Conflux Network:
Engineering An Economic Design
Andreas Park1,2 and Andreas Veneris1,3,4
1

Conflux Foundation Advisor
The Rotman School of Management, University of Toronto
3
Dept. of Electrical and Computer Engineering, University of Toronto
4
Dept. of Computer Science, University of Toronto
andreas.park@rotman.utoronto.ca, veneris@eecg.toronto.edu
2

Abstract

Distributed ledgers or blockchains, in particular those based on Proof-of-Work (PoW)
protocols, rely as much on economic mechanisms as on technology. In this paper, we
describe how we approach the design of the economic mechanisms that underline Conflux, a high throughput/performance PoW blockchain, by providing a detailed analysis
of its economic viability. Conflux offers several innovations relative to well-understood
blockchain networks such as Bitcoin and Ethereum, both in terms of technology design
but also in terms of the economics that underpin the technology. Most notably, a major difference in Conflux when compared to the status-quo is that processing of blocks
occurs in parallel rather than serially, and users who commit code or information to theblockchain face ongoing costs and/or benefits for the duration they occupy chain space.
Hence, the ecosystem design requires to assess carefully those parameters including how
new block processing affects the fundamental limits of blockchain performance, and how
storage costs affect user incentives in this new decentralized ecosystem.

1

NOTICENOTHING IN THIS WHITEPAPER CONSTITUTES LEGAL, FINANCIAL, BUSINESS, OR TAX ADVICE AND YOU SHOULD CONSULT YOUR OWN LEGAL,FINANCIAL, TAX OR OTHER PROFESSIONAL ADVISER BEFORE ENGAGING
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WHO HAVE WORKED ON THE CONFLUX PLATFORM OR PROJECT IN ANY
WAY WHATSOEVER (THE CONFLUX TEAM) NOR ANY THIRD PARTY SERVICE PROVIDER SHALL BE LIABLE FOR ANY KIND OF DIRECT OR INDIRECT DAMAGE OR LOSS WHATSOEVER WHICH YOU MAY SUFFER IN CONNECTION WITH ACCESSING THIS WHITEPAPER, MATERIALS PRODUCED BY
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The Conflux and the Conflux team do not and do not purport to make, and hereby
disclaims, all representations, warranties or undertaking to any entity or person. All
statements contained in this Whitepaper, statements made in press releases or in any
place accessible by the public and oral statements that may be made by the Conflux
and/or the Conflux team may constitute forward looking statements (including statements regarding intent, belief or current expectations with respect to market conditions,business strategy and plans, financial condition, specific provisions and risk management practices). You are cautioned not to place undue reliance on these forward-looking
statements given that these statements involve known and unknown risks, uncertainties
and other factors that may cause the actual future results to be materially different fromthat described by such forward looking statements. These forward-looking statements
are applicable only as of the date of this Whitepaper and the Conflux and the Conflux team expressly disclaims any responsibility (whether express or implied) to release
any revisions to these forward-looking statements to reflect events after such date. You
understand that the Project and the creation and distribution of the Tokens involve
significant risks, including but not limited to, the risk that (i) the technology associatedwith the Conflux Project may not function as intended; (ii) the Conflux Project may failto attract interest or adoption, either from key stakeholders or the broader community;(iii) no guarantees that the price per Token determined by the market will be equal toor higher.

1

I.

Introduction
When NASA prepared to travel to space they spent millions to develop a ballpen

so that astronauts can write in zero gravity. Faced with the same problem, the Soviet
Union used pencils. This anecdote is Conflux’s philosophy in a nutshell: its main goal
is to take the best parts of existing permissionless blockchains and push those bounds
significantly.
What is Conflux? In brief, it is a Proof-of-Work (PoW) blockchain network thatallows the parallel processing of blocks and transactions, while eventually forming a
final serial chain. This feature contrasts other well-known networks, such as Bitcoin andEthereum, which process blocks strictly one-by-one.1 The parallel processing creates
economic incentives for miners that are notably different from serial chains and in thispaper we discuss how the differences improve the security and economic viability against
double-spending attacks.
Conflux also seeks to overcome the problem of the unpaid smart-contract space occupation. In Ethereum, when introducing a new contract, a user merely pays at the timeof the inclusion of the code in the chain whereas the community as a whole faces theburden of keeping the contract in storage. Conflux introduces ongoing costs of contract
maintenance which give users an economic incentive to avoid wasting resources.
To provide intrinsic value, Conflux seeks to attract users that actively use the networkfor value-added services. Conflux believes it is critical that there are no barriers-to-entry
for those who make meaningful contributions. This is why Conflux is a permissionless network with economic-driven governance mechanisms that incentivize community
1
Ethereum does allow a limited number of so-called “uncle” blocks to allow for faster processing, but
the setup of Ethereum is intrinsically not parallel.

2

contributions to ensure a secure, stable, and predictable environment for commercial
activities.
This document discusses several aspects of the Conflux network that involve economic
mechanisms. These mechanisms affect the users’ and miners’ costs and rewards and thus
their behavior, therefore it is crucial to plan ahead so as to avoid creating unintended
consequence. This paper is a companion paper to the technical Conflux manuscript. It
complements the engineering aspects by focusing on the underlying system’s micro- andmacro-economic mechanisms.
At its core, blockchain technology is an infrastructure solution that allows the secure(i) transfer of economic value and (ii) execution of programming state/storage, without
a trusted third party. To succeed in this scope, it needs to balance several core factors.
First, economic value transfers and payments for the cost of such usage rely on anative token. This token needs to be designed so as to serve as a medium of exchange
but also as a unit of account for blockchain-based data. It is also desirable that the token
can be used as a store of value so it can sustain long-run incentives for the different parties
to use the chain. Finally, as is common with PoW networks, the native token plays arole in the compensation of the network’s miners who are central to the operation andsecurity of the network. There are by now a number of papers that highlight how native
tokens can spur the adoption and usage of a network,2 and we build on this body ofliterature in our analysis.
In this document we describe the distribution of tokens as well as the usage rules
and the economic impact of the various rules. Namely, tokens are issued at genesis,
as interest payments on subsets of tokens that satisfy certain rules, and as rewards to2

See, for instance, Bakos and Halaburda (2018), Cong, Li, and Wang (2018), Fisch (2019), Canidio(2018), or Li and Mann (2018)).

3

miners who include new blocks. We then provide a calibrated model that simulates
the miners’ expected income. Tokens interact with the outside world in the sense that
there is a exchange rate to fiat currencies (as well as to other crypto-currencies), and wetherefore also discuss carefully how the issuance of tokens affects the exchange rates.
In the final part of the paper we provide two formal analyses to provide a better understanding of the economics of Conflux. First, there are some well-known constraints
on double-spending proofness for PoW blockchains3 and we highlight how the Conflux
Network expands the set of economically viable states relative to known networks. Second, we provide a formal equilibrium model of user and miner interaction to study howchanges in policy variables affect equilibrium outcomes.

II.

Cornerstones of the Existing Blockchain World
Before presenting the proposed economic system, we review key concepts from themain existing blockchain models.
Bitcoin is the first working cryptocurrency that solved the double-spending problem.
At its core, the Bitcoin blockchain is a one-trick pony that is designed for the transfer
of its native token, Bitcoins. It is conceptually set up to be slow as blocks of fixed sizeare produced serially at a approximately constant rate of one block, which can contain
only around 3, 500 transactions, per 10 minutes. Although for a good level of certainty
that the value transfer has indeed happened, it is not sufficient that a transaction has
been included in a block. The reason is that the block may not be a part of the longest
chain but of a fork. This can happen, for instance, when two blocks are created ataround the same time — only one of them will eventually become part of the longest
3

See Chiu and Koeppl (2017) and Budish (2018).

4

chain. One therefore needs to wait for a few block confirmations before the transaction
can be considered as final. The setup, with block formation time of 10 minutes and aeven longer confirmation time, is clearly unsuitable for day to day payments. Bitcoin
has also other limitations: once all Bitcoins have been mined through block rewards,
miners receive only user-determined transactions fees for securing the network. If wetake the current income of miners as a benchmark, these fees need to be rather large:
At the current block rewards of 6.25 BTC per block and a BTC price of approximately$10,000 (as of the day of this publication) each of the 3,500 transactions that fit into
a block needs pay a fee of around $18. All these features make Bitcoin unsuitable for
remittance payments and likely too expensive to be a substitute payment network forthe majority of business transactions (Auer 2019).
The main participants in the Bitcoin network, however, are the miners, short-term
speculators, and long-term holders. Very few network participants use Bitcoin for its
original purpose, as “peer-to-peer electronic cash.” In the future, the long-term holders
need to rely on short-term speculators to create sufficient transactions so that the miners
are willing to continue to provide the security for the network. This will likely become achallenge in the future. In other words, as it stands, the Bitcoin network today does notincentivize users of the token for meaningful and value-generating economic activity. In
addition, the technology infrastructure of Bitcoin has limitations and allows little beyond
transfers of Bitcoin. Without Turing-complete scripts, decentralized application (dApp)
developers have at most peripheral use for it through introduction of “side-chains” suchas the Lightning Network, etc. Governance is also a challenge. Changes to the Bitcoin
protocol require that miners agree. This can be difficult when those changes may have5

