Augur Whitepaper

Monday, May 7, 2018
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Augur: a Decentralized Oracle and Prediction Market Platform Jack Peterson, Joseph Krug, Micah Zoltu, Austin K. Williams, and Stephanie Alexander Forecast Foundation (Dated: March 5, 2018) Augur is a trustless, decentralized oracle and platform for prediction markets. The outcomes of Augur’s prediction markets are chosen by users that hold Augur’s native Reputation token, who stake their tokens on the actual observed outcome and, in return, receive settlement fees from the markets. Augur’s incentive structure is designed to ensure that honest, accurate reporting of outcomes is always the most profitable option for Reputation token holders. Token holders can post progressively-larger Reputation bonds to dispute proposed market outcomes. If the size of these bonds reaches a certain threshold, Reputation splits into multiple versions, one for each possible outcome of the disputed market; token holders must then exchange their Reputation tokens for one of these versions. Versions of Reputation which do not correspond to the real-world outcome will become worthless, as no one will participate in prediction markets unless they are confident that the markets will resolve correctly. Therefore, token holders will select the only version of Reputation which they know will continue to have value: the version that corresponds to reality. Augur is a trustless, decentralized oracle and predic- I. HOW AUGUR WORKS tion market platform. In a prediction market, individuals can speculate on the outcomes of future events; those who forecast the outcome correctly win money, and those who Augur markets follow a four-stage progression: cre- forecast incorrectly lose money [1–3]. The price of a pre- ation, trading, reporting, and settlement. Anyone can diction market can serve as a precise and well-calibrated create a market based on any real-world event. Trading indicator of how likely an event is to occur [4–7]. begins immediately after market creation, and all users Using Augur, people will have the ability to trade in are free to trade on any market. After the event on which prediction markets at very low cost. The only significant the market is based has occurred, the outcome of the expenses participants assume is compensation to mar- event is determined by Augur’s oracle. Once the out- ket creators and to users that report on the outcomes of come is determined, traders can close out their positions markets once the event has taken place. The result is and collect their payouts. a prediction market where trust requirements, friction, and fees will be as low as competitive market forces can Augur has a native token, Reputation (REP). REP is drive them. needed by market creators and by reporters when they Historically, prediction markets have been centralized. report on the outcome of markets created on the Augur The simplest way to aggregate trades in a prediction mar- platform. Reporters report on a market by staking their ket is for a trustworthy entity to maintain a ledger; sim- REP on one of the market’s possible outcomes. By do- ilarly, the simplest way to determine the outcome of an ing this, the reporter declares that the outcome on which event and distribute payouts to traders is for an impar- the stake was placed matches the real-world outcome of tial, trusted judge to determine the outcomes of the mar- the market’s underlying event. The consensus of a mar- kets. However, centralized prediction markets have many ket’s reporters is considered the “truth” for the purpose risks and limitations: they do not allow global participa- of determining the market’s outcome. If a reporter’s re- tion, they limit what types of markets can be created or port of a market’s outcome does not match the consensus traded, and they require traders to trust the market op- reached by the other reporters, Augur redistributes the erator to not steal funds and to resolve markets correctly. REP staked on the non-consensus outcome by this re- Augur aims to resolve markets in a fully decentralized porter to the reporters that reported with the consensus. way. Decentralized, trustless networks, such as Bitcoin[8] and Ethereum[9], eliminate the risk that self-interest will By owning REP, and participating in the accurate re- turn into corruption or theft. The only role of the Augur porting on the outcomes of events, token holders are enti- developers is to publish smart contracts to the Ethereum tled to a portion of the fees on the platform. Each staked network. The Augur contracts are totally automated: REP token entitles its holder to an equal portion of Au- the developers do not have the ability to spend funds gur’s market fees. The more REP a reporter owns, and that are held in escrow on-contract, do not control how reports correctly with, the more fees they will earn for markets resolve, do not approve or reject trades or other their work in keeping the platform secure. transactions on the network, cannot undo trades, can- not modify or cancel orders, etc. The Augur oracle al- Although REP plays a central role in Augur’s opera- lows information to be migrated from the real world to tions, it is not used to trade in Augur’s markets. Traders a blockchain without relying on a trusted intermediary. will never need to own or use REP, as they are not re- Augur will be the world’s first decentralized oracle. quired to participate in the reporting process.

2 Figure 1. Simplified outline of the lifetime of a prediction market. A. Market Creation reliable designated reporter, which should help markets resolve quickly. Augur allows anyone to create a market about any up- The no-show gas bond is intended to cover the first coming event. The market creator sets the event end time public reporter’s gas costs. This prevents the scenario and chooses a designated reporter to report the outcome where the first public reporter’s gas costs are too high of the event. The designated reporter does not unilat- for reporting to be profitable. The no-show gas bond is erally decide the outcome of the market; the community set at twice the average gas cost for reporting during the always has an opportunity to dispute and correct the previous fee window. designated reporter’s report. In the event that the designated reporter fails to re- Next, the market creator chooses a resolution source port, the no-show REP bond is given to the first public that reporters should use to determine the outcome. The reporter in the form of stake on their reported outcome, resolution source may simply be “common knowledge”, so that the first public reporter receives the no-show REP or it may be a specific source, such as “The United States bond if and only if they report correctly. As with the va- Department of Energy”, bbc.com, or the address of a lidity bond, the no-show REP bond is adjusted dynami- particular API endpoint.1 They also set a creator fee, cally based on the proportion of designated reporters who which is the fee paid to the market creator by traders who failed to report on time during the previous fee window.4 settle with the market contract (see Section I D for details The market creator creates the market and posts all on fees). Finally, the market creator posts two bonds: required bonds via a single Ethereum transaction. Once the validity bond, and the designated report no-show bond the transaction is confirmed, the market is live and trad- (also referred to as the no-show bond for brevity). ing begins. The validity bond is paid in ETH and is returned to the market creator if the market resolves to any out- come other than invalid.2 The validity bond incentivizes B. Trading market creators to create markets based on well-defined events with objective, unambiguous outcomes. The size Market participants forecast the outcomes of events by of the validity bond is set dynamically, based on the pro- trading shares of those market outcomes. A complete set portion of invalid outcomes in recent markets.3 of shares is a collection of shares that consists of one share The no-show bond consists of two parts: the no-show of each possible valid outcome of the event [10]. Complete gas bond (paid in ETH) and the no-show REP bond (paid sets are created by Augur’s on-contract matching engine in REP). These bonds are returned to the market creator as needed to complete trades. if the market’s designated reporter actually reports dur- For example, consider a market that has two possible ing the first three days after the market’s event end time. outcomes, A and B. Alice is willing to pay 0.7 ETH for a If the designated reporter does not submit their report share of A and Bob is willing to pay 0.3 ETH for a share during the allotted 3-day window, then the market cre- of B.5 First, Augur matches these orders and collects a ator forfeits the no-show bond and it is given to the first total of 1 ETH from Alice and Bob.6 Then Augur creates public reporter who reports on the market (see Section a complete set of shares, giving Alice the share of A and I C 6). This incentivizes the market creator to choose a Bob the share of B. This is how shares of outcomes come into existence. Once the shares are created, they can be traded freely. 1 For example, if a market on “The high tempera- ture (in degrees Fahrenheit) on April 10, 2018 at the San Francisco International Airport, as reported by Weather Underground” specifies a resolution source of 4 See Appendix E 2 for details. https://www.wunderground.com/history/airport/KSFO/2018/4/10/ 5 Initially,trades in Augur’s markets will use Ethereum’s native coin, DailyHistory.html, reporters would simply go to that URL and Ether (ETH). Subsequent releases of Augur will include support for enter the high temperature displayed there as their report. markets denominated in arbitrary tokens issued on the Ethereum 2 An invalid market is a market determined to be invalid by reporters network, including shares of other markets as well as tokens pegged because none of the outcomes listed by the market creator is cor- to fiat currencies (“stablecoins”), if/when these become available. rect, or because the market wording is ambiguous or subjective; see 6 The 1 ETH figure is used here for ease of discussion. The actual Section III F for discussion. cost of a complete set of shares is much smaller than this; see 3 See Appendix E 1 for details. docs.augur.net/#number-of-ticks for details.

