Ifjfails torespond thenωis understood to beAbstain

Tis a setof tokens,jis the owner of at least one token inT,Eis an event, andΩis an outcome spaceofE

algorithmF

j, is asked to report which elementωinΩ∪{Abstain}isTrue

input a tuple(T,φ)

eturns anΩ-partition ofT

input a tuple(E,Ω,T)

subroutinePay

all calls toFare assumed to be public, as are the resulting outputs

Each owner of tokens inTis queried to ask whichoutcome inΩisTrue. The owner’s tokens are assigned to the cell that corresponds to theoutcome they reported. If the owner does not respond (or if their response is not inΩ), then theirtoken are put in cellCAbstain

Each owner of tokens inTis given apro ratashare ofφ

not budget constrained

lways prefer actions that maximize their expectedutility

subroutinePluralityWinner

able to engage in costless communication with oneanother before making decisions

all token owners are queried simultaneously

all agents

Tokens removed from the reporting pool no longer earn their owners a reporting fee

never returnsAbstain, becauseX⊂ΩandAbstain/∈Ω

he caller pays theoracle a fee, denotedφ

all tokens in the reporting pool that were not used to tel

Beginning with a reporting pool of tokens of equal value

The oracle passes the query to the fork, which asks the owners of tokens in the reportingpool to report theTrueoutcome of the event. The response from the fork is interpreted as theoutcome of a plurality vote, and the outcome with the most votes is returned by the oracle

create an initialfinite set,Tgenesis, of tokens that have no intended value outside of their use in this contex

hose that query the oracle that determine which tokens were used to reporttruthfully during the previous call, and thus which token owners will be paid during the next call

there exists a Pareto efficient,subgame-perfect Nash equilibrium in the stage game which results inA0returning theTrueoutcome for the oracle quer

Ii<12(pi+1−p′i+1)|Ti|

he caller pays theoracle a fee, denotedφ

where every reporter always reports theTrueoutcome and the querier always removes from thereporting pool all and only those tokens used to lie—is in equilibrium in the stage gam

the benefit to reporterjfrom theoracle returning a false outcome in response to theith oracle query

create an initialfinite set,Tgenesis, of tokens that have no intended value outside of their use in this contex

when the economic soundness conditionis satisfied and all players are behaving the way we want them to, no player can do better forthemselves by unilaterally deviating from that behavior

paidout in any currency

A0is individually rational by demonstrating that the payouts for all players at thisequilibrium are positive and strictly greater than their minmax payouts

Ii,j

Ii=∑jIi,j

he economic soundness condition is satisfied exactly when the totalcost of forcing the oracle to lie exceeds the total collective benefit—including all “extraneous”benefit—from doing so

ncluding any “extraneous” benefi

themarket price of a token inTgenesis\Ti

If the economic soundness condition is satisfied andb>φ, then the simple oracleA0is individually rational

honest playrefer to the strategy profile in which every reporteralways chooses to reportTrueand the querier always chooses the movePunishFalse

If the economic soundness condition is satisfied, then always choosing the movePunishFalseis a best response by the querier to any strategy profile chosen by the reporters thatresults in the oracle returningTrue

the outcomesfor honest-play are better (or at least not worse) for all players than they would achieve by notplaying at all

the total benefit received by all reporters from the oracle returning afalse outcome in response to theith oracle query

I<12p|T|

speculation on thefuture value of a token can result in arbitrarily high token prices, so it is certainly alwayspossiblefor the economic soundness condition to be satisfied

p′

to all players during honest playare strictly greater than their minmax payouts: the minmax payout isφ−rj|T|for the individualreporterj, and−φ−Ifor the querie

open interest

the market price of a token that hasbeen removed from the reporting pool for lying

If the economic soundness condition is satisfied, thenA0is an incentive compatiblemechanism that decides theTrueoutcomes of oracle queries

we are not guaranteed to have the economic soundness condition be satisfiedin general. Under some conditions it is satisfied quite easily, and under other conditions it isnot. Moreover, the tenability of the economic soundness condition depends on some factorsoutside of the oracle implementer’s control, such as the market’s appetite for current yield anduser tolerance to the minimum required fees.