a negative impact on the miners’ income — even if the change itself serves the broader
ecosystem well.
The Ethereum Network is a much improved system relative to Bitcoin and features
Turing-complete smart contract functionality, which enables developers to code dApps
that run on the network. Ethereum’s smart contract language allows the creation of
tokens that can be used as non-native payment coins or even as securities. Ethereum’s
native token Ether has no hard cap on its token supply and can therefore grow organically as usage of the network expands and demand for tokens increases. Ethereum’s
governance follows a similar mechanism as Bitcoin, with some improvements: miners
receive not only block rewards for each block that they create, they also collect transaction fees for the execution of code. Therefore, more complex transactions or operations
are rewarded with higher fees.
However, as in Bitcoin, Ethereum also suffers from a low transaction throughput
rate: the network can currently process only a maximum around 40 transactions per
second. This is nowhere near the rate of need for modern commercial financial infrastructure. For instance, Payments Canada processes around 28 million transactions on
an average business day, while Canadian economy is ranked only the 10th by Nominal GDP (Times 2019). Assuming that most activities occur over 12 hours daily, a
blockchain payments network to handle this level of transactions would need an approximately minimal throughput of 650 transactions per second (tps). Furthermore, it isequally infeasible to use the Ethereum blockchain as a substitute infrastructure for securities trading: traditional centralized securities exchanges and over-the-counter securities
markets worldwide process billions of orders and transactions per day. As a matter offact, although there are many decentralized exchanges on the Ethereum network, at the6current throughput rates they are fundamentally unable to accommodate a meaningful
fraction of today’s financial market activities.
A second function issue for Ethereum is that users pay for a contract only at thetime of the inclusion of the contract code. Additionally, only the miner that includes
this code on the chain gets this one-time reward. Yet every new contract submitted to
the Ethereum chain not only requires the network to execute the code, the contract also
occupies “chain-space” (i.e., memory in the global state of the Ethereum chain) even
if it remains inactive after its submission. In summary, all full nodes of the networkneed to subsequently store the information resulting in a situation where users can store
data on the chain with a one-time inclusion fee, while the storing of such data canbe indefinitely long with no maintenance payment required. As such today, the vast
majority of the state-tree space of Ethereum is occupied by inactive smart contracts.
This unused data waste space in the state-tree of the blockchain, slow down the system,
and create undesirable network latency/overhead.
One of the goals for the Conflux project is to build on and vastly improve on thefeatures of existing blockchain systems: guaranteed execution of software code via aTuring-complete virtual machine on a permissionless consensus mechanism with a higher
performance while not sacrificing safety and decentralization.

III.

An Overview of the Conflux Network

Conflux is a new PoW network with a Turing-complete smart contract language
similar to this of Ethereum.4 The Conflux network provides significant performance
improvements with its processing of parallel blocks in a Directed Acyclic Graph (DAG)
4

See Li, Li, Zhou, Xu, Long, and Yao (2018) and .

7

structure, which lowers confirmation times and increases transaction throughput substantially.
To address the space congestion challenge, Conflux requires users to bond native tokens into storage to occupy space, which implicitly creates a disincentive to occupy space
unnecessarily. The disincentive stems from the payment of interest on existing tokens inthe system. The interest on the bonded storage is payed to miners instead of the users tocreate a long term income to the miners. To address the fairness attack challenge, Conflux assigns the block reward in a way that eliminates the winner-take-all characteristicof mining. Instead of competing for the longest chain, miners in Conflux receive block
rewards for all the blocks that they generate, albeit with some penalty mechanisms thatencourage following the consensus protocol. Competing blocks are jointly penalized sothat selfish mining is not profitable and different miners are incentivized to cooperate
along the protocol to keep the network stable and secure.
Similarly to Ethereum, Conflux operates with an account-based model that every
normal account associates with a balance and each smart contract account contains
the corresponding byte codes as well as an internal state. Conflux supports a modified
version of Solidity (the main contract language in Ethereum) and Ethereum Virtual
Machine (EVM) for its smart contracts, so that smart contracts from Ethereum canmigrate to Conflux easily.
A transaction in Conflux refers to a message that initiates a payment transaction, or
deploys/executes smart contract code. Each block consists of a list of transactions thatare verified by the proposing miner. Each node maintains a pool of verified, received
transactions that have not yet been included in a block. Miners compete with one another by solving PoW puzzles to include transactions into blocks. Similar to Bitcoin and8Ethereum, Conflux adjusts the PoW difficulty so as to maintain a stable block generation
rate. Each node also maintains a local state constructed from the received blocks.
The Conflux consensus algorithm operates with a special Directed Acyclic Graph(DAG) structure called TreeGraph. Unlike Ethereum which only accepts transactions
on a single chain into its ledger, the Conflux consensus algorithm safely incorporates andprocesses transactions in all concurrent blocks. There are two kinds of edges between
blocks, parent edges and reference edges. Each block (except the genesis) in the TreeGraph has exactly one parent edge to its chosen parent block. Each block can also havemultiple reference edges to refer previous blocks. All parent edges form a tree embedded
inside a Directed Acyclic Graph (DAG) of all edges.
At a high level, Conflux uses the novel Greedy Heaviest Adaptive SubTree (GHAST)
algorithm (Li and Yang (2020)), which assigns a weight to each block according to the
topologies in the TreeGraph. Under this weight assignment, there is a deterministicallyheaviest chain within the graph called pivot chain, which corresponds to the relatively
most stable chain from the genesis to the tip of the parental tree.
Parent edges, reference edges, and the pivot chain together enable Conflux to split
all blocks in a DAG into epochs. As shown in Figure 1, every block in the pivot chain
corresponds to one epoch. Each epoch contains all blocks that are reachable from thecorresponding block in the pivot chain via the combination of parent edges and reference edges and that are not included in previous epochs. Details about the consensus
algorithm can be find in (Li and Yang (2020)).
Experimental results have shown that Conflux is capable of processing 4, 000 transactions per second for simple payment transactions, at least two orders of magnitude
higher throughput than Ethereum and Bitcoin. The improvement in throughput is a9result of the TreeGraph structure and the consensus algorithm, so that the network can
operate with a much faster block generation rate, no forks are discarded, and with ahigher utilization of block space. According to the technical specification, the main net
of Conflux will run under a fixed block generation rate at two blocks per second. The
daily block generation rate is therefore 60 · 60 · 24 × 2 = 172, 800 blocks per day.

IV.

Token Rules

There is a unique native token on the Conflux network, hereafter referred to as CFX.
Each CFX contains 1018 Drip. Transactions on Conflux are handled similarly to thoseon the Ethereum network and CFX, therefore, plays a similar role as Ether. Namely,users submit transcation with a gas limit and a gas price; the latter is denominatedin CFX.
The Conflux Foundation is a non-profit entity established by Conflux to make adjustments when the allocation of resources deviates from an equilibrium, to provide incentives to overcome the cold start problem, and to promote participation/developmentin the network in the early stage.

A.

Genesis Tokens
The initial number of tokens is 5,000,000,000 (5 billion). All of these tokens arelocked at the launch of the main-net and will then be released gradually, in monthly
intervals. These initial tokens will be divided between the following parties:
1. Core Team10• Private Equity Investors: Up to 600 Million CFXs will be allocated to our
private investors. In the last investment round, CFX tokens are sold at 0.1
USD per CFX. See Section IV.B. for the unlock timeline of these tokens. At
the time of the writing of this paper, more than 520 Million CFXs in thiscategory are already sold to investors. Unsold tokens in this category at thelaunch of Conflux will be allocated as Foundation Holdings.
• Foundation Holdings: 200 Million CFXs plus any unsold CFXs in the previous
category will be allocated to support the long term financial need of Conflux
Foundation. These tokens will be unlocked monthly over 2 years.
• Genesis Team: 1,800 Million CFXs will be awarded to the founding teamincluding the IIIS team (of Tsinghua University) and Alt-Chain Technologies
shareholders (where Conflux spins off from), Conflux Foundation employees,
and advisors. The Genesis team’s tokens will be unlocked over 4 years.
2. Community and Ecosystem Building• Community Fund : 400 Million CFXs will be used for marketing and community building. These tokens will be unlocked over 4 years.
• Ecosystem Fund : 2,000 Million of CFXs in the Genesis Issue will become anecosystem fund to solve cold start problems and to invest promising dApp
projects that run on the Conflux network. These tokens will be unlocked over
4 years.

11

B.

Investor Token Unlock Rules
The allocated private investor CFX tokens will be unlocked monthly over two years

following the launch of Conflux. Based on the market spot CFX price, the investor
tokens may be unlocked in-advance to provide liquidity to the CFX market in facing
price volatility. The in-advance unlock rules are as follows.
1. If the last five-day average market spot price of CFX exceeds 0.6 USD, upon theapproval of Conflux Foundation, all private investors can receive the CFX tokens
that should be unlocked in the first two months following the launch of Conflux.
2. If the last five-day average market spot price of CFX exceeds 0.8 USD, upon theapproval of Conflux Foundation, all private investors can receive the CFX tokens
that should be unlocked in the first four months following the launch (i.e., two
additional months in-advance on top of the previous rule).
3. If the last five-day average market spot price of CFX exceeds 1.0 USD, upon theapproval of Conflux Foundation, all private investors can receive the CFX tokens
that should be unlocked in the first six months following the launch.
4. If the last five-day average market spot price of CFX exceeds 1.2 USD, upon theapporval of Conflux Foundation, all private investors can receive the CFX tokens
that should be unlocked in the first eight months following the launch.
5. If the last five-day average market spot price of CFX exceeds 1.5 USD, upon theapporval of Conflux Foundation, all private investors can receive the CFX tokens
that should be unlocked in the first ten months following the launch.