3 The Augur trading contracts maintain an order book 2. Participation Tokens for every market created on the platform. Anybody can create a new order or fill an existing order at any time. During any fee window, REP holders may purchase Orders are filled by an automated matching engine that any number of participation tokens for one attorep7 each. exists within Augur’s smart contracts. Requests to buy At the end of the fee window, they may redeem their or sell shares are fulfilled immediately if there is a match- participation tokens for one attorep each, in addition to ing order already on the order book. It may be filled a proportional share of the fee window’s reporting fee by buying shares from or selling shares to other partic- pool. If there were no actions (e.g., submitting a report or ipants, which, may involve issuing new complete sets or disputing a report submitted by another user) needed of a closing out existing complete sets. Augur’s matching en- reporter, the reporter may purchase participation tokens gine always sequesters the minimum amount of shares to indicate that they showed up for the fee window. Just and/or cash needed to cover the value at risk. If there is like staked REP, participation tokens may be redeemed no matching order, or the request can be only partially by their owners for a pro rata portion of fees in this fee filled, the remainder is placed on the order book as a new window. order. As discussed in Section II, it is important that REP Orders are never executed at a worse price than the holders are ready to participate in market resolution in limit price set by the trader, but may be executed at a the event of a fork. The participation token provides better price. Unfilled and partially-filled orders can be an incentive for REP holders to monitor the platform at removed from the order book by the order’s creator at least once per week, and, thus, be ready to participate any time. Fees are paid by traders only when complete if the need arises. Even REP holders who do not want sets of shares are sold; settlement fees are discussed in to participate in the reporting process are incentivized to more detail in Section I D. check-in with Augur once per 7-day fee window in order While most trading of shares is expected to happen to buy participation tokens and collect fees. This regular, before market settlement, shares can be traded any time active checking-in will ensure that they are familiar with after market creation. All Augur assets – including shares how to use Augur, will be aware of forks when they occur, in market outcomes, fee window tokens, shares in dispute and thus should be more ready to participate in forks bonds, and even ownership of the markets themselves – when they happen. are transferable at all times. 3. Market State Progression C. Reporting Augur markets can be in seven different states after creation. The potential states, or “phases”, of an Augur Once a market’s underlying event occurs, the outcome market are as follows: must be determined in order for the market to finalize • Pre-reporting and begin settlement. Outcomes are determined by Au- gur’s oracle, which consists of profit-motivated reporters, • Designated Reporting who simply report the actual, real-world outcome of the event. Anyone who owns REP may participate in the • Open Reporting reporting and disputing of outcomes. Reporters whose • Waiting for the Next Fee Window to Begin reports are consistent with consensus are financially re- warded, while those whose reports are not consistent with • Dispute Round consensus are financially penalized (see Section I D 3). • Fork • Finalized 1. Fee Windows The relationship between these states can be seen in Fig. 2. Augur’s reporting system runs on a cycle of consecu- tive 7-day long fee windows. All fees collected by Augur during a given fee window are added to the reporting fee 4. Pre-reporting pool for that fee window. At the end of the fee window, the reporting fee pool is paid out to REP holders who The pre-reporting or trading phase (Fig. 1) is the time participated in the reporting process. Reporters receive period that begins after trading has begun in the market, rewards in proportion to the amount of REP they staked during that fee window. Participation includes: staking during an initial report, disputing a tentative outcome, 7 One attorep is 10−18 REP. or purchasing participation tokens.

4 Figure 2. Reporting flowchart. but before the market’s event has come to pass. Gener- nated reporter stake8 on its reported outcome, which it ally, this is the most active trading period for any given will forfeit if the market finalizes to any outcome other Augur market. Once the event end date has passed, the than the one they reported.9 As soon as the designated market enters the designated reporting phase (Fig. 2a). reporter submits its report, the market enters the waiting for next fee window to begin phase (Fig. 2c), and the re- ported outcome becomes the market’s tentative outcome. 5. Designated Reporting 6. Open Reporting When creating a market, market creators are required to choose a designated reporter and post a no-show bond. If the designated reporter fails to report within the During the designated reporting phase (Fig. 2a) the mar- allotted three days, the market creator forfeits the no- ket’s designated reporter has up to three days to report show bond, and the market immediately enters the open on the outcome of the event. If the designated reporter fails to report within the allotted three days, the mar- ket creator forfeits the no-show bond, and the market 8 See automatically enters the open reporting phase (Fig. 2b). appendix E 3 for details on the size of the designated reporter stake. If the designated reporter submits a report on time, 9 Forfeited stake is added to the reporting fee pool of the market’s then the no-show bond is returned to the market creator. assigned fee window, and is used to reward honest reporters and The designated reporter is required to post the desig- disputers; see Section I D 3 for details.

5 reporting phase (Fig. 2b). As soon as the market enters S(ω, n) denote the total amount of stake on outcome ω at the open reporting phase, anyone can report the outcome the beginning of dispute n. Then the size of the dispute of the market. When the designated reporter fails to bond needed to successfully dispute the current tentative report, the first reporter who reports on the outcome of outcome in favor of the new outcome ω during round n a market is called the market’s first public reporter. is denoted B(ω, n) and is given by: The market’s first public reporter receives the forfeited B(ω, n) = 2An − 3S(ω, n) (1) no-show bond in the form of stake on their chosen out- come, so they may claim the no-show REP bond only The bond sizes are chosen this way to ensure a fixed if their reported outcome agrees with the market’s final ROI of 50% for reporters who successfully dispute false outcome. They also receive the no-show gas bond after outcomes (see Section II D). the market has finalized only if their reported outcome The dispute bonds need not be paid in their entirety agrees with the market’s final outcome. by a single user. The Augur platform allows participants The first public reporter does not need to stake any of to crowdsource dispute bonds. Any user who sees an in- their own REP when reporting the outcome of the mar- correct tentative outcome can dispute that outcome by ket. In this way, any market whose designated reporter staking REP on an outcome other than the tentative out- fails to report is expected to have its outcome reported come. If any outcome (other than the tentative outcome) by someone very soon after entering the open reporting accumulates enough dispute stake to fill its dispute bond, phase. the current tentative outcome will be successfully dis- Once an initial report has been received by the ini- puted. tial reporter (whether it was the designated reporter or In the case of a successful dispute, the market will first public reporter), the reported outcome becomes the either undergo another dispute round, or it will enter market’s tentative outcome, and the market enters the the fork state (Fig. 2e). If the size of the filled dispute waiting for next fee window to begin phase (Fig. 2c). bond is greater than 2.5% of all REP, then the market will enter the fork state. If the size of the filled dispute bond is less than 2.5% of all REP, then the newly chosen 7. Waiting for Next Fee Window to Begin outcome becomes the market’s new tentative outcome, and the market undergoes another dispute round. Once the market receives its initial report, it enters All dispute stake is held in escrow during the dispute the waiting for next fee window to begin phase (Fig. 2c). round. If a dispute bond is unsuccessful, then the dis- During this phase, reporting for the market is on hold un- pute stake is returned to its owners at the end of the til end of the current fee window. Once the next fee win- dispute round. If no dispute is successful during the 7- dow begins, the market enters the dispute round phase. day dispute round, the market enters the finalized state (Fig. 2f), and its tentative outcome is accepted as its fi- nal outcome. A market’s final outcome is the tentative 8. Dispute Round outcome that passes through a dispute round without being successfully disputed, or is determined via a fork. Augur’s contracts treat final outcomes as truth and pay The dispute round (Fig. 2d) is a 7-day period during out accordingly. which any REP holder has the opportunity to dispute All unsuccessful dispute stake is returned to the origi- the market’s tentative outcome.10 (At the beginning of a nal owners at the end of every dispute round. All success- dispute round, a market’s tentative outcome is the out- ful dispute stake is applied to the outcome it championed, come that will become the market’s final outcome if it and remains there until the market is finalized (or until is not successfully disputed by REP holders.) A dispute a fork occurs in some other Augur market). All dispute consists of staking REP (referred to as dispute stake in stake (whether successful or unsuccessful) will receive a this context) on an outcome other than the market’s cur- portion of the reporting fee pool 11 from the current fee rent tentative outcome. A dispute is successful if the to- window. tal amount of dispute stake on some outcome meets the dispute bond size required for the current round. The dispute bond size is computed as follows. 9. Fork Let An denote the total stake over all of this market’s outcomes at the beginning of dispute round n. Let ω The fork state (Fig. 2e) is a special state that lasts up be any market outcome other than the market’s tenta- to 60 days. Forking is the market resolution method of tive outcome at the beginning of this dispute round. Let 11 Any settlement fees and validity bonds collected during a fee win- dow get added to that fee window’s reporting fee pool. At the 10 The fact that the dispute rounds coincide with the fee windows is end of the fee window, the reporting fee pool is paid out to users purely a matter of convenience; in principle, dispute rounds and in proportion to the amount of REP they staked during that fee fee window durations could be different. window.

