<Source:https://en.wikipedia.org/wiki/Focal_point_(game_theory)>
Thomas Schelling describes
"focalpoint[s] foreach person's
expectation of what the other
expectshim to expect to be
expected to do"

History of Mechanism Design
<Source:https://en.wikipedia.org/wiki/Socialist_calculation_debate>
A new theoretical framework with which to tackle the comparison offundamentally
different types of economicorganization, such as capitalist and socialist institutions.
A discourse on the subject of howa socialist economywould perform economic
calculation given the absence of the law ofvalue, money,financial prices forcapital
goods, and private ownership ofthe means of production.*
Optimizing Social Institutions
Socialist calculation debate

Lange-Lerner model(Oscar Lange, Abba Lerner)*
<Source:https://brooklynrail.org/2018/07/field-notes/Dreams-of-National-Capital-Market-Socialism-Past-and-Present>

Key Concept of Mechanism Design
<Source:L.Hurwicz&S.Reiter,<Designing Economic Mechanisms> CambridgeUniversity Press,2008>
The goalfunction is the main "given",while the mechanism is the unknown.
Therefore,the design problem is the "inverse" of traditional economic theory,
which is typically devotedto the analysis ofthe performanceof a given mechanism.*
Mechanism design is a field in economics and game theory that
takes an engineering approach to designing economic mechanisms or incentives,
toward desired objectives,in strategic settings, where players act rationally.

Mechanism Design for Cake Cutting
<Source:Y.Narahari,<Game TheoryandMechanism Design> WorldScientificPublishing Company,2014>
• Oneof thekids wouldslicethe cake intotwo pieces.
• The otherkid gets the chanceto pick upany ofthe
pieces,leavingthe remainingpieceto the kidwho
slicedthe cake into two pieces.
• Child1, whocuts the cake willsliceit exactly into two
equalhalves, as any otherdivisionwillleavehim with
the smaller piece.
• Child2 is happybecause she gets to chooseand also
chooses what inher eyesis the larger of the two slices.

Structure of Mechanism Design
<Source:https://en.wikipedia.org/wiki/Mechanism_design>
.The upper-leftspace Θ depicts thetype space and the
upper-rightspace Xthe space of outcomes.
.The socialchoicefunctionf(θ)maps a type profileto an
outcome.
. In games of mechanism design,agents sendmessages M ina
game environmentg.
.The equilibriuminthegame ξ (M, g, θ)can be designedto
implementsome social choicefunctionf(θ).
§Amechanism design is a game ofprivate information in which one ofthe agents, called
the principal, chooses the payoff structure.*
à f(θ) : Θ → X (Definea social choicefunctionf(θ)mappingthe (true) typeprofiledirectlyto the
allocationofgoods receivedorrendered)

Incentive-compatibility and Revelation Principle
<Source:Y.Narahari,<Game TheoryandMechanism Design> WorldScientificPublishing Company,2014>
§Incentive compatibility essentially refersto offeringthe right incentivesthat make
agents reveal their types truthfully.*
. DominantStrategy IncentiveCompatibility(DSIC):Truth revelationis a best responsefor each agent
irrespectiveof what is reported bythe other agents.
. Bayesian Nash Incentive Compatibility(BIC):Truth revelationis a best response foreach agent in
expectationof thetypes ofthe rest ofthe agents.
§The Revelation principle :Any social choice functionthat can be implemented by any
arbitrary mechanism, can also be implemented by a truthful, direct-revelation
mechanism with the same equilibrium outcome.
.The RevelationPrincipleforDominant Strategy Equilibrium
.The RevelationPrincipleforBayesian Nash Equilibrium

Market and Equilibrium Price
What is
Market?
Finding an
Equilibrium
Price
üAMarket is an Institution where goods and services are exchanged
or traded.
üThe role ofa market is to determine who get what.
üPrice may affect people’s decisions, but may not be sufficient to
determine the ‘equilibrium’.
üOther forces (than price) are at work, and they need to be taken
into account.

Key Concept of Market Design*
<Source:NirVulkan, AlvinE.Roth,ZvikaNeeman, <TheHandbookofMarket Design> OxfordUniversity Press,2015>
‘Market Design’ is the term used to refer to a growing bodyof work that
might also be called microeconomicengineering and to the theoreticaland
empirical research that supportsthis effortand is motivated by it.
Science Art
it applies the formal tools ofgame
theoryandmechanism design.
Practical designoftencalls for
decisions that arebeyondthereliable
scientific knowledge of the field.