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C.

Token Forms
The issued tokens exist in two forms: liquid and illiquid. In the liquid form, they

can be immediately transferred/used on the Conflux network. There are also three ways
in which tokens can be locked up, which makes them illiquid. Illiquid tokens cannot betransferred. Locking can take three different forms.
1. Tokens can be staked so as to earn the user interest.
2. They can be placed into bonded storage to purchase space on the network (e.g.,
for running dApps).
3. They can be locked up for a pre-determined amount of time to purchase votes in
the network governance.

D.

Interest/Seignorage Payments
The network will distribute interest on all illiquid tokens at a fixed rate. Token

holders obtain this interest only if they stake their tokens (i.e., move them to the illiquidstate). The interest will be added to the user’s holdings at the time when the user
un-stakes the token and converts it to the liquid state.
Based on performance-tests from the test-net, Conflux creates two blocks every second so that there are approximately 63,072,000 blocks per year. We use rc for thesystem base interest rate, expressed in annual terms, and interest is compounded per
block. Therefore, a user that stakes for b blocks receives interest payment:
1+

rc
63, 072, 000

13

b
−1

per staked token. For instance, if the annual interest is rc = 4%, a user that stakes for
15,768,000 blocks (around a fiscal quarter) will receive interest 1% per staked token. In
those calculations we round the interest payment in tokens down to the nearest (1) drip.
By setting a nominal rate of rc , the resulting annual rate is given by:effective annual rate = 1 +rc63, 072, 000

63,072,000− 1.

For instance, for rc = 4% we have an effective annual rate ≈ 4.08%.5
The economic mechanism is straightforward: suppose, for simplicity, that all tokens
have been issued, that all tokens have been staked, and that no token has changed hands.
Then paying interest does not create new value — all that has changed is that there isan increase in the number of tokens (the “monetary base” ) that represent the network.
Owners of tokens neither gain nor lose anything in real terms.6 When users do not stake
their tokens, their interest goes to the public fund. Therefore, the interest payments
implicitly shift value from those who do not stake to those who stake.

E.

Storage Resources
A key component of the incentive system is the bonded storage. Anyone who wants

to deploy a smart contract on Conflux network needs to submit a number of tokens
to create a bonded storage. The interest payments to tokens in bonded storage arecontinually disseminated to the miners, instead of those who have locked those tokens.
Since we have large number of payment intervals, we can approximate limn→∞ (1 + x/n)n − 1 = ex .
Another analogy is that of stock splits: when a firm splits its stocks, say, 1:2, then owners receivefor each one “old” stock two “new” stocks. This process does not change the value of the firm, however,and therefor stockholders are no richer or poorer after the stock split.
5

6

14

Therefore, those interest payments create an implicit reward stream from the chain space
occupiers to the maintainers of the network.
The required deposit for storage resources is measured in the native token: 0.5 CFX
for 1 kB. The process is as follows: a user (such as a dApp developer) locks up a numberof tokens. The user then occupies space on the network (e.g., deploying a dApp or storingdata due to the execution of dApps), tokens are withdrawn from the locked tokens andput into bonded storage. The interest payments for tokens in bonded storage go to theminers. To release tokens from bonded storage, users must free up the space they occupy.

F.

Voting Rights
The medium term goal is that the public fund transforms to a DAO, and that Conflux

stakeholders vote on its operations using their voting rights. Users obtain voting rights
through the locking of tokens: to cast a vote, users must agree to lock up their tokens
and the lock-up time determines the number of votes. The lock up duration starts atthe time (aka block) of casting of a vote. The voting rights will be awarded

number of quarters × number of tokens × 0.25.

For instance,• Locking maturity less than a quarter : No voting rights• Locking maturity more than a quarter : One CFX has 0.25 votes• Locking maturity more than half a year : One CFX has 0.5 votes• Locking maturity more than a year : One CFX has 1 votes

15

We measure “time” in blocks based on the assumed number of 63,072,000 per year. While
tokens are locked to obtain votes, users retain the right to staking interest. The longest
locking duration for voting is 4 years. While tokens are locked to gain a voting right,
users cannot withdraw the tokens or decrease the locking duration.

G.

Network Bootstrap
We next discuss how to economically bootstrap the Conflux network and how theCommunity Fund and the Ecosystem Fund will be managed in the long term.
Community Bootstrap: To bootstrap the Conflux community, Conflux Foundation
offered bounties and grants in the form of FC (Fan’s Coin) tokens to those community
members who made contributions to Conflux prior its launch. Conflux Foundation will
convert the issued FC tokens into CFXs from the Community Fund once the Conflux
network goes live. Note that the scale of Conflux bounty and grant programs is moderate.
The total amount of issued FC tokens at the time of Conflux launch will be less than 20
millions. After the launch, we will continue the bounty and grant programs with CFXs
in the Community Fund at a similar scale.
Ecosystem Bootstrap: One challenge of bootstrapping the Conflux ecosystem is toattract developers to develop and deploy dApps on Conflux. Sending massive CFX
airdrops to developers is not an ideal solution because one can game the system and cansell the airdropped CFXs at the secondary market instead of using them for development.
To address this challenge, Conflux has a unique sponsor mechanism in which one canbecome a sponsor for a deployed smart contract to cover its transaction fees and storage
costs. Conflux Foundation will use the Ecosystem Fund to sponsor deployed smart
contracts on Conflux during the bootstrapping period. Unlike normal airdrops, the16sponsor mechanism in Conflux guarantees that these sponsoring CFXs will not go into
circulation unless they are paid first to the miners as transaction fees.
DAO Governance: Conflux Foundation plans to gradually transfer the governance of
the Community Fund and the Ecosystem Fund to the DAO of the Conflux stakeholders.
The current road map is to complete the transition within two years after the launch ofConflux.
Ecosystem Fund Investment: In the long term, we can use the Ecosystem Fund toestablish investment funds to invest on significant dApp projects that are beneficial for
the Conflux ecosystem. Conflux Foundation will invite prior Conflux private investors
to co-manage such investment funds. We believe the establishment of such investment
funds should be under the supervision of the Conflux stakeholder DAO.

H.

Mining Rewards
System Maintainers of the Conflux network will receive income from three sources:

transaction user fees, block rewards, and interest income that arises from users “renting”
space on the blockchain.
User Fees: Users will need to compensate miners when submitting transactions andchanging the state on the blockchain. The transaction user fee is distributed proportionally to the binary base factors of blocks as defined in Li and Yang (2020).
Block Rewards: As a common practice in PoW networks, the mining of a block involves
a coin-based reward that increases the monetary base and leads to inflation. We denote
this block-reward driven inflation rate by rb . Ignoring any market-driven price changes,
economically coin-based rewards are a transfer of wealth from existing holders of CFX
collectively to the winning miner.

17

The initial base block reward per block is 7 CFX, corresponding to rb = 8.83%.
The base block reward remains constant for the first four years. It then decreases at aquarterly rate of 0.958, effectively halving every four years, until the base reward reaches
1.75 CFX per block.
There are some technological subtleties that go beyond the scope of this paper,
but that we want to mention here. Namely, although block rewards are determined
deterministically in the decentralized network, there is no a pre-defined number of coinsthat a miner who successfully mines a block receives. Instead, blocks are organized in“epochs” and block rewards are determined/distributed for each epoch. For each block,the protocol assigns a “weight” based on so-called directed acrylic graph features, whichis effectively a measure of importance in the parallelly-arranged chain and the reward isbased on the block’s weight. For details, we refer the reader to the technical white paper.
Storage interest: When tokens are used as bonds for storage, the interest paid on those
tokens is given to miners. Similar to the block reward the total amount of interest frombonded storage will be distributed in proportion to the actually received base reward ofeach block.
Although the details of block rewards are non-trivial to describe, the basic principle
is the same as in any public PoW network: miners provide computing power, the more
power they provide the more likely they are to win a block, the more blocks they win,
the higher is their income, and so forth.
In the next section, we present a calibrated model of user uptake and inflation toprovide guidelines for the expected mining revenue.

18

Besides Genesis, A, B, G, otherblocks contain no transaction.