6 last resort; it is a very disruptive process and is intended Whichever child universe receives the most migrated to be a rare occurrence. A fork is caused when there is a REP by the end of the forking period becomes the win- market with an outcome with a successfully-filled dispute ning universe, and its corresponding outcome becomes bond of at least 2.5% of all REP. This market is referred the final outcome of the forking market. Un-finalized to as the forking market. markets in the parent universe may be migrated only to When a fork is initiated, a 60-day12 forking period be- the winning universe and, if they have received an initial gins. Disputing for all other non-finalized markets is put report, are reset back to the waiting for next fee window on hold until the end of this forking period. The forking to begin phase. period is much longer than the usual fee window because There is no time limit to migrate tokens from the par- the platform needs to provide ample time for REP hold- ent universe to a child universe. Tokens may be mi- ers and service providers (such as wallets and exchanges) grated after the forking period, but they will not count to prepare. A fork’s final outcome cannot be disputed. towards the determination of the winning universe. To Every Augur market and all REP tokens exist in some encourage greater participation during the forking pe- universe. REP tokens can be used to report on outcomes riod, all token holders who migrate their REP within 60 (and thus earn fees) only for markets that exist in the days of the start of a fork will receive 5% additional REP same universe as the REP tokens. When Augur first in the child universe to which they migrated14 . This re- launches, all markets and all REP will exist together in ward is paid for by minting new REP tokens.15 the genesis universe. Reporters that have staked REP on one of the forking When a market forks, new universes are created. Fork- market’s outcomes cannot change their position during a ing creates a new child universe for each possible outcome fork. REP that was staked on an outcome in the par- of the forking market (including Invalid, as discussed in ent universe can be migrated only to the child universe Section I D 2). For example, a “binary” market has 3 pos- that corresponds to that outcome. For example, if a re- sible outcomes: A, B, and Invalid. Thus, a binary forking porter helped fulfill a successful dispute bond in favor market will create three new child universes: universe A, of outcome A during some dispute round, then the REP universe B, and universe Invalid. Initially, these newly they have staked on outcome A can only be migrated to created universes are empty: they contain no markets or universe A during a fork. REP tokens. Sibling universes are entirely disjoint. REP tokens When a fork is initiated, the parent universe becomes that exist in one universe cannot be used to report on permanently locked. In a locked universe, no new mar- events or earn rewards from markets in another universe. kets may be created. Users may continue trading shares Since users presumably will not want to create or trade on in markets in locked universes, and markets in a locked markets in a universe whose oracle is untrustworthy, REP universe may still receive their initial reports. However, that exists in a universe that does not correspond to ob- no reporting rewards are paid out there, and markets in jective reality is unlikely to earn its owner any fees, and locked universes cannot be finalized. In order for markets therefore should not hold any significant market value. or REP tokens in the locked universe to be useful, they Therefore, REP tokens migrated to a universe which does must first be migrated to a child universe. not correspond to objective reality should hold no mar- Holders of REP tokens in the parent universe may mi- ket value, regardless of whether or not the objectively grate their tokens to a child universe of their choice. This false universe ends up being the winning universe after choice should be considered carefully, because migration a fork. This has important security consequences, which is one-way; it cannot be reversed. Tokens cannot be sent we discuss in Section II. from one sibling universe to another. Migration is a per- manent commitment of REP tokens to a particular mar- ket outcome. REP tokens that migrate to different child 10. Finalized universes ought to be considered entirely separate tokens, and service providers like wallets and exchanges ought to A market enters the finalized state (Fig. 2f) if it passes list them as such. through a 7-day dispute round without having its tenta- When a fork is initiated, all REP staked on all non- tive outcome successfully disputed, or after completion of forking markets is unstaked so that it is free to be mi- a fork. The outcome of a fork cannot be disputed and is grated to a child universe during the forking period.13 always considered final at the end of the forking period. 12 Forking periods can be less than 60 days: a forking period ends 14 This occurs even when the forking period has ended early due to when either 60 days have passed, or more than 50% of all genesis more than 50% of all REP being migrated to some child universe. REP is migrated to some child universe. 15 The effect of this addition to the money supply of REP is small. 13 The only exception is the REP staked by the initial reporter when For example, if 20% of all existing REP is migrated during the they made the initial report. That REP remains staked on the forking period of a fork, this bonus would result in a 1% increase initial reported outcome and is automatically migrated to the child in the money supply of REP. Moreover, forks are expected to be universe that wins the fork. exceedingly rare events.

7 Once a market is finalized, traders can settle their po- ETH, then traders will receive C/N ETH for each share sitions directly with the market. When a market enters settled with the market contract.16 the finalized state, we refer to its chosen outcome as the final outcome. 3. Reputation Redistribution D. Market Settlement If a market finalizes without initiating a fork, all REP staked on any outcome other than the market’s final outcome is forfeited and distributed to the users who A trader can close their position in one of two ways: by staked on the market’s final outcome in proportion to selling the shares they hold to another trader in exchange the amount of REP they staked. The dispute bond sizes for currency, or by settling their shares with the market. are chosen such that anyone who successfully disputes Recall that every share comes into existence as part of a an outcome in favor of the market’s final outcome is re- complete set when a total of 1 ETH has been escrowed warded with a 50% ROI on their dispute stake.17 This is with Augur.6 To get that 1 ETH out of escrow, traders a strong incentive for reporters to dispute false tentative must give Augur either a complete set or, if the market outcomes. has finalized, a share of the winning outcome. When this exchange happens we say traders are settling with the market contract. II. INCENTIVES AND SECURITY For example, consider a non-finalized market with pos- sible outcomes A and B. Suppose Alice has a share of out- There is a strong relationship between the market cap come A that she wants to sell for 0.7 ETH and Bob has of REP and the trustworthiness of Augur’s forking proto- a share of outcome B that he wants to sell for 0.3 ETH. col. If the market cap of REP is large enough18 , and at- First, Augur matches these orders and collects the A and tackers are economically rational, then the outcome that B shares from the participants. Then Augur gives 0.7 wins the fork should correspond to objective reality. In ETH (minus fees) to Alice and 0.3 ETH (minus fees) to fact, it would be possible for Augur to function properly Bob. without using designated reporters and dispute rounds. As a second example, consider a finalized market whose Using only the forking process, the oracle would report winning outcome is A. Alice has a share of A and wants truthfully. to cash it in. She sends her share of A to Augur and in However, forks are disruptive and time consuming. A return receives 1 ETH (minus fees). fork takes up to 60 days to resolve a single market, and can resolve only one market at a time. During the 60 days in which the forking market is being resolved, all 1. Settlement Fees other non-finalized markets are put on hold.19 Service providers have to update, and REP holders have to mi- grate their REP to one of the new child universes. There- The only time Augur levies fees is when market par- fore, forks should be used only when they are absolutely ticipants are settling with the market contract. Augur necessary. Forking is the nuclear option. levies two fees during settlement: the creator fee, and Fortunately, once it has been established that forks can the reporting fee. Both of these fees are proportional be trusted to determine truth, incentives can be used to to the amount being paid out. So, in the pre-finalized encourage participants to behave honestly without hav- settlement example above, where Alice receives 0.7 ETH ing to actually initiate a fork. It is the credible threat of and Bob receives 0.3 ETH, Alice would pay 70% of the a fork, and the belief that the fork will resolve correctly, fees while Bob would pay 30%. that are the cornerstones of Augur’s incentive system. The creator fee is set by the market creator during Next, we discuss the conditions under which the fork- market creation, and is paid to the market creator upon ing system can be trusted to determine truth. We then settlement. The reporting fee is set dynamically (see Sec- discuss the incentive system and how it encourages quick tion II C) and is paid to reporters who participate in the and correct resolution of all markets. reporting process. 16 Trades cannot simply be unwound if a market resolves as Invalid 2. Settlement of Invalid Markets due to technical limitations. Shares of outcomes are just tokens, which can be traded directly between users; the ETH and shares are thus not under Augur’s control and cannot be given back to In the event that a market resolves as Invalid, traders the original owner if the market finalizes as Invalid. who settle with the market contract receive an equal 17 See Theorem 3 in Appendix A. amount of ETH for shares of each outcome. If the mar- 18 See Section II A for details. 19 Traders can continue trading on those markets, but those markets ket had N possible outcomes (not including the Invalid outcome), and the cost of a complete set of shares was C cannot finalize until after the forking period.