What a Market Needs to Work*
Market
Thickness
Avoid
Congestion
Make
the market
safe
• We need ‘enough’actors from both sides.
• In a thin market, there are fewbuyers and sellers, which can have negative
effects,such as increasing price volatility or reducing competition.
• Most people prefer to participate in markets that are safe and simple.
• Without propersafety, participants may wish to transact outside of the
market.
• Congestion in a market is like a traffic jam.
• The market must mitigate traffic jams to enable the freeflow of
transactions.

Principles of Market Design Applied to Tokens
<Source:https://medium.com/tokenfoundry/market-design-with-tokens-348a4d097a85>
IncreasingThickness
Mining,Partnerships,
Referral Bonuses
Reducingcongestion ProvidingSafety
Transaction Fees,
MembershipDeposits
Governance, Smart Contracts,
Attestations,Staking
Through the pillars of market thickness, congestion,and safety,
we can orient tokens, smart contracts, and game-theoretic mechanisms
towards higher goals.*

Simple Auctions : A Definition*
§Bidding format rules (theform of the bids)
.Bids can be priceonly,multi-attribute, priceand quantity, orquantity only.
§Bidding process rules
.Closing/timingrules, availableinformation,rules for bidimprovements/counter-bids
§Price and allocation rules
.Final price(s) andquantities, winningbidders
§An auction is referred as
.A type ofmarket mechanism, whichuses prices to determineallocations(who gets what).
.A pricediscoverymechanism.

Auctions are everywhere
§eBay,Art sales, house foreclosure,etc.
§Treasury bonds
§Internet ads(Google, Bing, Facebook, Twitter, etc.)
§Public facilities(bridges, tunnels, etc.)
§Daily quotation at stock exchanges
§Course allocations at business schools
§Spectrum licences(wireless communication)
§Smart Contract Transaction Fee

Ascending Auctions
Ascending auction : the price starts low and goes up (gradually) until a winner is
declared(or the auction is cancelled).*
Types
•Only bidders announce prices: English outcry auctions
•Only the auctioneer announces prices : Japanese button auction
Ticking
Price
•The amount by which the price has to go up or down
•Price increment rule
Truthful
Bidding
•pressing the button until the displayed price equals one’sown valuation
•In the English auction, truthfulbidding is a dominant strategy.

Second-Price Auction
Vickrey Auctionis an auction that is aimed at capturing what we have just described for
an ascending price auction.
.Each biddersecretly submits a bidto the auctioneer.It is a sealed-bidauction.
.The winneris the bidderwiththe highest bid;theother bidders losethe auction.
.The pricepaid bythe winneris equalto the second-highestbid.
§English vs Vickreyauctions
.The Vickreyauctionis a strategic formgame :bidders can neverlearn the bidsof theiropponents.
.The Englishauctionis an extensiveform game : biddersmay observethe bids oftheir opponents.

First-Price Auction
The first-price auction is a static auction that looks similar to the Vickrey auction, with
the only differencebeing the price paid by the winner.
.Each biddersecretly submits a bidto the auctioneer.It is a sealed-bidauction.
.The winneris the bidderwiththe highest bid;theother bidders losethe auction.
.The pricepaid bythe winneris equalto the highest bid.
§The payoffof bidder i is
.0 if bi < bmax
.1/(|{𝑗:𝑏𝑗=𝑏 𝑚𝑎𝑥}|)(𝑣𝑖−𝑏𝑖) if 𝑏𝑖 = 𝑏 𝑚𝑎𝑥

Optimal Bids in the First-Price Auction
§AStrategy ofa bidder maps avaluation to a bid. (v à s(v))
.Assumption 1 - Eachbidder uses the same strategy : forany pair of bidders,i and j,si = sj.
.Assumption 2 - Thebiddingfunctions is strictly increasing.So ifbidderi’s valuation is higher
than bidderj’s valuation, thenbidderi bids higherthan bidderj.
.Assumption 3 - For each bidderi = 1, …, n,s(vi) ≤ vi.
§Equilibrium : a bidding strategy for each bidder such that no bidder can be better
offby bidding according to a different strategy
§Result : When there are n bidders and their valuations are uniformly distributed,
and bidders’bidding strategies satisfy assumptions 1, 2, and 3, then a bidder with
valuation v bid in equilibrium
.s(v) =
()*
(
𝑣

Dutch Auction
§The Dutch/descending price auction isa first-price auction.
.There is a ‘clockprice’that displays a pricethat is decreasingover time.
.The auctionstops as soonas someonesays ‘Mine’.
§Dutch vs first-price auction :
- Strategically equivalent to a first-price sealed-bid auction
- Bidding one’s valuation is not a dominant strategy(in practice, not so equivalent).
. Bidders use thesame strategies.
. Bidders obtainthe same payoffs.
. Theseller get the same revenue.