GenesisTx0: Mint 10 coin to X
Tx1: Mint 10 coin to Z

D

Ref. edge:

Tx4: Z sends 8 to Y

A

C

H

E

New BlockTx2: X sends 8 to Y

B
Tx3: X sends 8 to Z
Tx4: Z sends 8 to Y

Epoch of Genesis

Parent edge:G

Epoch of A

Epoch of CFJEpoch of E

IK

Epoch of H

Figure 1
TreeGraph structure example in Conflux
Anti-cone Penalty Ratio: The mining block reward of a block is modified by ananti-cone penalty ratio in Conflux. In this paper, we define the penalty ratio of block b:(
max 0, 1 −|Anticone(b)|
100

2 )

where Anticone(b) denotes the set of blocks that are not in the past sub-graph of b(i.e., reachable via parent and/or reference edges from b) and that are not in the future
sub-graph of b (i.e., reachable via parent and/or reference edges to b). For example,
Anticone(F ) = {A, C, D, G} in Figure 1. Because the anti-cone of a block may keep
growing, Anticone(b) here only includes blocks that are within 10 epochs after the epoch
where b resides in. Note that for simplicity, we exclude difficulty adjustment from theconsideration of the formula and assume the difficulty remains constant. See Li andYang (2020) for the full formula.
For a new block, the base reward is the maximum block reward the generator canpossibly receive. For every anti-cone block of the new block, a portion of the block
reward will be deducted till zero. Intuitively, this block reward formula encourages thegenerator to conform with the honest behavior as defined by the consensus protocol. It

19encourages the generator to refer as many blocks as possible to avoid anti-cone blocks
due to unreferenced blocks. It also encourages the generator to propagate the new block
as soon as possible to avoid anti-cone blocks due to network delay. Unlike the winnertake-all mining game for the longest chain in Bitcoin, all blocks in Conflux receive block
rewards and miners who cooperate with one another minimize the anti-cone. This makes
Conflux secure against selfish mining attacks which exploit the winner-take-all natureof Bitcoin mining; see Eyal and Sirer (2013).
In our calibrations, we abstract from the anti-cone and set it to zero; the implicit
assumption is that all miners reference all previous blocks correctly and make no errors.

I.

Evolution of the Conflux Rate
The market price of the freely traded CFX tokens due to the permissionless natureof the network is evidently beyond the control of Conflux. Although one cannot prevent
speculation, eventually one could argue that (like any other asset or commodity) the
price of the token will be driven by demand for Conflux services. In what follows weprovide a formal model to underline the relationship between service usage and price.
Fundamentally, the price of CFX depends on two main parameters: the built-in
inflation of the system, and the impact of market price in the outside world. It isanalogous to covered interest parity, which is an economic concept to describe exchange
rate changes over time. If we use p0 to denote the price for CFX today in fiat currency(i.e., how much in fiat one pays for one CFX), p1 for the price of the token one year
into the future (formally, the 1-year forward rate), rc + rb for the real interest rate inConflux (caused by both block rewards and storage interest payments), and r for thecompounded-average real interest rate of the fiat-economy (e.g., over a basket of major

20

fiat currencies)
p1 = p0 ×

1+r.
1 + rc + rb

In other words, if Conflux pays a higher interest rate than what is available in fiat
markets, then the price of CFX is expected to mechanically decrease over time.

V.

Calibrated Model for Miner Rewards

A.

Overview
One important factor for a PoW network to function is that miners are willing tospend resources on mining blocks in exchange for some form of compensation. The
security of such a network is directly related to the computational power provided byparticipating miners. As computational power can be costly, sufficient miner compensation is required to sustain the involvement of miners, and hence crucial to the security of
the chain. In this section, we develop our approach to determine the expected revenues
that miners gain from participating in such a system. We calibrate our model based on
our technical specification as well as observations from a blockchain project, Ethereum
given the similarity in available features.
Miners receive direct revenue from three sources: block rewards, user fees, and interest paid on the tokens that users need to deposit as bonds when they want to store
data on the blockchain.
Block rewards are newly minted tokens and therefore, they increase the monetarybase of Conflux. Ignoring changes to the price of Conflux tokens, an increase in themonetary base lowers the value of each Conflux token and block rewards are therefore avalue transfer from native token holders (who receive “security” and ledger consistency21

as a service) to miners. As such, it is our view that the appropriate way to think about
block rewards is in terms of the annual inflation rate they create. We will formally
discuss how block rewards and block inflation interact in the next subsection.
User fees depend on the ultimate usage of the blockchain, and therefore to determine
user fees, we need to develop a model of user uptake; we do this in Subsection C. and thenwe derive the associated fee revenue in Subsection D.. Interest payments also increase themonetary base and we develop a model for these payments in Subsection E.. Moreover,interest payments to miners depend on how much storage users choose to occupy; webuild a model for this in Subsection F. and then derive interest payments to miners in
Subsection G.. Miners likely have to pay their bills (for electricity and h/w equipment)
in fiat. Therefore, one needs build a model for the price of CFX to accommodate thispricing, a topic that is discussed in Subsection H.
In Subsection I. we align all these components to determine the total revenue thatminers will obtain. As the final part of this exercise, we present simulation results forthis revenue and different parameters in Subsection J.
All notations introduced in this Section is summarized in Table I below.

22

23

genesis tokens, 5B
number of seconds in a day, 60 × 60 × 24
days since main-net launch
block reward
block rewards per day, defined in equation (1)annual inflation rate from block rewards
user uptake rate ∈ (0, 1); estimated from Ethereum data using equation (2)estimated user uptake rate using Ethereum as a benchmark, described in equation (3)user uptake rates, modelled based on Ethereum but one where shift in growth occurs faster andanother where it occurs slower; defined in equations (4) and (4)transactions on day d; computed as u(d) × D × 4000 (maximum theoretical throughput)
average transaction fee paid in fiat-equivalent terms
total transaction fees paid to miners on day d, defined in equation (6)fraction of tokens that an average user locks up to receive interest payments
annual rate of inflation created by interest payments in the Conflux network
daily interest rate for compound transactions; derived in equation (7)fraction of gas used by computations that are not plain token transactions; estimated using
equation (8) and defined in equation (9)system required fraction of tokens that need to be put in bonded storage for occupying spaceinterest income from bonded tokens for miners; defined in equation (10)price of CFX on day on main-net launch
inflation adjusted price on day d, defined in equation (12) and in reduced form in equation (13)number of coins outstanding on day d; it is genesis plus interest tokens plus block reward tokens,described in equation (11)total revenue for miners on day d, derived in equation (14)total miner revenue averaged over 1 year
hypothetical daily growth rate of the CFX price so that after 3 years, the market value of all Conflux
tokens is the same as the market value of all ETH at the beginning of 2020

G
D
d
B
b(d)
rb
u(d)
uETH
ufast (d), uslow (d)

m(d)
m̄(d)
g

β
I(d)
p(0)
p(d)
G(d)

T (d)
f
F (d)
α
rc
R
γ(d)

Meaning

SymbolTable I
List of Symbols for Section V.

B.

Miner Block Rewards
Miners receive a reward per block mined and the exact amount depends on where

the block is in the chain relative to the pivot chain and its anti-cone. Notably, for thecalibration presented, instead of presenting the exact per block reward, we compute theaggregate daily block award amount.
According to the technical specifications, there the network produces two new blocks
per seconds, and thus 60 · 60 · 24 × 2 =: D × 2 new blocks per day. Assuming a constantmining rate, there are D · 730 blocks mined per year. As such, if B denotes the numberof newly minted tokens created as block reward to the miners, the system needs issue
B · D · 730 new tokens annually as block rewards. Block rewards increase the monetarybase and create inflation. In other words, by setting a block reward rate the system candirectly determine the inflation rate created by newly minted blocks. This inflation isa transfer from coin holders to miners, and in setting the block rate Conflux can pivot
how much wealth it redistributes during a given year. Specifically, Conflux’s objective is
to set the block reward based on an annual inflation target rate of rb ∈ (0, 1). Therefore,
for target value rb , the block reward must solve

B · D · 2 · 365 ≡ G · rb ⇔ B =

Grb
.
730D

Note, in Conflux blocks are created continuously and may in fact be empty when there
are no valid transactions. Overall, on any given day d, total block rewards, denoted byb(d) are thereforeb(d) =

24

Grb
.
365

(1)

usage rate of blocks

C.

20
20
ja
n
01

20
19
ja
n
01

20
18
01

ja
n

20
17
ja
n
01

01

ja
n

20
16

0

.2

.4

.6

.8

1

Figure 2
Adoption Rate for Ethereum and the fitted logistic function

fitted logistic function

User Uptake
User adoption of the network will determine the demand for transactions and com-putations, the fees paid by users, and the storage rent distributed to miners. We discussthese quantities in later subsections as here our objective is to develop a model concerning user adoption.
A common feature of new technologies is that their adoption follows a S-shaped
pattern with slowly increasing usage early on and then a sudden jump of activity. An
example is the uptake of the Ethereum network, depicted in Figure 2, where we plot the
average daily fraction of the gas limit that has been used; this graph is based on data25

from https://etherscan.io/charts.7 As Conflux is a new technology, it is reasonable
to expect that uptake of Conflux will also follow an S-shaped pattern provided the
network is successful. Conflux and Ethereum have many similar features and we will
therefore use Ethereum’s historical adoption data to estimate what we believe to be areasonable uptake rate for Conflux.
As a first step, we characterize the Ethereum’s user uptake rate in form of a parametric functional. There are multiple ways to describe an S-shaped function (also known asa sigmoid curve), a standard one being logistic function which has the form:

Y =

ξ0
,
−ξ
1 + e 1 ·(X−X0 )(2)

In the equation above, Y is the uptake rate at time X, ξ0 is the maximum value for
uptake, ξ1 is the growth rate, and X0 is the time-value of when the curve reaches 50% of
its supremum value (formally, the value of the horizontal axis at the sigmoid’s midpoint).
Our estimation results are in Table II, Figure 2 also plots the fitted function.
Blocks can theoretically be filled up to 100% of the gas limit, yet the estimate forξ0 indicates that the Ethereum blockchain’s usage rate currently maxes out at 83%.
There could be several explanations for this: one is that miners collude so to not include
transactions that offer low transaction fees. Another is that the 83% usage rate isa steady-state, day-to-day “technological” upper bound of what miners can actually
include taking account of validation and transaction submission latency. Finally, it ispossible that once the network becomes congested, users no longer send new transactions
7

A graph of daily transactions would have a similar shape. We note that there is an upper boundin transactions because the total amount of gas per block is limited.