8 A. Integrity of the Forking Protocol 2. Parasitic Open Interest is Unknowable Here we discuss the reliability of the forking process Augur can accurately and efficiently measure Ia . How- and the conditions under which it can be trusted. For ever, Ip cannot be known in general, as there may exist ease of discussion, when referring to forks, we will refer arbitrarily many offline parasitic markets, each with arbi- to the child universe that corresponds to objective reality trarily large open interest. Since the maximum possible as the True universe, and any other child universe as a benefit to an attacker includes the unknowable quantity False universe. We will refer to the child universe which Ip , one can never be objectively certain that the oracle receives the most REP migration during the forking pe- is secure against economically rational attackers. riod as the winning universe and all other child universes However, if we are willing to assert that Ip is reason- as losing universes. ably bounded in practice, then we can define conditions Naturally, we always want the True universe to be the under which we may assert that the oracle is secure. winning universe, and the False universes to be the losing universes. We say that the forking protocol has been suc- cessfully attacked whenever a False universe ends up be- 3. Minimum Cost of a Successful Attack ing the winning universe of a fork – thus resulting in the forking market (and, potentially, all non-finalized mar- Next, consider the cost of attacking the oracle. Let kets) being paid out incorrectly. P denote the price of REP. Let ǫ denote one attorep22 . Our approach to securing the oracle is to arrange mat- Let M denote the total amount of REP in existence (the ters such that the maximum benefit to a successful at- “money supply” of REP). Let S denote the proportion tacker is less than the minimum cost of performing the of M that will be migrated to the True universe during attack. We formalize this below. the forking period of a fork. Thus the product SM represents the absolute amount 1. Maximum Benefit to an Attacker of REP migrated to the True universe during the forking period of a fork, and the product P M is the market cap of REP. An attacker who successfully attacks the oracle would Let Pf denote the price of REP migrated to a False cause all non-finalized Augur markets to migrate to a universe of the attacker’s choosing. Note that if P ≤ Pf False universe. If the attacker controls the majority of then the oracle would not be secure against economically REP in the False universe, the attacker can then force all rational attackers, because it would be at least as prof- non-finalized markets to resolve however she wants. In itable to migrate REP to the False universe as it would the most extreme case, she would also be able to capture be to not migrate at all. all funds escrowed in all of those markets.20 Definition 1. We define, and denote by Ia , Augur’s na- tive open interest as the value of the sum of all funds 4. Integrity escrowed in unfinalized Augur markets.21 Definition 2. We define a parasitic market as any mar- Assumption 1. Reporters that are not attackers will ket that does not pay reporting fees to Augur, but does never migrate REP to a False universe during a fork.23 resolve in accordance with the resolution of a native Au- By design, a successful attack on the oracle requires gur market. more REP to be migrated to some False universe than Definition 3. We define, and denote by Ip , the parasitic to the True universe during the forking period of a fork. open interest as the value of the sum of all funds escrowed By assumption, only the attacker will migrate REP to in all parasitic markets that resolve in accordance to non- a False universe. The amount of REP migrated to the finalized, native Augur markets. True universe during the reporting period is denoted by SM . Thus, for an attacker to be successful, they must In the most extreme case, an attacker would also be migrate at least SM + ǫ REP. For simplicity, we will able to capture all funds in all parasitic markets which ignore the negligible ǫ, and say that a successful attack resolve in accordance to non-finalized, native Augur mar- requires migrating at least SM REP, which has a value kets. of SM P before the migration, to some False universe. Observation 1. The maximum (gross) benefit to an at- tacker who successfully attacks the oracle is Ia + Ip . 22 One attorep is 10−18 REP. 23 There may be cases where some non-malicious reporters do migrate 20 This would require the attacker to capture all shares of some given REP to a False universe accidentally or carelessly. However, such outcome, and then force the market to finalize to that outcome. behavior is, in practice, indistinguishable from collaborating with 21 This includes external markets that pay reporting fees to Augur. an attacker.

9 If an attacker migrates SM REP during the report- B. Our Assumptions and Their Consequences ing period of a fork, they will receive SM REP on the child universe to which they migrate.24 If the attacker We believe traders will not want to trade on Augur in a migrates to a False universe then the value of those coins universe where reporters have lied. We also believe that becomes SM Pf . Thus the minimum cost to the attacker market creators will not pay to create Augur markets is (P − Pf )SM . in a universe where there are no traders. In a universe without markets or trading, REP does not provide any Observation 2. The minimum amount of REP a suc- dividends to those holding it. Therefore, we believe REP cessful attacker must migrate to a False universe during sent to a False universe will hold no non-negligible mar- a fork is SM , which costs the attacker (P − Pf )SM . ket value and we model this by letting Pf = 0. Note that if S > 12 then an attack is impossible because We think it is reasonable to expect at least 20% of ex- there does not exist enough REP outside of the True isting REP to be migrated to the True outcome during universe for any False universe to become the winning the reporting period of a fork, and we model this by let- universe. ting S ≥ 15 . We are also willing to accommodate parasitic Pitted against economically rational attackers, the or- open interest as large as 50% of the native open interest, acle will resolve to outcomes that correspond to objec- and so we let Ia ≥ 2Ip . tive reality if the maximum benefit to an attacker is less Under these assumptions, Theorem 1 tells us that the than the minimum cost of attack. By observations 1 forking protocol has integrity whenever the market cap & 2 we can see that this occurs whenever S > 21 or of REP is at least 7.5 times the native open interest.25 Ia + Ip < (P − Pf )SM . This gives us our formal def- inition of integrity. C. Market Cap Nudges Definition 4. (Integrity Property) The forking protocol has integrity whenever S > 12 or whenever Ia + Ip < Augur gets information about the price of REP in the (P − Pf )SM . same way it gets any other information about the real world: through an Augur market. This gives Augur the The above inequality can be solved for P M to see the ability to compute the current market cap of REP. Augur relationship between forking protocol integrity and the can also measure the current native open interest, and market cap of REP. can thus determine what market cap ought to be targeted Theorem 1. (Market Cap Security Theorem) The fork- in order to meet Augur’s integrity requirements. ing protocol has integrity if and only if: Every universe begins with a default reporting fee of 1%. If the current market cap is below the target, then 1. S > 21 , or reporting fees are automatically increased (but will never be higher than 33.3%), putting upward pressure on the 2. Pf < P and the market cap of REP is greater than price of REP and/or downward pressure on new native (Ia +Ip )P (P −Pf )S . open interest. If the current market cap is above the target, then reporting fees are automatically decreased Proof. Suppose the forking protocol has integrity. Then, (but will never be lower than 0.01%) so that traders are by definition, S > 12 or Ia + Ip < (P − Pf )SM . Suppose not paying more than needed to keep the system secure. Ia +Ip < (P −Pf )SM . Since Ia +Ip ≥ 0 and SM > 0, we The reporting fees are determined as follows. Let r be know that Pf < P . Then, solving Ia + Ip < (P − Pf )SM the reporting fee from the previous window, let t be the (I +I )P target market cap, and let c be the current market cap. for P M , we see that (Pa−Ppf )S < P M . Thus the first direction is proved. Then the n reporting fee for the current o fee window is given  t 333 1 Now suppose that S > 21 , or that Pf < P and by max min c r, 1000 , 10,000 . (Ia +Ip )P 1 (P −Pf )S < P M . If S > 2 , then the forking protocol has (I +I )P integrity by definition. If Pf < P and (Pa−Ppf )S < P M , D. Leveraging the Threat of a Fork then, solving the inequality for Ia + Ip , we see that Ia + Ip < (P − Pf )SM , and the forking protocol has As mentioned above, forks are a disruptive and slow integrity. way for markets to reach finalization. Rather than using the forking process to resolve every market, Augur lever- ages the threat of a fork to resolve markets efficiently. 24 Inpractice, the attacker would receive 1.05SM REP in the child universe because of the 5% bonus for migrating within 60-days of the start of a fork. We ignore the 5% bonus here for ease of discussion. To see a discussion that includes the 5% bonus, see 25 See Appendix B for some alternative assumptions and their conse- Appendix C. quences.

