Economics \(\cap\) Blockchain\(\not=\emptyset\)

 

Andreas Park

 



 

Topics I will now cover

     0. Intro to econ thinking 

  1. Work on consensus protocols (PoW and PoS) as economic equilibria
  2. Selfish mining attacks
  3. Incentivizing PoS Committees 
  4. Transactions fees
  5. Consensus and scaling

Blockchain Research

Two key components of blockchain

technology

economics

Intro to on economic thinking & blockchain

Economics 101 (from George Mankiw's 10 Principles of Economics)

  • Rational People Think at the Margin
  • People Respond to Incentives
  • Markets Are Usually a Good Way to Organize Economic Activity
  • Governments Can Sometimes Improve Economic Outcomes
  • Also: economists are by default interested in "welfare" and "social surplus" which is a global view and not "taking sides"

My naive understanding of computer science agents

  • Honest vs. Byzantine
    • Honest = act as intended by the system
    • Byzantine = act in an unintended manner (manipulative, faulty, opportunistic)

A super-high level view of economic agents in "protocols"

  • All are rational:
    • Participation constraint: participate in protocol only if benefit outweighs cost
    • Incentive compatibility: do desired action \(X\) only if net benefit of \(X\) is better than net benefit of any other action \(X'\) 
  • Work as intended iff PC and IC are both satisfied.

Some examples

  • In proof-of-stake: 
    • if everyone else validates a proposed block, why should I? 
  • DAO voting
    • marginal voter paradox: you are unlikely to matter, why bother voting?
  • blockchains are communally run  by a large number of validators
    •  why expense the resources to participate?

Proof-of-Work vs Proof-of-Stake

external punishment
\(\to\) misbehavior results in commercial/legal/social punishment

We must trust that records are correct. How achieved?

Economic Design of Recording Technology

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

Blockchain Consensus

  • What do you need? An equilibrium in which
    • ​new transactions are processed correctly
    • new transactions are being processed
    • blocks are appended in sequence on a unique chain

Philosophical Requirement: Decentralization

  • additional philosophical requirement: "decentralization"
    • no need to trust a party or rely on government enforcement
    • e.g., reputation incentive "not enough"
    • collusion gets "harder" with more players
  • decentralization = no central of single party
  • \(\to\) random selection of new block producer possible

Economic Considerations

  • you want many participants?
    • you need to pay enough for them to stay
    • you need to pay enough for them to come
    • ensure low barrier to entry
  • ​Incentives to
    • ​keep adding to the chain (liveness)
    • keep adding to the end of the chain (safety)
  • ​Structurally:
    • ​\(\to\) dynamic game

Results from the Economics Literature

  • Bruno Biais, Christophe Bisière, Matthieu Bouvard, Catherine Casamata
    • ​Proof of Work is an equilibrium (but only one of many)
  • ​Fahad Saleh
    • ​Proof of Stake is an equilibrium
    • persistent forking is precluded equilibrium because validators \(=\) stakeholders.

Robustness to Attacks

related model: Budish (2018)

Selfish Mining Attack

  • cost of mining a block: \(c\)
  • number of miners: \(N\)
  • block reward: \(B\)

basic economics:

expected gain of mining \(\ge\) cost of mining

\(\Rightarrow\) probability of winning \(\times\) block reward \(\ge\) cost

\frac{1}{N}\times B\ge c

\(\to\) holds for all miners

\(\to\) in equilibrium: aggregate cost of mining \(=\) aggregate benefit

\Leftrightarrow~c\cdot N=B

related model: Budish (2018)

Selfish Mining Attack

  • value of attack: \(V\)
  • to gain 50% control, pay: \(c\cdot N\)
  • need to gain \(A>1\): (\(A/(A+1)>.5\)
  • block confirmation convention: \(t\)

\(\to\) cost of attack: \(t\cdot A\cdot c\cdot N\)

total benefit of attack

  • attack value \(V\)
  • block rewards \(t\cdot B\)

\(\to\) for unattractive attack: cost \(>\) benefit

t\cdot A\cdot \underbrace{c\cdot N}_{=B} >V+t\cdot B
t\cdot B(A-1)> V
\Rightarrow \exists \mathbb{V} \text{~s.t.~} \forall \tilde{V}>\mathbb{V}~~\tilde{V}>t\cdot B(A-1)

means amounts above \(\mathbb{V}\) cannot be secured

Double spend attack prevention

  • Validation rewards are taken as given, but they are crucial in
    • determining incentives to participate,
    • to support the chain, and
    • to expense electricity and computing power

Basic idea of competitive equilibrium

aggregate mining cost = aggregate reward

Double spend - selfish mining attack

  • win \(N\) block rewards until confirmation block
  • ability to double-spend
     

condition that prevents it
(Chiu & Koeppl RFS 2018)


 

\text{mining reward} \times (N+1)N > \text{double spend amount}

Selfish Mining Attack (v2)

However! with attacking don't you
shoot yourself in the foot?