If the economic soundness condition is satisfied and the querier always choosesthe movePunishFalse, then reporting theTrueoutcome is always the best response by everyindividual reporter

the fee paid by the querier to the reporters

the querier would do better for herself by not engaging with the mechanismat all than to engage and play dishonestly

ince players have the choice of not participating, we want our mechanismto satisfy an individual rationality constraint.

we want to know whether the reporting fee can, simultaneously, be small enoughthat the querier is willing to pay it and large enough to make the market price of tokens

dominant strategy incentive compatible

the querier receives a payout of−φ+b, which is non-negative whenb>φ

high enough to satisfy the economic soundnesscondition

s an open question

b

the economic soundnesscondition is dependent on factors outside of the implementer’s contro

is an openquestion

φ

It is onlywhen the querier considers the larger repeated game setting that always choosingPunishFalsebecomes more appealing than the alternatives

arasite problem

honest play results in individual reporters beingpaid apro ratashare ofφ, which is always non-negative

always choosingPunishFalsewere a strictly dominant strategy

A0has no strictly dominant strategiesfor any of the players at al

economic soundnes

the strategies played during honest playare not strictly dominant

or example,

third-party derivatives increase the value ofIbut may not increase the market cap of reporting tokens, and thereby jeopardize the incentivecompatibility of the oracle

s dependent upon things outside of the oracle implementer’scontrol

we conjecture that it isunsolvable for all public oracles, both centralized and decentralized

the cost (tothe oracle operators) of lying be greater than the ben-efit.

individually rational

the ora-cle to be decentralized in order to avoid both censorshipand a single point of failure

truth-tellingmust be incentive compatible when the output of theoracle is consumed to control the irreversible payout oflarge amounts of cryptocurrency

reporters

incentive compatible

unlikely that thecoordination-game approach to decentralized oracle de-sign will work in practice

mechanisms based upon repeatedgames

theoracle to have a non-negative expected return for the op-erators

engage in pre-play communication and makebinding agreements

eachstage game corresponds to an oracle query and the out-come of each stage game determines how the oracle re-sponds to the query

wecan quantify this risk and state precisely how much ex-traneous incentive the design can handle before losingincentive compatibility

queriers

ΩE

For all eventsE

finite set of possibleoutcomes ofE

algo-rithm that accepts

no outcomespace contain the special elementAbstain

outputs someω∈Ω

con-tain the special elementInvalid

oracle

A propositionPis

an eventE

a correspondingoutcome space Ω

common knowledgeamong a group of agentsGif all agents inGknowP, they all know that they allknowP, they all know that they all know that they allknowP, and so on

A call to the oracleis referred to as aquery

unique outcome in Ω tobe thetrue outcomefor the query

If there existsa unique outcomeω∈Ω\{Invalid}such that – at thetime of the oracle query – it is common knowledge thatthe outcome of eventEisω, thenωis the true outcomefor the query. Otherwise,Invalidis the true outcomefor the query

ev-ery outcome in Ω that is notTrueis afalse outcome

The fact thatthe outcome corresponds to objective reality must alsobe common knowledge at the time of the query

A query whoseTrueoutcomeis notInvalidis referred to avalid query

Tis a finite set of tokens,Eis an event

Ω is an outcome space ofE

Ω-partition ofTis an indexed family of|Ω|+ 1 mutu-ally disjoint subsets ofT

indexed

cells

by Ω∪ {Abstain}where the union of the cells isT

the separation of the tokens into “piles” (cells) that arelabeled by the outcomes in Ω∪{Abstain}

algorithmReport

Tis a set of tokens,jisthe owner of at least one token inT,Eis an event, andΩ is an outcome space ofE

in-put a tuple (j,E,Ω,T)

thefork

, is asked to re-port which elementωin Ω∪{Abstain}isTrue. Ifjfailsto respond thenωis understood to beAbstain.Reportreturns the tuple (ω,R), whereRis the set of all tokensinTthat are owned byj

returns an Ω-partition ofT

all token owners are queried simul-taneously

Each owner oftokens inTis queried to ask which outcome in Ω isTrue.The owner’s tokens are assigned to the cell that corre-sponds to the outcome they reported. If the owner doesnot respond (or if their response is not in Ω), then theirtoken are put in cellCAbstain. Once all tokens inThavebeen assigned to a cell,Freturns the collection of cells,which is an Ω-partition ofT