10 Recall that any stake successfully disputing an out- situations (see Section II C), these nudges are reactionary come in favor of the market’s final outcome will receive and are adjusted only once per 7-day fee window. a 50% ROI on their dispute stake.26 In the event of a It is worth noting, however, that speculators who wit- fork, any REP staked on any of the market’s false out- ness the sudden increase in open interest may buy REP comes should lose all economic value, while any REP in anticipation of the reactionary market cap nudge, thus staked on the market’s true outcome is rewarded with driving the market cap of REP up, perhaps to a point 50% more REP in the child universe that corresponds where the integrity of the forking protocol is no longer to the market’s true outcome (regardless of the outcome threatened. So the length of time during which the ora- of the fork). Therefore, if pushed to a fork, REP holders cle is vulnerable may not be long enough for an attacker who dispute false outcomes in favor of true outcomes will to successfully exploit the vulnerability. always come out ahead, while REP holders who staked on false outcomes will see their REP lose all economic value. C. Inconsistent or Malicious Resolution Sources We believe this situation is sufficient to guarantee that all false tentative outcomes will be successfully disputed. During market creation, market creators chose a reso- lution source that reporters should use to determine the outcome of the event in question. If the market creator III. POTENTIAL ISSUES & RISKS chooses an inconsistent or malicious resolution source, honest reporters may lose money. A. Parasitic Markets For example, suppose the market in question has out- comes A and B, and the market creator, Serena, has cho- Recall that a parasitic market is any market that does sen her own website, attacker.com, as the resolution not pay reporting fees to Augur, but does resolve in ac- source. After the market’s event end time, Serena – who cordance with the resolution of a native Augur market. is also the designated reporter for the market – reports Because parasitic markets do not have any reporters to outcome A, and updates attacker.com to indicate that pay, they can offer the same service as Augur with lower outcome B is the correct outcome. Honest reporters who fees. This can have serious consequences for the integrity check attacker.com will see that the initial report is in- of Augur’s forking protocol. correct and, during the first dispute round, should suc- cessfully dispute the tentative outcome in favor of out- In particular, if parasitic markets attract trading inter- come B. Serena would update attacker.com to indicate est away from Augur, then Augur’s reporters will receive that outcome A is the correct outcome, and the market less in reporting fees. This would put downward pressure would then enter its second dispute round. Again, re- on the market cap of REP. If the market cap of REP porters who check attacker.com will see that the tenta- falls too low, the integrity of the forking protocol is put tive outcome (outcome B) is incorrect, and may success- in jeopardy (Theorem 1). As a result, parasitic markets fully dispute it. Serena can repeat this behavior until have the potential to threaten the long term viability of the market resolves. No matter how the market resolves, Augur, and should be vehemently opposed. some honest reporters will lose money. Our best defense against parasitic markets is to make Several variations of this attack exist. Simply ignoring trading on the Augur platform as cheap as possible (while markets with dubious resolution sources is not sufficient, still maintaining the integrity of the oracle), in order to for in the event that such a market causes a fork, all minimize the reward for running a parasitic market. REP holders will have to choose a child universe to which to migrate their REP. Reporters should remain vigilant against markets with dubious resolution sources. Such B. Volatility of Open Interest markets should be publicly identified so reporters can coordinate to make sure such markets finalize as invalid. Large, sudden, and unexpected increases in open in- terest – like those that may be seen during a popular sporting event – result in rapid increases in the market D. Self-Referential Oracle Queries cap requirement for forking protocol integrity (Theorem 1). When the market cap requirement exceeds the mar- Markets that trade on the future behavior of Augur’s ket cap, there is a risk of economically rational attackers oracle may have undesirable effects on the behavior of the causing a fork to resolve incorrectly. While Augur does oracle itself [11]. For example, consider a market that attempt to nudge the market cap upwards during such trades on the question, “Will any designated reporter fail to submit a report during their three-day reporting period before December 31, 2018?” Bets placed on the No outcome of this market may act as a perverse incentive 26 Measured in REP that exists in a universe that corresponds to the for designated reporters to intentionally fail to report. market’s final outcome; see Theorem 3 in Appendix A. If a designated reporter can buy up enough Yes shares

11 at a low enough price to compensate for the loss of the F. Ambiguous or Subjective Markets no-show bond, they may intentionally fail to report. If the market cap of REP is large enough (Theorem 1) Only events that have objectively knowable outcomes then these self-referential oracle queries will not threaten are suitable for use in Augur markets. If reporters be- the integrity of the forking protocol. However, they may lieve that a market is not suitable for resolution by the negatively affect the performance of Augur by causing platform – for example, because it is ambiguous, subjec- delays in market finalizations. While markets would still tive, or the outcome is not known by the event end date finalize correctly, this sort of behavior is disruptive and – they should report the market as Invalid. If a market undesirable. resolves as Invalid, traders are paid out at equal values for all possible outcomes; for scalar markets, traders are paid out halfway between the market’s minimum price and maximum price. E. Uncertain Fork Participation It is possible to imagine markets where some reporters are certain that the outcome is A and others are cer- We cannot know in advance how much REP will be mi- tain that the outcome is B. For example, in 2006, Trade- grated to the True universe during the forking period of a Sports allowed its users to speculate on whether North fork, thus we cannot know in advance whether the market Korea would fire a ballistic missile that would land out- cap is large enough for the oracle to have integrity (Theo- side of its airspace before the end of July 2006. On July rem 1). Our belief in the integrity of the forking protocol 5, 2006, North Korea successfully fired a ballistic missile can be no stronger than our belief in our assumptions that landed outside of its airspace, and the event was about the lower bound on honest participation during a widely reported by the world media and confirmed by forking period. We assume that at least 20% of all REP many U.S. government sources. However, the U.S. De- will migrate to the True child universe during the forking partment of Defense had not confirmed the event, as period of a fork, but we cannot guarantee this. was required by TradeSports’ contract. TradeSports con- Augur forks differ from blockchain forks in one impor- cluded that the contract’s conditions had not been met, tant respect: after a blockchain fork, a user who owned and paid out accordingly.27 a coin on the parent chain will now own a coin on both This is a case where the spirit of the market – to predict forks. Ignoring replay attacks, blockchain forks pose lit- the missile launch – was clearly satisfied, but the letter tle risk to users. After an Augur fork, however, a user of the market – to predict whether the U.S. Department who owns a REP token in the parent universe can mi- of Defense would confirm the launch – was not. Trade- grate that coin to only one of the child universes. If the Sports, being a centralized website, was able to unilater- user migrates their token to any universe other than the ally declare the outcome of the market. If such a situa- consensus universe, their token may lose all value. Thus tion arises in an Augur market, REP holders may have migrating REP during the forking period of a fork, before differing opinions about how the market should resolve, it is clear which child universe has achieved consensus, and stake their REP accordingly. In the worst case, this exposes the user to risk. That risk may discourage par- could result in a fork where REP in more than one child ticipation during the forking period of contentious forks. universe maintains a non-zero market value. In an effort to compensate for this risk and encour- age participation during forking periods, all token holders who migrate their REP within 60 days of the start of a ACKNOWLEDGMENTS fork will receive 5% additional REP in the child universe to which they migrated (see Section I C 9). However, we We thank Abraham Othman, Alex Chapman, Serena cannot know in advance whether this 5% bonus will be Randolph, Tom Haile, George Hotz, Scott Bigelow, and enough to compensate for the risk and incentivize par- Peronet Despeignes for their helpful feedback and sug- ticipation during a forking period. gestions. [1] J. Wolfers and E. Zitzewitz. Prediction markets. Journal ket. Journal of Economic Behavior & Organization, of Economic Perspectives, 18(2):107–126, 2004. 60(4):449–459, 2006. [2] James Surowiecki. The Wisdom of Crowds. Anchor, 2005. [4] D.M. Pennock, S. Lawrence, C.L. Giles, and F.A. Nielsen. [3] R. Hanson, R. Oprea, and D. Porter. Information ag- The real power of artificial markets. Science, 291:987– gregation and manipulation in an experimental mar- 988, 2001. [5] C. Manski. Interpreting the predictions of prediction markets. NBER Working Paper No. 10359, 2004. [6] J. Wolfers and E. Zitzewitz. Interpreting prediction market prices as probabilities. NBER Working Paper 27 See https://en.wikipedia.org/wiki/Intrade#Disputes for details. No. 10359, 2005.

12 [7] S. Goel, D.M. Reeves, D.J. Watts, and D.M. Pennock. Prediction without markets. In Proceedings of the 11th ACM Conference on Electronic Commerce, EC ’10, pages 357–366. ACM, 2010. [8] S. Nakamoto. Bitcoin: a peer-to-peer electronic cash sys- tem. https://bitcoin.org/bitcoin.pdf, 2008. [9] V. Buterin. A next generation smart con- tract and decentralized application platform. https://github.com/ethereum/wiki/wiki/White-Paper, 2013. [10] J. Clark, J. Bonneau, E.W. Felten, J.A. Kroll, A. Miller, and A. Narayanan. On decentralizing prediction mar- kets and order books. In WEIS ’14: Proceedings of the 10th Workshop on the Economics of Information Secu- rity, June 2014. [11] A. Othman and T. Sandholm. Decision rules and de- cision markets. In Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Sys- tems: Volume 1 - Volume 1, AAMAS ’10, pages 625– 632. International Foundation for Autonomous Agents and Multiagent Systems, 2010. [12] J. Peterson and J. Krug. Augur: a decentral- ized, open-source platform for prediction markets. arXiv:1501.01042v1 [cs.CR], 11 2014.