The Basic Matching Model
§The basic matching problem consists of matching two sets of agents.
§One-sides matching problems : We only have one set of individuals and we have
to form groups of two or more individuals.
§Many-to-Onematching problems : Several individuals from one side can be
matched to the same individual from the other side.
§Many-to-many matching problems :Any individual fromany side can be matched
to several individuals formthe other side.

Matching Market
§Economicsstudies howgoodsand services are exchanged or distributed via a
market.
§Traditionally, markets determine allocation through prices, which are sufficient
statistics to determine who gets what.
§But in some cases prices may not be enoughto characterize allocations(e.g.,
College admission, labor market, etc.)
§Matching markets are typical examples ofmarkets where there is no monetary
transactions(and thus no price).
. Schoolassignment, Medical match,Allocationof dorms,Assignment ofcadets to branches,
Organ transplants, Allocationofsubsidized/publichousing,etc.

Matching Definition
§ A matching is simply a mapping (or a function)fromthe set of all individuals to the set
of all individuals.
§ A matching is afunction µ : M∪S à M∪S such that :
-For eachsingler s∈S, µ(s)∈M∪{s}, and foreach musician m∈M, µ(m)∈S∪{m}.
-If µ(s) = m, thenµ(m) = s.
§Amatching µ is stable if :
.it is individuallyrational,meaningthat for eachindividualv∈M∪S,vweakly prefers µ(v) tov; and
.there are no blockingpairs, meaningthat thereis no singer-musicianpair (s, m) such that µ(s) ≠ m
and mPs µ(s) andsPm µ(m).
à Stabilitycan beunderstoodastheequivalentoftheequilibriumin a“classic” supply-demandproblem.

The Deferred Acceptance(Gale-Shapley) Algorithm*
Step 1 Step k, k≥2 End
•Each singerproposes to the
musician whois ranked first
among his preferences.
•Each musicianwhoreceivedat
least oneoffertemporarily holds
the offerfrom the most
preferred singeramong the
singers who made a proposal to
her and whoare acceptable, and
rejects the other proposals.
•Each singerwhose proposalwas
rejectedin theprevious step
proposes to his most preferred
musician among themusicians to
whomhe has no yetproposed.
•Each musicianreceivingnew
proposals temporarily holds the
proposal ofthe singer she prefers
the most among
- thesingerswho justproposedtoher
and are acceptabletoherand
-thesingerwhoseproposalsheheld
from thepreviousstep.
•The algorithm stops whenno
singer’s offeris rejected.
•Each musicianis matched to the
singer who made the offershe
was holdingwhenthealgorithm
stopped.

Deferred Acceptance and Stable Matchings*
PBob PJohn PDavid
PDinah PMelanie PJanis
Dinah
Melanie
Janis
Bob
Dinah
Melanie
Janis
John
Dinah
Janis
Melanie
David
Bob
John
David
Dinah
Bob
David
John
Melanie
Bob
John
David
Janis
- Step1 :µ(Bob)=Dinah,µ(John)=John,
µ(David)=David,µ(Melanie)=Melanie,
µ(Janis)=Janis
- Step2 :µ(Bob)=Dinah,µ(John)=Melanie,
µ(David)=Janis
àNo singer is rejectedin this step, so the
algorithm stops.
• Finally,since allsingers and musicians prefertheir match to beingsingle,the matching µ described
aboveis individuallyrational.
• So the µ is a stable matching.

Behavioral Economics for Market Design
Cryptoeconomistis a behavioral public policy maker.
Extrinsic Motivation Intrinsic Motivation
《ChoiceArchitect》based on ‘LibertarianPaternalism’
Libertarian paternalism is the ideathat it is bothpossible and legitimatefor private and publicinstitutions
to affect behaviorwhilealso respectingfreedom ofchoice,as wellas theimplementationof that idea.
<Source:https://en.wikipedia.org/wiki/Libertarian_paternalism>

What role do Cryptoeconomics play?