Tis a finite set of tokens andφissome amount of currency

algorithmF

input an Ω-partitionand returns an outcome in Ω whose corresponding cellin the Ω-partition is of the maximum size.

tiesare broken uniformly at random

input a tuple (E,Ω,T)

lways prefer actions that maximizetheir expected utility

never returnsAbstain, becauseX⊂Ω andAbstain/∈Ω

all calls toFare assumed to be pub-lic, as are the resulting outputs

quasilinear in money

risk neutral and having utility functions that are

subroutinePay

we conjecturethat it is unsolvable for all public oracles, both central-ized and decentralized.

parasite problem

Each owner of tokens inTisgiven a pro rata share ofφ

If the economic soundness conditionis satisfied and the querier always chooses the movePunishFalse, then reporting theTrueoutcome is alwaysthe best response by every individual reporter

honest play is also in equilibriumin the repeated game

subroutinePluralityWinner

queriers are unlikely to engage with themechanism at all unless they intend to engage in honestplay.

If the economic soundness condition is sat-isfied thenA0is an incentive compatible mechanism thatdecides theTrueoutcomes of oracle queries

rationa

to all playersduring honest play are strictly greater than their minmaxpayouts: the minmax payout isφ−rj|T|for the individ-ual reporterj, and−φ−Ifor the querier

s an open questio

f the economic soundness condition is sat-isfied then always choosing the movePunishFalseis abest response by the querier to any strategy profile chosenby the reporters that results in the oracle returningTrue.

is an open ques-tion

Since players have the choice of not participating,we want our mechanism to satisfy an individual ratio-nality constraint.

the payouts

always choosingPunishFalsewere astrictly dominant strategy

b

the querier woulddo better for herself by not engaging with the mechanismat all than to engage and play dishonestly.

the outcomes for honest-play are better (or at least

φ

dominant strategy in-centive compatible

conomicsoundness

for ex-ample

s dependent upon things outside ofthe oracle implementer’s control

not worse) for all players than they would achieve bynot playing at all

f the economic soundness condition is sat-isfied andb > φthen the simple oracleA0is individuallyrational

fee paid by thequerier to the reporters.

the bene-fit the querier receives when the oracle returns theTrueoutcome

honest play results in individual reportersbeing paid a pro rata share ofφ, which is always non-negative. Also from Figure 2 we can see that the querierreceives a payout of−φ+b, which is non-negative whenb > φ

we want to know whether the report-ing fee can, simultaneously, be small enough that thequerier is willing to pay it and large enough to make themarket price of tokens

third-party derivatives increase the value ofIbut may notincrease the market cap of reporting tokens, and therebyjeopardize the incentive compatibility of the oracle

we are interested in whether the reporting feesalonecan justify a high enough token price for the eco-nomic soundness condition to be satisfied

the maximum benefit that the setof reporters could gain by making the oracle lie

igh enough to satisfy the economicsoundness condition

speculation on the future value of a token can result inarbitrarily high token prices, so it is certainly alwayspos-siblefor the economic soundness condition to be satisfied

he economic soundness condition is dependenton factors outside of the implementer’s contro

open interest

we are not guaranteed to have the eco-nomic soundness condition be satisfiedin general. Un-der some conditions it is satisfied quite easily, and underother conditions it is not. Moreover, the tenability of theeconomic soundness condition depends on some factorsoutside of the oracle implementer’s control, such as themarket’s appetite for current yield and user tolerance tothe minimum required fees

the strategies played during honest play are notstrictly dominant

A0has no strictly dominant strategies for any of the play-ers at all. Reporting truthfully is a best response forindividual reporters only if the querier always choosesPunishFalse. However, always choosingPunishFalseis only aweaklydominant strategy for the querier

It is only when the querier consid-ers the larger repeated game setting that always choosingPunishFalsebecomes more appealing than the alterna-tives

honest playrefer to thestrategy profile in which every reporter always choosesto reportTrueand the querier always chooses the movePunishFalse