13 Appendix A: Finalization Time & Redistribution Lemma 2. S(ω̂n , n) = 2S(ω̂n , n), for n ≥ 2. Proof. Suppose a market enters dispute round n, where We begin with some notation, definitions, and obser- n ≥ 2. During dispute round n − 1, the outcome ω̂n−1 vations. must have been successfully disputed in favor of outcome Definition 5. For a given market M , let ΩM be the ω̂n . According to Eq. 1, the size of that dispute bond is outcome space (or set of outcomes) of M . B(ω̂n , n − 1) = 2An−1 − 3S(ω̂n , n − 1). Using observation Definition 6. For n ≥ 1 and ω ∈ ΩM , let S(ω, n) denote 3, this can be rewritten as the total amount of stake on outcome ω at the begin- ning of dispute round n. This includes all stake from all B(ω̂n , n − 1) + S(ω̂n , n − 1) = 2S(ω̂n , n − 1) (A1) successful dispute bonds in favor of ω over all previous dispute rounds. We know the dispute bond was successfully filled dur- ing round n − 1. Using observation 4, we see that Definition 7. For n ≥ 1 and ω ∈ ΩM , let S(ω, n) denote B(ω̂n , n − 1) + S(ω̂n , n − 1) = S(ω̂n , n). Observation 5 the amount of stake on all outcomes in ΩM except for ω tells us that the total amount staked on ω̂n is unchanged at the beginning of dispute round n: from round n − 1 to n, 2S(ω̂n , n − 1) = 2S(ω̂n , n). Thus, X Eq. A1 reduces to S(ω̂n , n) = 2S(ω̂n , n). S(ω, n) = S(γ, n) γ∈ΩM Theorem 3. Any REP holders successfully disputing an γ6=ω outcome in favor of a market’s final outcome will receive Definition 8. For n ≥ 0, let An denote the total stake a 50% ROI on their dispute stake (measured in REP that over all outcomes M at the beginning of dispute round exists in a universe that corresponds to the market’s final n: outcome), unless the market is interrupted by some other X market causing a fork. An = S(ω, n) ω∈ΩM Proof. During a fork, all users who successfully filled dis- pute bonds in favor of the forking market’s final outcome Observation 3. It follows that An − S(ω, n) = S(ω, n). are given (via coins minted during the fork) a 50% return Definition 9. For n ≥ 1, let ω̂n denote the tentative out- on their dispute stake when they migrate their dispute come at the beginning of dispute round n. For example, stake to the corresponding child universe. Thus, in the ω̂1 is the outcome reported by the initial reporter. case where the market in question has caused a fork, the Definition 10. For n ≥ 1 and ω 6= ω̂n , let B(ω, n) theorem is immediately true. denote the amount of stake required to successfully fill a Now consider the case where the market in question dispute bond in favor of outcome ω during dispute round resolves without causing a fork, and reporting is not in- n. terrupted by some other market causing a fork. Denote the market’s final outcome by ωFinal and sup- Recall that the amount of stake required to successfully pose the market resolves at the end of reporting round fill a dispute bond in favor of outcome ω during dispute n, where n ≥ 2. That means the tentative outcome round n, where ω 6= ω̂n is given by Eq. 1, B(ω, n) = for round n is ωFinal , and that outcome is not success- 2An − 3S(ω, n). fully disputed during round n. In other words: ω̂n = Observation 4. If a dispute bond is successfully filled in ωFinal . Then by Lemma 2 we know that S(ωFinal , n) = favor of outcome ω during dispute round n, then S(ω, n+ 2S(ωFinal , n). 1) = B(ω, n) + S(ω, n). That is, the successful dispute Since the market resolves at the end of round n with no stake is the only new stake applied to outcome ω at the further stake added to any outcome, the above equation end of dispute round n. shows the final amount of stake on the market’s final outcome, ωFinal , and the sum of all stake on all of the Observation 5. For all ω 6= ω̂n , S(ω, n − 1) = S(ω, n). market’s other outcomes, ωFinal . Note that there is ex- That is, if a dispute bond is not entirely filled in favor of actly twice as much stake on the market’s final outcome outcome ω, then no additional stake is added to outcome as there is on all other outcomes combined. ω at the beginning of the next dispute round. This is due Augur redistributes all stake on the non-final out- to the fact that all unsuccessful dispute stake is returned comes to users who staked on ωFinal , in proportion to to the users at the end of the dispute round. the amount of REP they staked. Therefore the users Observation 6. For all n ≥ 2, An = An−1 + B(ω̂n , n − who successfully filled a dispute bond in favor of ωFinal 1). That is, the total stake over all outcomes at the get a 50% ROI on their staked REP. beginning of a dispute round is simply the total stake from the beginning of the previous dispute round plus Next, consider the maximum number of dispute rounds the successful dispute stake from the previous dispute required to resolve a market. Eq. 1 is minimized when ω round. All other stake is returned to users at the end of is chosen to be the non-tentative outcome that begins the the previous dispute round. dispute round with the greatest amount of stake. Lemma

14 2 implies that the non-tentative outcome with the great- S(ω̂3−1 , 3) = S(ω̂2 , 3) = 2d = 23 (3d) = 23 B2 = 32 B3−1 , est amount of stake is the previous dispute round’s ten- so part 1 of the lemma holds for n = 3. tative outcome. Therefore, the smallest possible dispute A3 = 6d = 2(3d) = 2B2 = 2B3−1 , so part 2 of the bond size that can be successfully filled during dispute lemma holds for n = 3. round n, where n ≥ 2, is B(ω̂n−1 , n). B3 = 6d = 3d23−2 , so part 3 of the lemma holds for In other words, the dispute bond size grows slowest n = 3. when the same two outcomes are repeatedly disputed in favor of one another. It follows that the number of dis- Therefore the lemma, in its entirety, holds true for the pute rounds required for a market to initiate a fork is base case of n = 3. maximized when the same two outcomes are repeatedly disputed in favor of one another. Therefore we can deter- (Induction) Suppose the lemma is true for all n such mine the maximum number of dispute rounds that any that 3 ≤ n ≤ k. We want to show that the lemma holds market may undergo before initiating a fork by finding for n = k + 1. That is, we want to show that: the maximum number of dispute rounds that can occur in the particular case where the same two market out- (a) S(ω̂k , k + 1) = 23 Bk comes are repeatedly disputed in favor of on another. (b) Ak+1 = 2Bk and We examine that case now. Suppose that every successful dispute bond is filled in (c) Bk+1 = 3d2k−1 favor of the previous dispute round’s tentative outcome. Then the two tentative outcomes that are iteratively dis- First, we prove part (a). By observation 8: puted in favor of one another other are ω̂1 and ω̂2 . S(ω̂k , k + 1) = S(ω̂k , k − 1) + Bk−1 Observation 7. In the case where the same two ten- tative outcomes are repeatedly disputed in favor of one By observation 7 we can rewrite the above as: another, ω̂n = ω̂n−2 for all n ≥ 3. S(ω̂k−2 , k + 1) = S(ω̂k−2 , k − 1) + Bk−1 Definition 11. Let d denote the amount of stake placed on ω̂1 during the initial report. Because the tentative By the induction hypothesis, we can rewrite outcome for each round is known in this situation, we can S(ω̂k−2 , k − 1) as 32 Bk−2 on the right-hand side to get: simplify our notation for the dispute bond sizes. Define a shorthand Bn to denote the bond size required for round S(ω̂k−2 , k + 1) = 32 Bk−2 + Bk−1 n, so that B1 = 2d and Bn = B(ω̂n−1 , n) for all n ≥ 2. This will make for easier reading and comprehension. By the induction hypothesis, we can write Bk−2 as 3d2k−4 and Bk−1 as 3d2k−3 : Observation 8. In the case where the same two ten- tative outcomes are repeatedly disputed in favor of one S(ω̂k−2 , k + 1) = d2k−1 another, S(ω̂n−1 , n) = S(ω̂n−1 , n − 2) + Bn−2 for n ≥ 3. (That is, every other successful dispute bond is added to Applying observation 7 to the left-hand side we get: the same outcome.) S(ω̂k , k + 1) = d2k−1 Lemma 4. If the same two tentative outcomes are re- peatedly disputed in favor of one another, then for all n Finally, note that by the above equation and the in- where n ≥ 3: duction hypothesis, S(ω̂k , k + 1) = d2k−1 = 32 (3d2k−2 ) = 2 3 Bk . This proves part (a). 1. S(ω̂n−1 , n) = 32 Bn−1 Next, we prove part (b). By observation 6: 2. An = 2Bn−1 and Ak+1 = Ak + Bk 3. Bn = 3d2n−2 By the induction hypothesis, Ak = 2Bk−1 : Proof. (By induction on n) Suppose the same two tentative outcomes are repeat- Ak+1 = 2Bk−1 + Bk edly disputed in favor of one another. (Base Case) By definition and Eq. 1 we make the fol- By the induction hypothesis, Bk−1 = 3d2k−3 , so the lowing observations. right-hand side can be simplified to • S(ω̂1 , 1) = d, S(ω̂2 , 1) = 0, A1 = d, and B1 = 2d Ak+1 = 3d2k−2 + Bk • S(ω̂1 , 2) = d, S(ω̂2 , 2) = 2d, A2 = 3d, and B2 = 3d By the induction hypothesis, Bk = 3d2k−2 to rewrite the right-hand side as • S(ω̂1 , 3) = 4d, S(ω̂2 , 3) = 2d, A3 = 6d, and B3 = 6d Ak+1 = 2Bk ,