Where is Cryptoeconomics useful?
<Source:https://medium.com/l4-media/making-sense-of-ethereums-layer-2-scaling-solutions-state-channels-plasma-and-truebit-22cb40dcc2f4>
Consensus Protocol
Level
Layer 2 Scaling
SolutionLevel
dApp/
Ecosystem Level
• Economicdesigncanhelpensure that users contribute
resources as the foundingteamintended.
• Cryptoeconomicsisalso appliedto design tokensales or
ICOs.
• The economicmechanismsused by layer 2 solutionstend to
be interactivegames : theywork by creatingincentivesfor
differentparties to competeagainst or “check” oneanother.
• State Channel,Plasma, Truebit,etc.*
• Onthe contributionsofminers who maintain theblockchain
• Onhow muchpoweris exerted by thoseminers
• Onhow costlythe system is to run, whichbothinfluence
whetherusers or apps willwant to adopt it

Cryptoeconomic Design Case : Transaction Fee Market
<Source:https://github.com/zcash/zcash/issues/3473>
Mismatch between volatility of
transaction fee levels and
social cost of transactions
Inefficienciesof first price auctions
Instability ofblockchains
with no block reward
• The protocolinternallymaintains a fee level
f, and a minerthat creates a blockthat
includesd bytes must pay a feeoff * d,
whichgets put into a pot.
• There is a maximum weight limitM.
• If the last blockwas 50% full,leavethe fee
unchanged,ifthe last blockwas 10% full,
drop itby 10%, if thelast blockwas 90% full,
increase it by10%.
• In every block,a minergets a reward equal
to 1/N (eg.1/10000) ofthe money
remainingin thepot.
Three Major Problem
in Transaction Fee Market
Alternative Mechanism
(Suggested by Vitalk Buterin)

Cryptoeconomic Design Case : Layer 2 Solutions
<Source:https://medium.com/l4-media/making-sense-of-ethereums-layer-2-scaling-solutions-state-channels-plasma-and-truebit-22cb40dcc2f4>
§Cryptoeconomicconsensusgives us a corehard kernel ofcertainty.
§The insight behind layer 2 solutions isthat we can use this core kernelof certainty as an
anchor — a fixed point to which we attach additional economicmechanisms.
§ABC application can assume that a given claim is likely true, because we’ve created a
strong incentive for another party to provide information showing it to be false.
State
Channel
In state channels, this is how we confirm the final state of the
channel — by giving parties a chance to “rebut” each other.
Plasma In Plasma, it’show we manage fraud-proofsand withdrawals.

Agent based Modelling for Cryptoeconomics
<Source:https://en.wikipedia.org/wiki/Agent-based_model>
“Agent-Based Model(ABM)”is a class of computational models
for simulating the actions and interactions ofautonomousagents
with a viewto assessing their effectson the system as a whole.
Interactions
Rewards
Observations
EnvironmentAgent(Miner,User)
ABM allows us to bypass any theoretical limitations
and modelthe agents of our assumptions directly,
while taking into account any kind of constraint or assumption we want.
[ComplexAdaptive System]

A New Typology of Political Economy
In a cryptoeconomyboth the economyand the ledgers are decentralised.
Blockchains take the state out of both planning and verification.*
<Source:https://medium.com/cryptoeconomics-australia/byzantine-political-economy-de25bf8f047e>

From Authority to Governance
üDecentralized platforms, like those that utilize blockchain technology are complex economic
system that require rigorous design because they lack authority.*
üOn decentralized platforms, authority has to be replaced by incentives and other mechanisms.
<Source:https://prysmgroup.attach.io/B1KdY0dEm?viewer=new>
(Bureaucratic)
Authority
Rule of Office
Bureaucratic Paper-basedSystem
(Algocratic)
Governance
Rule of Code
Technologically drivenCode-basedSystem

Crypto Constitutionalism*
<Source:https://medium.com/cryptoeconomics-australia/crypto-constitutionalism-c25d0c503ac>
Rule-Systems in which
individuals(or firms, or algorithms) can make economicand political exchanges.
ü Blockchains have systems of governance.
ü Blockchains look a lot like countries.
ü They have currencies(tokens),property(digitalassets), laws(protocols),
corporations(DAOs),and security systems(proof-of-work,orproofof stake, or
delegated byzantine fault tolerance, etc.).
Blockchainsare constitutionalorders!

“Only recently have we economists started to
understand enough about how markets work
so that we can help in that process.”
”
- Alvin E. Roth
2012 Nobel Prize laureate (withLloydShapley)
“for the theoryofstable allocations and the practice of market design.”

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