26

Table II
Logistic Curve-Fitting for Ethereum’s User Uptake Rate
The table contains the results for the non-linear least squared regression of (2) using data for Ethereum’s user uptake
rate Y , measured as the fraction of the gas limit used per block and day X. T-stats are in parentheses. *, **, *** indicate
statistical significance of the coefficients at the 10%, 5%, and 1% levels.

ξ0

ξ1

X0

Estimate

0.83***
0.02*** 690.54***(244.800) (30.809) (316.067)

Observations
R-squared

1,631
0.978

1,631
0.978

1,631
0.978

to the chain because of the long delay; this would create an endogenous upper boundon demand (reflected in the size of the mempool) for transaction processing.
Following https://bitinfocharts.com/ethereum/, transaction fees consistently
account for less than 3% of miner revenue per block and it appears that miners arelikely not too concerned about using the entire space in a block.
We will henceforth use the estimations from Table II as our benchmark for modelinguser uptake u(d) ∈ (0, 1). In other words, we assume (predict) that on day d a fraction
u(d) of Conflux’s total capacity is used. In the testnet, Conflux has a transaction
throughput of 4,000 per second. As a day has 86, 400 seconds, on day d, there will beu(d) × 4, 000 × 86, 400 many transactions. Using the results from Table II, we obtain:

uETH (d) =0.83
1 + e−0.017·(d−690).

(3)

Under this model, it will take 718 days until Conflux reaches a network capacity of 50%
and 793 days (i.e., approximately two years) to reach capacity 70%.
27

Undoubtedly, the uptake of Conflux may vary from the model described above interms of the time needed to reach a specific adoption rate. Ecosystem investments anddApp development may enable a faster uptake. Conflux’s smart contract platform iscompatible with Solidity, one of the main programming languages for smart contracts
on Ethereum. This interoperability implies that many current blockchain dApp developers from the Ethereum community face a shallow adoption curve. In contract, when
Ethereum was launched, there was a significantly smaller community of developers proficient in Solidity. Hence, it is reasonable to expect a faster user uptake of Conflux
comparing to Ethereum.
In calibrating our model, we provide analysis under two different adjustments tosuggested model. Firstly, we shift the adoption curve 180 days to the right, meaningthat adoption is delayed by a quarter. In the second, we shift the adoption curve 180
days to the left, meaning that adoption is sped up by a quarter. Formally, this shift is anincrease/decrease in parameter X0 to 870 and 510 calendar days, respectively, so that:ufast (d) =uslow (d) =0.83
1 + e−0.017·(d−510)
0.83
1 + e−0.017·(d−870)

,

(4)

.

(5)

Figure 3 illustrates the three different adoption rate models, labelled as fast (ufast (d)),
Ethereum (uETH (d)), and slow (uslow (d)).
At capacity, Conflux processes 4,000 transactions per second. With a long-run adoption rate of u(d) = 80%, this amounts to an expected 3,200 tps utilization. With an
uptake rate of u(d), the average daily number of transactions is

T (d) = u(d) · 4, 000D = u(d) · 345.6 × 106 .
28

Ethereum

fitted 180 days faster

02
0
an
2
01
j

01
9
an
2
01
j

01
8
an
2
01
j

01
7
an
2
01
j

01
j

an
2

01
6

0

.2

.4

.6

.8

Figure 3
The Three Calibrated Adoption Rates

fitted 180 days slower

We note that we use data from Ethereum to estimate the fractional usage of the
maximum capacity, and we expect that the actual update rate in Conflux will exceed
the previously stated number. We justify this opinion as follows: Ethereum is arguably
at capacity most of the time (see Figure 2 and its mem-pool of unsettled transactions is
non-empty). Since Ethereum is at capacity, there is a limited incentive for developers to
introduce new dApps, especially for enterprise-scale use-cases. Conflux’s higher throughput mitigates the concerns that the transactions do not get confirmed timely, and since
Conflux is compatible with Solidity, developers face a flat learning curve. Together thisshould contribute to a fast adoption of Conflux.

29

D.

User Fees
Users pay for computational cycles, aka gas used. It is a common practice to de-nominate blockchain capacity by transactions per second, where a transaction refers toa simple transfer of the native token from one address to another. Such a transaction
require a fixed amount of gas; e.g., on Ethereum, it is 21,000 gas. We therefore follow
this convention and equate user fees with the fees that users pay for address-to-addresstransfers.
We assume that users on average pay a transaction fee of value f . Therefore, average
daily fees, as a function of day F (d), are calculates as follows:

F (d) :=

f
|{z}

×

average daily fee

T (d)
|{z}

= F · u(d) · 4, 000 · D.

(6)number of transactions on day d

The table below presents examples for the annual fee income on the Conflux Networkthat “at capacity” usage rate provides to miners for different levels of the average fee f .

average$0.001$0.005$0.010$0.020$0.050per dayannual$276,480$88,300,800$1,382,400$441,504,000$2,764,800$883,008,000$5,529,600 $1,766,016,000$13,824,000 $4,415,040,000

For Ethereum, at its current block reward and thoughput, total rewards are on theorder of $2.3M daily or about $840M annually, including both the block rewards and the30user fees. As a result, user fees account for less than 3% of the rewards.8 In Conflux,
with a similar block-usage rate, user fees would provide the same total fee income as
the total revenue (fees plus block rewards) in Ethereum as long as user are willing to
pay on average $0.01 per transaction. Even for a moderate willingness of users to pay
fees, annual income can be substantial. In comparison, the median transaction fee on
the Ethereum blockchain for January–February 2020 has been between $0.08 and $0.15(source: ycharts.com).
It is also of interest to compare these numbers to the fees in the traditional retailpayment networks. For example, in credit card transactions, the different entities involved in a transaction, credit card companies such as Visa or Mastercard as well the thepayment processing banks, currently charge between 1%-3% of the transaction value forretail transactions. Namely, any transaction value greater than $2.5 incurs a minimal
fee of $0.05.9 On another payment platform, FinTech company Square charges a flatfee of 2.75% per transaction; in other platforms that charge a flat rate per transaction,
users usually encounter a transaction fee of at least $0.15.
E.

Interest Payments to Users
Conflux plans on paying users interest to whom their tokens are on hold. As weoutlined in the preceding section, the issued tokens exist in two forms: liquid and illiquid.
In the liquid form, they are “free,” and can be immediately transferred and used on the8

As most of the empirical analysis in this paper, these figures are based on the state of the Ethereum
blockchain in early 2020. Over the second half of 2020, however, usage fee on Ethereum have skyrocketed
as a result of the congestion of the chain, caused by a strong uptake in decentralized finance applications.
Our view at this point in time is that this congestion is not a steady state but most likely a temporary
phenomenon. We thus based our analysis on the more conservative assessment that we present here.
9This is different for debit card transactions. In the U.S., the Durbin Amendment of the Dodd-FrankAct restricts the interchange fees for debit transactions to 0.05% + $0.21; before this law came into
effect by 2011, average fees were about $0.44. In addition to these fees, payment processors usuallycharge a markup in the range of $0.10-$0.20 plus a percentage of the transaction value.

31

Conflux chain. These liquid tokens receive no interest. This state is similar to money
kept in a “chequing” or “current” account at a bank: in most western countries today
such funds do not earn interest but they are available for immediate use.
User can also designate their tokens as “stake”. In that case, they are locked, notavailable for immediate use, and therefore illiquid. Such staked tokens receive interest
payments in the form of newly minted tokens. This interest per token accrues while
the token is staked and it will be paid at the time when the user unlocks their token
and converts it to the liquid form. The staking/locking and un-staking/unlocking process, however, takes time and consumes gas costs. It is analogous to money kept ina savings account: such funds receive interest payments but are usually not available
for immediate use and/or may incur fees while releasing them. The technical details ofstaking/unstaking can be found in the technical white paper of the Conflux network.
We present an analysis on interest payment in the following content. For the sake ofsimplicity, we assume that the locked genesis tokens are released at a constant rate daily
over a 4-year period (they are released at quarterly intervals). Let G = 5, 000, 000, 000
be the amount of genesis tokens that are locked at main-net launch. To simplify the
analysis, we assume that these are released at a constant rate of n per day since thelaunch such that n · 365 · 4 = G.10 In other words: n ≈ 343K tokens are released
each day.
Assume that users (including those who hold released genesis tokens) will lock/stakeon average a fraction α of their tokens. Then α·d·n tokens are eligible to receive interest
payments on day d, while the remaining (1 − α) · dn tokens are liquid and available fortransactions. For much of our analysis, we assume that users stake all their tokens,
10

Most of these tokens are released at fixed, contracted intervals.