15 and part (b) is proved. Appendix B: Alternative Assumptions & Finally, we prove part (c). By Eq. 1: Consequences Bk+1 = 2Ak+1 − 3S(ω̂k , k + 1) Recall that: By observation 8, we can write S(ω̂k , k+1) as S(ω̂k , k− • S is the proportion of total REP that is migrated 1) + Bk−1 : to the True universe during the forking period Bk+1 = 2Ak+1 − 3 (S(ω̂k , k − 1) + Bk−1 ) • P is the price of REP in the True universe By observation 7, ω̂k = ω̂k−2 : • Pf is the price of REP that has been migrated to a False universe of the attacker’s choosing Bk+1 = 2Ak+1 − 3 (S(ω̂k−2 , k − 1) + Bk−1 ) • Ia is Augur’s native open interest By observation 6, Ak+1 = Ak + Bk : • Ip is the parasitic open interest Bk+1 = 2 (Ak + Bk ) − 3 (S(ω̂k−2 , k − 1) + Bk−1 ) Augur makes certain assumptions about S, Pf , and Ip in order to arrive at a target market cap. In particular, By the induction hypothesis, Ak = 2Bk−1 and Augur assumes that at least 20% of all REP will be mi- S(ω̂k−2 , k − 1) = 32 Bk−2 : grated to the True universe during the forking period of a fork, REP migrated to a False universe will have no Bk+1 = 2 (2Bk−1 + Bk ) − 3 32 Bk−2 + Bk−1  non-negligible value, and parasitic open interest will be at most half of the native open interest. In other words: By the induction hypothesis, Bk = 3d2k−2 , Bk−1 = S ≥ 0.2, Pf = 0, and Ia ≥ 2Ip . Under these assump- 3d2k−3 and Bk−2 = 3d2k−4 . Making these substitutions tions, Theorem 1 tells us that the forking protocol has and simplifying yields: integrity whenever the market cap of REP is greater than Bk+1 = 3d2k−1 7.5 times the native open interest. You can make your own assumptions about S, Pf , and This proves part (c), and concludes the proof of the Ip to arrive at your own conclusions about how large the lemma. market cap needs to be for the oracle to have integrity in practice. We list some alternative scenarios here for your Theorem 5. If not interrupted by some other market convenience. causing a fork, a given market may undergo at most 20 dispute rounds before finalizing or causing a fork. Scenario 1. More than 50% of existing REP migrates to the True universe during the forking period. In this case Proof. Suppose that a given market is not interrupted by Pf and Ip do not matter at all. Since S > 21 , the forking some other market causing a fork. Then, as shown above, protocol has integrity no matter what the market cap we know that the number of dispute rounds required for a happens to be. There would not exist enough remaining market to initiate a fork is maximized when the same two REP on the market for an attacker to be successful. outcomes are repeatedly disputed in favor of one another. Part 3 of Lemma 4 tells us that, in this situation, the Scenario 2. 48% of existing REP migrates to the True dispute bond size required for successfully disputing the universe during the forking period, no parasitic markets tentative outcome during round n is given by 3d2n−2 , exist, and REP sent to a False universe has no value. In where d is the amount of the stake placed during the this case S = 0.48, Ip = 0, and Pf = 0. Under these initial report. assumptions, the market cap of REP must be greater We know that forks are initiated after the successful than about twice the native open interest for the forking fulfillment of a dispute bond with size at least 2.5% of protocol to have integrity. all existing REP, and we know that there are 11 million Scenario 3. 20% of existing REP migrates to the True REP in existence. Thus a fork is initiated when a dispute universe during the forking period, parasitic open interest bond of size 275,000 REP is filled. We also know that is equal to native open interest, and REP migrated to a d ≥ 0.35 REP, because the minimum amount of stake on False universe trades at 5% of the value of REP migrated the initial report is 0.35 REP28 . to the True universe. In this case S = 0.2, Ip = Ia , and Solving 3(0.35)2n−2 > 275, 000 for n ∈ Z yields n ≥ 20. Pf = 0.05P . Under these assumptions, the market cap Thus, we can guarantee that a market will resolve or of REP must be greater than about 10.5 times the native cause a fork after at most 20 dispute rounds. open interest for the forking protocol to have integrity. Scenario 4. Only 5% of existing REP migrates to the True universe during the forking period, parasitic interest 28 See appendixes E 2 and E 3 is twice as large as native open interest, and REP sent to

16 a False universe trades at 5% of the value of REP sent result in the oracle reporting incorrectly, but it would to the True universe. In this case S = 0.05, Ip = 2Ia , and result in disruptive forks happening often. Pf = 0.05P . Under these assumptions, the market cap To prevent this behavior Augur needs to make sure of REP must be greater than about 63 times the native that the cost of initiating a fork is greater than the max- open interest for the forking protocol to have integrity. imum value that can be gained from the 5% inflation bonus. Here, we derive a lower bound on cost of initiat- ing a fork in order to prevent this perverse incentive. Appendix C: The Effect of the Early Migration Let P0 denote the price of REP before the fork and P1 Bonus on the Integrity of the Forking Protocol denote the price of REP after the fork. Let M0 denote the money supply before the fork and M1 denote the money For ease of discussion, we ignored the 5% early migra- supply after the fork. Let S denote the proportion of tion bonus and a small term when discussing the integrity M0 migrating to the True universe during the forking of the forking protocol. Here we revisit Theorem 1 taking period of the fork. Let b denote the amount of REP that those two things into consideration. must be economically burned (that is, staked on a False As before, the amount of REP sent to the True universe outcome) in order to initiate a fork. We assume b > 1. during the reporting period is denoted by SM . Thus for For the purposes of this section, we make the conser- an attacker to be successful, they must migrate at least vative assumption that all REP that migrates during the SM + ǫ REP, which has a value of (SM + ǫ)P before forking period is controlled by the attacker. We further migration, to some False universe. assume (because it minimizes the cost of this attack this If an attacker migrates SM +ǫ REP to a False universe attack) that all REP that migrates during the forking during the reporting period of a fork, they will receive period is migrated to the True universe. 1.05(SM + ǫ) REP on the child universe to which they With this notation, SM0 is the amount of REP mi- migrated. By definition of Pf , the value of those coins grated during the forking period, while (1 − S)M0 is the is given by 1.05(SM + ǫ)Pf . Thus the minimum cost to amount of REP not migrated during the forking period. the attacker is (SM + ǫ)P − 1.05(SM + ǫ)Pf , which can be expressed as (SM + ǫ)(P − 1.05P f ). M0 = SM0 + (1 − S)M0 (D1) As before, the maximum (gross) benefit to an attacker When a total of SM0 REP is migrated during the fork- is given by Ia + Ip . Thus we would say the forking pro- ing period, a total of 0.05SM0 REP is created via infla- tocol has integrity whenever S > 21 or: tion: Ia + Ip < (SM + ǫ)(P − 1.05Pf ) (C1) M1 = 1.05SM0 + (1 − S)M0 (D2) Solving the above inequality for the market cap, P M , Focusing only on the effects of inflation, and for the we can see that the forking protocol has integrity if and sake of simplicity, we are assuming that the market cap only if: after the fork will be the same as the market cap before the fork29 : 1 1. S > 2 or P0 M0 = P1 M1 (D3) 2. 1.05Pf < P and the market cap of REP is greater than P (Ia +Ip −ǫ(P −1.05Pf )) Substituting D1 and D2 into D3 and simplifying gives S(P −1.05Pf ) us: As we can see, the effect of the early migration bonus 20P0 P1 = (D4) on the market cap requirement is very small. 20 + S The (gross) benefit to the attacker for initiating a fork Appendix D: The Effect of the Early Migration and taking advantage of the early migration bonus is the Bonus on the Minimum Cost of a Fork value of her migrated REP after migration minus the value of her migrated REP before migration: To encourage greater participation during a fork, all 1.05SM0 P1 − SM0 P0 (D5) token holders who migrate their REP within 60 days of the start of a fork will receive 5% additional REP in the Substituting D4 into D5 we get an alternative expres- child universe to which they migrated. This reward is sion for the (gross) benefit to the attacker: paid for via currency inflation. 20P0 This bonus can become a perverse incentive if the cost 1.05SM0 − SM0 P0 (D6) of initiating a fork is too low. In particular, if an attacker 20 + S can gain more value from the 5% REP bonus than she would lose by initiating a fork, then we would expect 29 We forks to happen as often as possible. This attack, which think this is conservative. In practice, we expect the market we refer to as the inflation milking attack, would not cap to decrease after a fork.

