Andreas Park PRO
Professor of Finance at UofT
Problem: double-spending
How can we trust that
Cryptography
\(\Rightarrow\) signature cannot be hacked
Contains transaction from Alice to Bob
Question: Can Alice rewrite history?
Where to add a new block \(B_7\)?
Equilibrium for "the longest chain"? - Yes!
"The blockchain folk theorem" by Biais, Bisière, Bouvard, and Casamatta, RFS 2018
Note:
Contains transaction from Bob to Alice
Bob wants to undo the transaction by rewriting history with B6
How?
\(\to\)
create predictability of mining
\(\to\)
have 51% of mining
(= confirmation) power
NB: there is a slightly more subtle view of selfish mining in which the miner creates a block but holds it back to keep mining exclusively on a part of the chain. Sapirshtein, Sompolinsky, and Zohar (2015) show that 23.21% of mining power is sufficient for such an attack
transactions per second | T per 12 hours (business day) | |
---|---|---|
Bitcoin | 7 | 302,400 |
Ethereum | 30 | 1,296,000 |
Algorand | 2000 | 86,400,000 |
Conflux | 4000 | 172,800,000 |
Athereum | 5000 | 216,000,000 |
Payments Canada ACSS | 648 | 28,000,000 |
US retail | 7639 | 330,000,000 |
Canada number of equity trades | 46 | 2,000,000 |
Orders on Canadian equity markets | 3588 | 155,000,000 |
external punishment
\(\to\) misbehavior results in commercial/legal/social punishment
allow rents:
\(\to\) running the ledger is profitable
\(\to\) misbehavior causes lack of trust
\(\to\) lack of trust makes people not use the ledger
\(\to\) rents gone
physical resource cost
\(\to\) running the ledger is costly
\(\to\) if I misbehave in the future then lack of trust
\(\to\) my previous investment is destroyed
based on: Blockchain Economics by Abadi & Brunnermeier 2019
related model: Budish (2018)
basic economics:
expected gain of mining \(\ge\) cost of mining
\(\Rightarrow\) probability of winning \(\times\) block reward \(\ge\) cost
\(\to\) holds for all miners
\(\to\) in equilibrium: aggregate cost of mining \(=\) aggregate benefit
related model: Budish (2018)
\(\to\) cost of attack: \(t\cdot A\cdot c\cdot N\)
total benefit of attack
\(\to\) for unattractive attack: cost \(>\) benefit
means amounts above \(\mathbb{V}\) cannot be secured
Double spend attack prevention
Basic idea of competitive equilibrium
aggregate mining cost = aggregate reward
Double spend - selfish mining attack
condition that prevents it
(Chiu & Koeppl RFS 2018)
G
G
Garrat & van Oordt (WP 2020)
Garrat & van Oordt (WP 2020)
drop in exchange rate S
=loss
Conflux: Consensus with TreeGraph
•Blocks are organized in a directed acyclic graph (DAG)
•No concurrent blocks are discarded, leading to higher throughput
Transaction Processing
Disclaimer: token design strongly influenced by yours truly
Goes life on October 29, 8 a.m.
going back to Budish (2018)
Serial Chain
Conflux Chain
In Conflux, withholding a block leads to greater anti-cone size
Intuition: Anticone = blocks created without properly referencing others blocks in its vicinity
Root Problem
Solutions
https://blog.stephantual.com/what-are-state-channels-32a81f7accab
Where to add a new block B7?
My personal problem: I have not yet seen a convincing theoretical model of PoS
economic result: Fahad Saleh (2021) Review of Financial Studies, "Blockchain Without Waste: Proof-of-Stake" shows that PoS is an equilibrium
current state:
coinbase reward to miners
creation and redemption process as part of blockchain operation
examples: Bitcoin, Bitcoin Cash, Ether, Lumens, Cardano
native to a blockchain and essential for operation
\[\text{Fundamental Value}= \sum_{t=1}^\infty \frac{E(\text{cash flow}_t)}{(1+r)^t}.\]
consumption budget constraints
consumption decision
\(\to\) price for crypto
Convenience yield \(T\)
Intuition: transaction benefit \(\theta\) net of transactions costs \(F'\)
There could be multiple equilibria.
Price \(p=0\) at all dates is an equilibrium.
pricing kernel
convenience yield \(T\cdot p_{t+1}\)
{
{
(captures correlation between marginal utility of consumption and the crypto price)
crypto price at time \(t+1\):\(p_{t+1}\)
\(+\)
convenience yield \(=\) scalar \(\times\) crypto price
Ceteris paribus \(p^c \nearrow \Rightarrow\) convenience yield \(\nearrow\).
Not so for stocks in perfect market
stock price at \(t\) reflects the \(E[p_{t+1}+d_{t+1}]\)
dividends at \(t+1\) do not depend on the \(t+1\) stock price.
\(\Rightarrow\) for stocks, dividends cause fundamental value and therefore prices
For the cryptocurrency, prices cause convenience yields
and therefore fundamental value.
equilibrium price is a function of
Network | Multiple verifiers | Free entry for verifiers | Asset | Unity |
---|---|---|---|---|
DTCC | n | n | public equity | n |
Bitcoin | y | y | bitcoin | y |
Ethereum | y | y | ether | y |
Ethereum | y | y | ERC-20 tokens | n |
Ripple | y | n | XRP | n |
objective function user: \(\max \left(\text{transactional service}+\text{resale value}\right) \times \text{network security} -\text{cost}\)
unstable equilibrium
unstable equilibria are also possible with unity tokens
stable
equilibrium
Note: \(p=0\) is always an equilibrium!
unstable
=smallest network with positive price equilibrium; any smaller network has price=0
There is a threshold \(\bar{\rho}\) such that:
\(\rho<\bar{\rho}\): \(\frac{\partial\text{price}}{\partial\rho}>0\)
\(\rho>\bar{\rho}\): \(\frac{\partial\text{price}}{\partial\rho}<0\)
measured in growth rate of coinbase reward \(\rho\)
@financeUTM
andreas.park@rotman.utoronto.ca
slides.com/ap248
sites.google.com/site/parkandreas/
youtube.com/user/andreaspark2812/
By Andreas Park
This is the slide deck discusses the role of economics in blockchain tech.