32α = 1, so that they receive interest whenever possible and unstake only right before
they want to use their tokens.
Conflux pays a daily amount of accrued interest R per staked token in the form of
newly minted tokens. Those tokens expand the monetary base and therefore lead to
inflation. We also assume that Conflux will set a goal for the annual rate rc such thatover a year, G·rc newly minted tokens from interest payments are added to the monetarybase. To simplify the exposition, we further assume here that the newly minted interest
tokens are returned to miners as liquid tokens.
Since interest is compounded per block creation during which the tokens are locked,
for an annual equivalent rate r one needs to find the value for R such that the totalinterest payments add up to G · rc tokens

G · rc| {z }

365
X=

total annual interest|d=1

R·α·d·n
{z

⇔ R=

8 rc
· .
366 α

(7)

}

sum of individual interest payments

F.

Transactions vs. Computations
In the description so far we treat transactions as a synonym of the usage of theunderlying network. However, notably, a Turing-complete blockchain can do much morethan process transactions. To understand this issue, consider Figure 4. The solid blackline plots the daily transactions on the Ethereum blockchain. The gray line plots thefraction of Gas attributable to transactions in percentile.11 As the figure illustrates, overtime plain vanilla token transactions account for a decreasing proportion of transactions.
11

Formally, we derive this line as follows. We obtain from etherscan.io/chart the data series fordaily transactions and daily Gas used. A simple transfer of ETH transaction requires 21,000 Gas, andwe therefore obtain the non-transaction Gas amount by subtracting the number of transactions times
21,000 from the total gas.

33

0
01
ja
n2
02

9
01
ja
n2
01

8
01
ja
n2
01

7
01
ja
n2
01

01
ja
n2
01

6

20

40

60

80

100

Figure 4
Transactions vs. Computations

30−day moving average fraction of gas used for transactions
quadratic fitted values

As with user uptake, we use the Ethereum blockchain activities as a benchmark forthe expected behavior on the Conflux network. Specifically, we run an OLS regression
for a quadratic fit for the non-transaction rate:% non-transaction gas = α + β1 · d + β2 · d2 + ,

(8)where d is the number of days since main-net launch. The goal here is to measure the %non-transactional gas as a quantity ∈ [0, 100]. Table III contains our estimation results.
In additional to the raw rate, which is very noisy at the beginning of the sample, we use
the 30-day moving average of the fraction of non-transactional gas used. The results are34

Table III
Quadratic Curve-Fitting for Ethereum’s Non-Transaction Gas Usage Rate
The table contains the results for our non-linear least squared regression of (8) using data for Ethereum’s the fraction ofdaily non-transaction gas usage on Ethereum. MA refers to a 30-day moving average. T-stats are in parentheses. *, **,*** indicate statistical significance of the respective coefficients at the 10%, 5%, and 1% levels.

β1
β2
α

Observations
R-squared% non-transactions

MA(% non-transactions)-0.04***(-17.952)
0.00***(5.598)71.88***(94.875)-0.04***(-26.239)
0.00***(7.710)72.07***(141.995)

1,623
0.615

1,623
0.782

very similar. We note that the parameter estimated for the quadratic term, β2 , is verysmall, around 7.05 × 10−6 , owing to the size of the associated variable.
So far in this subsection, we have discussed the usage of gas for non-transaction purposes. In what follows, we need to determine the amount of interest that miners receive
for storing smart contract code. We measure miner income against transactions becauseuser fees are paid per transaction and a block has a fixed capacity in terms of numberof transactions. A more intuitive approach would be to measure this quantity against
gas usage. To keep the analysis coherent, we convert the fraction of non-transactional
gas into hypothetical transactions and then we make the interest payments a functionof these hypothetical transactions. Specifically, let γ(d) denote the fraction of gas usage that is not attributable to remittance-like CFX transactions. Following Table III,35

we obtain:γ(d) := 1− 72 − 0.04 · d + 7.05 · 10−6 · d2 /100 = −0.0000000007(d−2, 837)2 +.85. (9)Therefore, when there are T (d) transactions on day d, we say that (1 − γ(d)) · T (d) of
these are simple coin transfers and γ(d) · T (d) involve smart contract executions that
require data storage on the chain.

G.

Interest Payments to Miners
When using the chain to store information (such as smart contract code), users haveto put a certain number of tokens into bonded storage. These tokens earn interest, andthe interest is paid to the miners (and not to those who put the tokens into storage).
In calibrating the model, there is a possible scenario that a user buys storage (i.e.,
put tokens into bonded storage) but never executes the contract hereafter. To tackle
this, we make the assumption that users make the decision of whether to keep tokens
in bonded storage each day and, therefore, that the total transactions fully reflect theextent of interest payments. In other words, we account for only “new” bonding of
tokens. As such, the calibration model likely conservatively underestimates the interest
income to miners.
Conflux determines how many tokens users must put into bonded storage relative
to the amount of space that the contract occupies. We assume that this amount is
proportional to the gas usage of the contract or, as one may argue, the number of actual
transactions since each of them requires gas.
As such, for x transactions, users need to put β · x tokens into bonded storage andon day d it is γ(d) · T (d) transactions that require users put tokens into bonded storage.
36

In total, the required amount is β · γ(d) · T (d). We conclude that each day the miners
receiving interest paid on these bonded tokens as described in (7) is the below:

I(d) := β × γ(d) · T (d) × R.

H.

(10)

CFX Price
Roughly speaking, the market cap of the Conflux network is the market price of thetokens multiplied with the number of outstanding tokens. In addition to market-drivenchanges to the token price, CFX changes subject to built-in inflation because the priceper token relative to fiat money, ceteris paribus, falls when the number of outstanding
tokens increases. This is not to say that the network becomes less valuable, it merelymeans that there are now more tokens available for usage in the network. This inflation
rate is caused by the expansion of the monetary base in the forms of block rewards andinterest payments.
Let p(0) denote the initial price of a CFX token. At the launch of the mainnet, thenumber of tokens outstanding is G = G(0). After d days, the number of tokens has
increased by the block rewards and interest payments as illustrated below:

G(d) = G(0) + b(d) · d +| {z }
block rewardsdX

R · α · j · n,

j=1

|

{z

}

interest payments

where the interest payments simplify todX
j=1

R·α·j·n=d(d + 1)
G(0) · rc .
365 · 366

37

(11)

Assuming no exogenous forces, the market driven changes to the price of CFX token on
day d is:p(d) = p(0) ·

G(0)
.
G(d)

(12)

Using the derivations in (1) and (7), the price of CFX is therefore:


d
d d+1
p(d) = p(0) · 1 +
rb +
rc
365
365 366

−1
.

(13)

Based on our current information, at main-net launch a CFX will have nominal value of$0.1 and the aggregate value of the network is $500M. As of the beginning of 2020, theEthereum network had a market cap of around $16B, that is, x32 times that of Conflux.
Notably, Ether’s price started to trade around $1 at launch and it is now above $300. In
the later part of this paper, we develop an equilibrium model of token usage and mining
costs that helps underpin how the token price depends on the utility that the network(and therefore, the miners) provide to users.

I.

Total Miner Revenue
To summarize, total miner revenue,12 denoted by m(d), consists of (a) the block

reward from equation (1), (b) interest income from bonded tokens as shown by equation (10), and (c) user fees expressed by equation (6):m(d) = p(d) · b(d) + p(d) · I(d) + F (d)= p(d) ·Grb+ p(d) · β × γ(d) · T (d) × R + f · T (d).
365

12

(14)

We assume that block rewards and interest income is converted to fiat equivalent using the price of
CFX as derived by equation (13).

38

In the next subsection, we provide simulations to illustrate possible revenue levels withreasonable model parameters.

J.

Calibration of Miner Revenue
Before presenting the calibration results for Conflux miner revenue, we shed somelights on what Ethereum miners currently earn for their work. There are around 6,500
blocks created per day, paying around 13,500 ETH so that the total average daily block
rewards is a just shy of $3M USD (based on ETH prices of early 2020).13 For Ethereum,user-paid transaction fees play a negligible role in miner income, whereas for Conflux user
fees are expected to play a more significant role due to its high throughput. However,as early on, there will be few transactions while the network gains traction. Therefore,
for our calibration we average miner income over relatively long horizons. Below, we
compute year-long averages in 91-day intervals:(i+4)·91+dX
1
m(d0 ),
m̄(d) =
365 d0 =i·91+di = 0, . . . , 7.

We use four values for average transaction fees, f ∈ {.005, .01, .02, .08}, where the highest
number $0.08 corresponds to the low-end median fee paid on Ethereum in early 2020, as
we discussed earlier. For the uptake rate, we consider the three benchmark rates ufast (d),uETH (d), and uslow (d) from Subsection C. For the required amount of bonded storage,
we use β = 1% meaning that if the user occupies space on the blockchain for futurecomputation that is equivalent to what 1 virtual-machine opcode transaction occupies,
then this user has to put 1/100 of a CFX token into bonded storage.
13

Source: bitinfocharts.com/ethereum/.

39

In the below, we make no assumptions about market-driven price appreciations except where explicitly stated.
As a first step, we separately plot the three components of miner revenue: block
rewards, interest income, and user fees. Figure 5 plots these daily revenues. Thesefigures use an annual interest payments of rc = 4%, and average fees of $.01.