17 Recall that b is the amount of REP that must be eco- on the behavior of participants during the previous fee nomically burned in order to initiate a fork. Thus, the window. Here we describe how we adjust those values. cost of initiating a fork is bP0 . Therefore, paying the cost We define the function f : [0, 1] → [ 12 , 2] by:31 of initiating a fork in order to take advantage of the early ( 100 migration bonus is worthwhile whenever the following in- x + 98 for x > 100 1 equality is satisfied: f (x) = 99 1 99 1 (E1) 50x + 2 for x ≤ 100 20P0 0 < 1.05SM0 − SM0 P0 − bP0 (D7) The function f is used to determine the multiple used 20 + S in these adjustments, as described in the subsections be- Observing that P0 > 0, and S 6= −20, we solve for b low. In brief, if the undesirable behavior occurred exactly and see that the attack is profitable when: 1% of the time during the previous fee window, then the 21M0 S bond size remains the same. If it was less frequent, then b< − M0 S (D8) the bond size will be reduced by as much as half. If it S + 20 was more frequent, then the bond size will be increased In order to prevent the perverse incentive, Augur must by as much as a factor of 2. arrange matters such that: 21M0 S 1. Validity Bond b≥ − M0 S (D9) S + 20 Noting that S is restricted to the interval [0, 1], we see During the very first fee window after launch, the va- that the value of the right-hand √ side of inequality D9 lidity bond will be set at 0.01 ETH. Then, if more than is maximized when S = 2 105 − 20 ≈ 0.4939. That is, 1% of the finalized markets in the previous fee window this attack is most profitable for the attacker when about were invalid, the validity bond will be increased. If less 49.39% of all existing REP is migrated during the forking than 1% of the finalized markets in the previous fee win- period. Being conservative, we use this value for S.30 dow were invalid, then the validity bond will be decreased Substituting S = 0.4939 into D9 we get b ≥ (but will never be lower than 0.01 ETH). 0.012197M0 . Therefore, if the cost to initiate a fork is at In particular, we let ν be the proportion of finalized least 1.2197% of existing REP then the inflation milking markets in the previous fee window that were invalid, attack is not profitable. and bv be the amount of the validity bond from the pre- Recall that a fork is initiated only after a successful vious fee window.  1Then the validity bond for the current dispute bond is filled that is greater than 2.5% of existing window is max 100 , bv f (ν) . REP. Suppose that such a dispute bond were filled in favor of outcome ω and a fork were initiated. Outcome ω is either true or false. 2. No-Show REP Bond If outcome ω is false, then at least 2.5% of existing REP was staked on a false outcome, and thus economically During the very first fee window after launch, the no- burned. So inflation milking is not profitable when ω is show REP bond will be set at 0.35 REP. As with the false. validity bond, the no-show REP bond is adjusted up or If outcome ω is true, then Lemma 2 tells us that at down, targeting a 1% no-show rate with a floor of 0.35 least 1.25% of existing REP (in total) is staked on false REP. outcomes, and thus economically burned. So inflation Specifically, we let ρ be the proportion of markets milking is also not profitable when ω is true. in the previous fee window whose designated reporters It is for this reason that fork initiation requires suc- failed to report on time, and we let br be amount of the cessfully filling a dispute bond that is at least 2.5% of no-show REP bond from the previous fee window. The existing REP. the amount of the no-show REP bond for the current fee window is max {0.35, br f (ρ)}. Appendix E: Bond Size Adjustments 3. Designated Reporter Stake The validity bond, the no-show REP bond, and the designated reporter stake are dynamically adjusted based During the very first fee window after launch, the amount of the designated reporter stake will be set at 0.35 REP. The amount of the designated reporter stake 30 Inpractice, the attacker cannot prevent other participants from mi- grating their own REP during the forking period, and thus cannot guarantee that S would not exceed her ideal value of about 0.4939. However, since we are defending against the worst case scenario, 31 Thisformula may change once empirical data from live markets is we use S = 0.4939. obtained.

18 is dynamically adjusted according to how many desig- proach is that it reduces the average fees paid by traders, nated reports were incorrect (failed to concur with the which should make Augur more competitive. final market outcome) during the previous fee window. In particular, we let δ be the proportion of designated reports that were incorrect during the previous fee win- 3. Universes dow, and we let bd be the amount of the designated re- porter stake during the previous fee window, then the In the old design, there was only one “version” of REP, amount of the designated reporter stake for the current and its total supply was fixed. In the current design, REP window is max {0.35, bd f (δ)}. can fork into many different versions (universes), each of which can end up with more or less total REP than the original version. If a fork is contentious, the REP supply Appendix F: Design Changes in each child universe might be only a fraction of the total supply in the parent universe. In a non-contentious We arrived at the current design of Augur after three fork, the early migration bonus to fork participants could years of research and iteration. The design that emerged result in a child universe that has more total REP than from this process differs substantially from the vision laid its parent universe. out in our old whitepaper [12]. Here, we discuss three sig- The new versions of REP spawned by a fork are all dif- nificant changes as well as the rationale for the changes. ferent tokens, each with its own price and total supply, and service providers should treat them as such. When Augur first launches, there will be a single universe (the genesis universe) and a single version of REP, just as it 1. Reporting Fees exists now. However, as soon as a fork occurs, the single version of REP will split into many versions: for example, In the old design, the market creator would set a trad- a forking market with outcomes A and B would spawn new ing fee which would be split 50/50 with reporters. In the tokens REP-A, REP-B, and REP-Invalid. Wallets and current design, the fees for the market creator and the re- exchanges that support REP would now have four differ- porters are independent, and the reporters’ fees are tuned ent versions of REP which they could (in theory) support dynamically by Augur itself to keep the system secure. – REP-genesis (the original version of REP, which would The fees paid to reporters impact the price of REP, now be locked), REP-A, REP-B, and REP-Invalid.32 which has a direct effect on the security of the forking The total supply of REP in each child universe depends protocol (Theorem 1). If the fees paid to reporters are too on how much REP migrated to it, and when that migra- low, then the integrity of the oracle is at risk. If the fees tion occurred. Migrating REP during a fork, before it paid to reporters are too high, then the threat of parasitic is clear which child universe has achieved consensus, ex- markets increases. Thus, it is important that the fees poses the user to a small (but non-zero) amount of risk paid to reporters be adjusted dynamically to maintain (see Section III E), which may discourage participation Augur’s security, rather than being decided arbitrarily during the forking period of contentious forks. In order by market creators. to encourage participation during a fork, users must be Decoupling reporters’ fees from the choices of market compensated for the risk. creators also ensures that reporters (and thus, forking Users who do not participate during the forking period protocol integrity) are not harmed by competition among of a fork could be penalized by losing some portion of market creators to create markets with the lowest fees. their REP holdings. In fact, the old design had a “use it Quality markets and quality reporting should be mea- or lose it” mechanism that penalized non-participants as sured and rewarded separately. Competition should be if they were reporters who reported incorrectly. However, allowed to drive market creator fees towards zero, with- punishing users who do not participate creates significant out dragging the fees paid to reporters down as well. usability problems. Punishing users who do not partic- ipate is problematic for wallets and exchanges who are the custodians of their customers’ REP. In the event of a 2. Trading Fees fork, exchanges would need to migrate their customer’s REP to some child universe during the forking period, or In the old design, fees were collected from traders on lose some portion of their REP holdings.33 every trade. In the new design, fees are collected from traders only when settling directly with market contracts. This change was made, in part, because Augur cannot 32 As a practical matter, service providers may find it easiest (and police offline trading. Shares of market outcomes are least disruptive to their users) to encourage their users to partici- simply tokens, which can be traded freely between users. pate in the fork, and then to simply support the winning universe Since collecting fees on every trade is infeasible, Augur once the fork has resolved. instead collects fees only when traders settle directly with 33 We also found, as a practical matter, that the smart contract code the Augur market contracts. An added benefit of this ap- needed to implement forking rewards only using redistribution was

19 Instead of penalizing non-participants, fork partici- migrates to a losing universe – of which 1.25% to 2.5% pants who migrate during the forking period are re- has already been committed as dispute stake – then all warded by minting a 5% bonus in the child universe to universes will have a smaller total supply of REP than which they are migrating. If 4.762% of REP (or more) the parent universe. inordinately complex. Contract code complexity is itself a secu- rity risk, so we have tried to simplify the implementation wherever possible.