40

41
Panel B: Interest Income

Panel A: Transaction Fee Revenue

Figure 5
Miner Revenues over time as a Function of the Adoption Rate

Panel A: Block Rewards

Figure 6
Miner Revenues over time as a Function of the Adoption Rate
In Figure 5, the $-value of block rewards (Panel A) declines because the price declines
due to inflation; note that we assume that the number of tokens given as a block reward
is constant within the interval. For the remaining two panels, we set the annual blockinflation rate to rb = 5%. Interest income (Panel B) rises with blockchain usage, but it
is small in magnitude. Finally, user fee revenue (Panel C) plots fee income. The values
recorded on the vertical axis indicates that these fees are expected an order of magnitudelarger than interest income or block reward income, except immediately after the launchof the main-net.
Combining these three figures, Figure 6 plots expected daily miner revenue m(d) overthree years following the launch of the main-net for the three different user uptake speed
scenarios. This figure uses an annual block inflation rate of rb = 5%, annual interest
payments of rc = 4%, and average fees of $.01.

42

Figure 7
Miner Revenues over time as a Function of Average Fees
Figure 7 shows the time series of expected miner revenues per day with the four
different average transaction fees. When Conflux is at capacity, even for moderate feesof $0.02, miner revenue will be around $2.5M. This figure uses block inflation rate of
5%, interest payments of 4%, and Ethereum-like adoption rates.
For the sake of the argument, we also consider a situation when market forces lead toincreases in the price of CFX tokens such that in three years Conflux has the same market
valuation as Ethereum today, that is, roughly a $15B market-cap. Further assume thatthe price change follows linear growth at some rate g such that the price at time d ispETH (d) = p(0) · (1 + g)d . The rate g that ensures that the market evaluation of Conflux
three years after launch is the same as Ethereum at the beginning of 2020 is g ≈ 0.0031.
We now compute total miner revenue using the “speculative” price pETH (d), i.e., in (14),43Figure 8
Miner Revenues if prices would grow to ETH levels
we substitute p(d) with pETH (d) so that we obtain:

mETH (d) = pETH (d) · b(d) + pETH (d) · I(d) + F (d)(15)

Figure 8 shows the time series of expected miner revenues per day for this alternative
price path, pETH , where we plot only the first 650 days. In this Figure, we use a blockinflation rate of 5%, interest payments of 4%, Ethereum level adoption rates, and willingness to pay fees at current Ethereum rates ($0.08). We also include the revenue casewhen there is no price growth (it corresponds to the most “optimistic” case in Figure 7)
as a point of reference. The key takeaway from this figure is that when we assume thatprices rise significantly, miner income in the medium run is not affected, simply because
transaction fees continue dominate.

44

Figure 9
Hashing Power over time as a Function of Average Fees
Since miners compete to build blocks and incur a notable cost of computation power,
the expected revenues relate directly to the miners’ willingness to provide hash power. At
current prices, miners receive on average $12.5 per GigaHz of hashing power.14 Figure 9transfers Figure 7 by relating the hashing power that miners would be willing to provide
given the predicted the mining rewards.
Finally, we show how inflation from block rewards and interest payments affect mining revenue. Figure 10 plots the average mining revenue as a function of the block
reward, measured through block inflation. We plot the curves for the first year (allmedium-gray lines), and then for the second to fifth quarter (black), and third to sixth
quarter (light gray). We use interest payments of 1%, 5%, and 10%, and average fees of$.01. Adoption is based on the Ethereum adoption levels (uETH ). The figure indicates14
To obtain this number, we use data from etherscan.io on total daily hashing power of the network
and average block revenue.

45

Figure 10
Average Revenue and Block Inflationthat block rewards have a significant effect on miner income, while the interest rate has
limited impact.
Figure 11 confirms these latter insights. In this Figure, we plot the average mining
revenue as a function of the interest rate. Again we plot the curves for the first year(all medium-gray lines), then for the second to fifth quarter (black), and finally third tosixth quarter (light gray). For this, we use block inflation rates of 1%, 5%, and 10%,and average fees of $.01. Adoption is again based on the Ethereum adoption levels(uETH ). The lines are essentially flat, as indicated by the earlier figures, simply because
miner income from interest rate is so small. We conclude that early on, block rewards
play the most important role in miner income at the beginning, whereas, once a certain
adoption rate is reached, user fees will be the most important source of income. We
emphasize, however, that this is not to say that interest is irrelevant for user decisions.

46

Figure 11
Average Revenue and Interest Rates
Instead, there will be many users who each have to pay a small but possibly for theircase significant implicit fee for storing data on the network.

VI.

Economic Limits against Attacks

In this section, we examine the limits of the Conflux network under two different
attacks, the selfish mining attack and the double-spending attack.

A.

Selfish Mining Attacks
If a participant in Bitcoin holds more than 23.21% of the network computation

power, she can gain more mining profit by strategically withholding her mined block fora period of time before broadcasting them to the network (Sapirshtein, Sompolinsky,
and Zohar 2015). This is because Bitcoin only gives reward to the blocks in the longest47

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Figure 12
Penalty of attackers on different attacker ratios of block generation power(A)
chain. When she withholds the newly mined block, she has the exclusive privilege tomine under her new block which is the current longest chain. Of course, withholding theblock brings the risk that someone else may mine a new block concurrently to become
the new longest chain, but the study shows that if the participant has more than 23.21%of the network computation power, the benefit of withholding will outweighs the risk;
see Sapirshtein, Sompolinsky, and Zohar (2015). Because Bitcoin mining is a winnertake-all game, honest miners expect to get less reward comparing to their computation
power when the selfish participant launches such fairness attacks.
Conflux is more resilient against selfish mining attacks because withholding a blockleads to less reward. Unlike Bitcoin, all blocks receive reward in Conflux and the reward
of a block is discounted by its anti-cone size. Withholding the block will prevent future
new blocks from referencing it. Therefore, it increases the anti-cone size of the block andconsequently decreases the block reward. Given all network participants are rational,
honest mining is incentive compatible.

48

Figure 12 presents our experimental results to illustrate the resilience of Conflux
against selfish mining attacks. We run a Conflux network simulation with 10000 nodes.
One of them is the attacker which will withhold her generated block for a certain periodof time. In the simulation, normal nodes have the network delay (4.1 seconds in average).
The attacker, however, has the capability of instantly receive and send its block to allother nodes. We run the simulation for 2000 blocks and measure the reward ratio theattacker receives comparing to the normal honest strategy for the last 1000 blocks under
different the block generation power and the block withholding period. Our results showthat the attacker consistently receives less reward than she would with the normal honest
strategy (i.e., the reward ratio is less than 1). The longer she withholds the blocks, theless reward she will receive. More computation power will help the attacker to receive
more reward, but even with 40% of the computation power of the whole network, theattacker would still get more reward if she just participates the network honestly.

B.

Double Spending Attacks
Several works in the economics literature highlight that PoW networks face funda-

mental constraints in terms of the economic incentives that can sustain ongoing securityof the network (Auer 2019). The Conflux network is no different but in what follows, we
argue that the constraints of Conflux are “looser” when compared to existing networks.
In this section, we impose the limitation that the attacker is not capable of reversing
cryptographic functions, therefore honest miners behave correctly even with the presence of an attacker. We focus on double-spending attacks with selfish mining throughwithholding of blocks.

49

We first repeat the arguments from Budish (2018) which apply to serial blockchains.
We assume that the mining of each block involves a cost c (including physical equipment
and electricity) and that there are N identical miners who compete. For the scenario withnegligible user fees, the most significant revenue is the block reward B per block. The
miners’ participation constraint requires the expected gain to exceed the expected cost,that is:probability of winning the block × B ≥ cost ⇔ B/N ≥ c.
This condition holds for all identical miners, and in equilibrium it must hold that theaggregate cost of mining agrees with the aggregate benefit:c × N = B.

(16)

Now suppose an attacker wants to double-spend a transaction of value V . The attack
proceeds in the sense that the attacker builds an alternative chain faster than all remaining miners. Assume that to gain 50% power, the attacker has to pay c × N , and to
gain a majority they have to pay in excess of this. If the attacker spends A × c × N on
equipment, with A > 1, they gain an advantage of A/(A + 1) > 50%; the larger A, thelarger the advantage (and thus the faster they finish the attack). For a successful attack,they earn value V , which is the amount that they can double spend. Assume that, conditional on the equipment advantage A, it takes t blocks (in expectation) to complete
the attack, that is creating a longer chain than the chain honest miners collaboratively
generating. Then the cost of the attack is:

t × A × c × N.

50

Once successful, however, the attacker earns not only the attack value V but also rewards
for the t blocks. Therefore, for attacks to be unattractive, it must hold that:t × A × c × N > V + t × B.

(17)

Using equation (16), we obtain the following:t × B(A − 1) > V.

(18)

Therefore, for an expected attack time t, there exists a value V such that for all V > V,t × B(A − 1) = V < V, and the transaction of value V cannot be secured. Inequality(18) is a firm constraint on the economics (and the security) of a serial chain such as
Bitcoin.
Conflux subjects to a different lower bound for V . First, to be successful in an
attack, the attacker’s alternative chain must become the pivot chain. Since any epoch
may contain multiple blocks, not only the attacker needs to create blocks faster, butalso to generate a “heavy” chain, which will require relatively more time (and thus moreresources). To simplify the argument, we abstract from this issue and assume, as before,that the honest chain contains a single block per epoch.
Next, when creating the alternative chain, an attacker does not receive the full reward
because block rewards are assigned based on the relative position in the block’s anticone in the next 10 epochs. As before, suppose the attack succeeds after t periods,
and there is a single attacker in the system. Then the attacker’s first block in thealternate chain has an anti-cone of size min{t − 1, 10}, the second of min{t − 2, 10},and so forth. Therefore, the block reward for block a since the start of the attack is51


B × 1 − (min{t − a, 10}/100)2 assuming a fixed per block reward B. For the longest
chain (now the pivot chain) of length t since the start of the attack, the attacker will
therefore earn:
B·

t
X

|i=1


1−

min{t − i, 10}
100
{z
Πt

2 !
< t × B.
}

Using the same argument as above, and therefore, the economic constraint for Conflux
becomes:
B(tA − Πt ) > V(19)

In other words, there exists a value V 0 such that for all V ∈ (V, V 0 ], the following holds:

B(tA − Πt ) > V > B(tA − t)

The implication of this relationship is that the set of transaction values V that can be
secured on the Conflux network is strictly larger than in “traditional” serial blockchainssuch as Bitcoin.

VII.

The Storage Cost Model of Conflux

In this section, we develop a simple model to understand Conflux’s storage cost rules.
We begin with the observation that users have the choice between consuming aservice on Conflux or choosing to do so with an alternative technology. The latter does
not have to be an alternative blockchain but could be, for instance, a financial service
or a computing service in traditional economy. Users in this model, for all practical
purposes, are developers who use Conflux as an infrastructure. In our theoretical model,
we abstract from many complications, such as price fluctuations and other external forces52beyond the network’s control, and focus on two groups of constituents: miners and users.
Explicitly, the model does not consider holding of CFX for speculative purposes.
We write the model in static form with an implicitly assumption of a steady-stateoutcome. For instance, we assume that there are existing users who are paying forstorage, so that miners receive storage rewards.

A.

MinersThis portion of our model is inspired by He, Tang, and Wang (2019).15 Miners buy

or rent equipment to mine and they incur per block costs for mining and data storage,such as electricity and equipment; we denote these costs c as in the preceding section.
Miners are non-strategic (i.e., they are price takers) and identical.
Miners receive income from three sources: the block reward B of newly minted
tokens, user fees, and interest on user storage, I. We measure these items in Conflux
tokens, and use p for the exchange rate of fiat money per token (i.e., the USD price ofa token); consequently, p · B is the miner’s income in fiat from receiving a block reward
B. In our analysis here, we abstract from transaction fees to simplify the exposition.
When users consume quantity x of the blockchain good (e.g., contract executions,gaming transactions, all measured in tokens units), they need to put a fraction q (to be
determined by the system) of tokens, i.e., β × x, into bonded storage. These tokens (aswell as all other tokens in the system) receive interest β × x × rc , where rc is the inflation
rate set by the system. As we outlined above, this interest payment is distributed tothe miners.
15

They employ a standard economic model to analyse whether the Bitcoin chain is viable in theabsence of block rewards, which is similar to our analysis.

53

We assume that miners are identical in terms of the hashing power that they areproviding. Therefore, they have an equal chance of mining a block. There is free entry
into mining, and therefore the aggregate hash rate H is akin to the total number ofminers. If miners use hashing power h, they win the block with chance h/H. Since
miners are identical, we set h = 1 to simplify the notation. In competitive mining, costs
balance benefits and thereforec=B.

p(B + I)
1
× p(B + I) ⇔ H =
.
H
c

(20)

Blockchain Users
Users dedicate a total of w to the particular service that the blockchain or its alter-

native provide. The analysis is therefore a partial-equilibrium because we begin when
the user has already made the decision to devote a certain portion of her budget to thisservice. The user chooses the amounts of the normal good and special (aka blockchain)goods to maximizes her utility. We denote the consumption of normal goods c and therequested blockchain service x is measured in CFX. Our implicit assumption is that all
consumption occurs (or rather, it is assessed by the user) in fiat currency and therefore
the user consumes p × x of the blockchain good in that fiat.
When deciding to use the blockchain good, the user needs to obtain tokens for direct
payment and additionally β × x tokens to put into bonded storage.
After one period, the users consumes the residual amount that was in bonded storage
in the form of the alternative good.16 Since the Conflux chain creates new tokens in theinterim, the purchasing power of these tokens (i.e., the value of the tokens measured
16

The inspiration here is that of an overlapping generations model where a user can consume one
type of good only when she is young.

54

in fiat) declines and the stored tokens is worth only p × β × x/(1 + rc ), measured intoday’s prices. Here, p/(1 + rc ) is effectively tomorrow’s price of CFX. Moreover, future
consumption gets discounted at a rate δ < 1.17
Miners receive interest from the bonded storage, where we implicitly assume a stationary equilibrium in the sense that at the time of forming the block, a past (representative) user has put an equivalent amount of tokens into storage as the current user.
Blocks are produced at rate b over a common storage horizon, usually 1 year if we use
annual rates for δ and rc . Therefore,

I = βx × rc × b.

Miners ensure the security of the chain, and we assume that chain security is increasing in the hash rate H. Security becomes relevant for the second period consumption in
the sense that this consumption occurs with probability Pr(secure|H) = µ(H), µ ∈ [0, 1),µ0 > 0, µ00 < 0.
We assume the following additive form of the user’s utility function:

U (c, x) = uc (c) + ub (x × p) + δE[uc (β × x × p/(1 + rc ))|H],(21)

with u0 > 0, u00 < 0 and E[uc ] = f (H)uc . The user’s budget of consumption c, tokens forusage x, and tokens for bonded storage βx must satisfy:c + xp + βxp ≤ w.
17

(22)

In a competitive equilibrium, the real interest rate r in the fiat money market will capture time
discounting and then β = 1/(1 + rfiat ).

55

Taken together, the user maximizes their utility by choosing the blockchain good consumption as

max U (x) = uc (w − xp(1 + β)) + ub (x × p) + δf (H)uc (β × x × p/(1 + rc )). (23)x

The solution to this maximization problem equals to:

0 = −p(1 + β)u0c + pu0b + δf (H)u0c β × p/(1 + r)C.

δf (H)u0⇔ 1+β 1−
= 0b .
1 + rcuc

Equilibrium Market Clearing
The total number of coins outstanding is M > 0. To simplify to analysis, without

loss of generality here we assume a single representative consumer who behaves as a
price taker. In equilibrium, the market must clear so that:x∗ (1 + β) = M

As such, users must choose the quantity of tokens x∗ that maximizes their utility, andminers must pick the break-even hash rate H ∗ .

D.

Equilibrium Illustration and Comparative Statics
As a simple example of a utility function of consumption the logarithmic functionuc (c) = ln(c) and for ub (c) = θ · ln(c). This then gives rise to the equilibrium conditionsp∗ =w δθ + f (H),M δθ + f (H) + 1

56

(24)

and equilibrium quantity

x∗ =

w 1
δθ + f (H),∗p 1 + β δθ + f (H) + 1(25)p∗ (B + βrc x∗ )
,
C

(26)

and for the hash rateH=
while normalizing b to 1.
The amount w can be interpreted as the overall size of the economy that the blockchain
tries to replace, and w/p is the size of the economy measured in tokens. The linear logutility formulation ensures that the hash rate and the inflation rate do not directly affectthe user’s choice. Implicitly, the inflation rate and the required bonded storage β andrc have similar effects as both raise the cost for the user and it is intuitive that one issufficient as a policy variable.
From the above equilibrium conditions we can obtain by differentiation of the equilibrium variables some first order effects.
1. The hash rate and demand are positively associated and positively re-inforcing.
(e.g., demand increases in the hash rate, and the hash rate increases in demand).
2. An increase in the monetary base lowers the price.
3. An increase in the fiat market’s interest rate (a decline in δ) decreases demand.
4. An increase in the Conflux inflation rate leads to an increase in the hash rate andthereby an increase in the token price (we note that miners do not account forholding costs of tokens — the implicit assumption is that they convert tokens into
fiat immediately to pay their costs).
57

5. An increase in the money allocated to blockchain like activities or an increase inuser preferences for blockchain goods (an increase in w or θ) increases the priceand the hash rate.
6. An increase in the bondage requirement β depresses demand directly but increases
the hash rate. The total amount is indeterminate and depends on the relative sizeof the aggregate marginal storage return, M · rc , and the block reward B.

VIII.

Conclusion

Proof-of-work blockchains need to be carefully designed so as to create the proper
incentives for users participate and use their resources mindfully: miners must be willingto secure the network, and users/developers must be incentivized top use the blockchain
services. This paper describes how the engineering of the Conflux Network, a highthroughput proof-of-work blockchain, leads to sound economic incentives that support
a socially desirable behavior. In this paper, we parameterize the level of income, andthus network security, that Conflux can generate, and describe how this depends on user
behavior and “policy variables” such as block and interest inflation. We also discuss how
the underlying economic engineering design extends the Conflux Network beyond legacy
PoW blockchains.
We emphasize that we are describing our understanding of the economic effects thatthe engineering of the network generates. We do not know, however, how users will
ultimately behave.
There are some questions that are beyond the scope of this text. For instance, itremains to be determined how the community, eco-system, and public funds will operate.
It is imaginable that they will all get merged. Although the system has provisions of58

DAO-like voting, the respective funds has not yet been set up. In the long run, theprotocol needs to be developed further, and maintenance of network components will
be necessary. It is imaginable and advisable that Conflux sets up a regular source ofincome to support the long-term viability of protocol development. One example is todivert a de minimis portion of the gas payments from transactions to the fund, similar
to a value-added-tax.

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