  • First attack in May 2018
  • double spent of $18 million worth of Bitcoin Gold
  • \(\to\) Loss of confidence in Bitcoin Gold and decline in exchange rate
  • Only 1/6 of pre-attack value
  • transactions \(\searrow\) one-third

G

  • models:  per period flow cost of mining
  • Prat & Walter (2019): 2/3 of mining cost are fixed costs.

    G

However! with attacking don't you
shoot yourself in the foot?

Garrat & van Oordt (WP 2020)

However! with attacking don't you
shoot yourself in the foot?

Garrat & van Oordt (WP 2020)

drop in exchange rate S

=loss

An alternative design: Conflux (developed by UofT Prof)

Greedy Heaviest Adaptive SubTree (GHAST) algorithm

  • Blocks are assigned a weight according to the topologies
  • Exists a deterministically heaviest chain called pivot chain
  • An epoch contains one pivot chain block and its reachable blocks

Transaction Processing

  • Blocks are processed sequentially ordered by epoch, topological order and id
  • Only the first occurrence of the transaction is processed
  • 3200 tps for simple payment transactions

going back to Budish (2018)

Selfish Mining Attack in Conflux

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

Selfish Mining/Double-Spent Attack in Conflux

Proof-of-Stake (BFT) Committees

Validation and leader election

random

random

random

Committee 1

Committee 2

random

Block formation

Committee 1

Committee 2

...

Committee 32

attest

attest

Slot 1

Slot 2

Slot 32

...

12 seconds

Finality!

...

checkpoint

...

vote

vote

When final?

2/3 of stake has voted

So what's the problem? (here: for BFT PoS)

  • validity checks
    • are not free
    • are not observable
    • \(\to\) moral hazard problem
  • thought experiments
    • if everyone else is honest, why do the check?
    • if everyone else cheats, my checking is irrelevant
    • if others cheat I may get punished
  • results:
    • prescribed protocol is not an equilibrium
    • there is an equilibrium with invalid blocks
      (happens if slashing cost too low)
  • There exists a modified protocol so that consensus is reached
    • requires some "opportunistic" voters to be pivotal
  • Prescribed protocol:  all committee members are instructed to verify blocks.
  • Modified protocol: verify blocks if and only if their index is strictly lower than a certain number (essentially  flushes out the invalidly proposed blocks)

Transaction Fees

Transaction Fee Considerations

  • fees are an important part of incentivizing blockchain validation
  • may become more important for bitcoin as coinbase rewards disappear
  • general rule: miners favour transactions with larger fees
    • ​sometimes referred to as a "first price auction"
      (winning bit pays their bid)
    • correct statement is a "discriminatory price auction"
       

bids sorted by price
\(\to\) quantity sold

price

block capacity

area = fees earned

Other pricing formats

  • second price auction
    \(\to\) pay the losing bid
  • correct formulation in multi-unit: "uniform price auction"
  • any difference?
    • ​second price auction: bid your valuation
    • first price auction: bid less than your valuation
  • ​in single unit auctions:
    • ​revenue equivalence: in expectation the seller earns the same
  • in multi-unit auctions:
    • tricky: Klemperer (1999) argues that uniform>discriminatory because of more aggressive bidding
    • empirical evidence is mixed

discriminatory
price
auction

uniform
price
auction

Other pricing formats

"StableFees: A Predictable Fee Market for Cryptocurrencies"
Soumya Basu, David Easley , Maureen O’Hara , Emin Gün Sirer

  • propose uniform price auction
  • smaller fee payments but
  • much smaller variance in fee income
  • \(\to\) may still benefit miners

Vickery-Clarkes-Groves algorithm

  • users truthfully submit how much they value an item
  • winning = maximize total welfare
  • payment = user share of total welfare:
    • user pays difference between the total value to others without their participation minus sum of winning bids by other successful bidders.
    • measures the benefit the winner's participation brings to welfare.

Real-world use case?

Google Ad Auctions!

EIP-1559: Objectives

what are the goals for a transactions fee protocol:

  1. users should bid their true valuation 
  2. miner should follow the envisioned inclusion rule
  3. there are profitable side deals between miners and users

problems:

  • first price auction fails 1.
  • Vickery-Clarkes-Groves fails 2. (miners can create fake transactions and extract more from users)
  • many approaches have other problems

EIP-1559: What is it an why does it help?

Roughgarden (2021): EIP-1559 satisfies 2. and 3. and almost always 1.

EIP-1559

  1. reserve price/base fee (time varying)
  2. base fee gets burned and doesn't go to miners
  3. block size varies by demand

The Blockchain Research
Eco-System

Blockchain Research Problems

technology

business

  • ever-expanding state space
     
  • MEV in block creation
     
  • scaling
    • sharding
    • roll-ups
       
  • overcoming pseudonimity

economics

  • costly space
     
  • MEV = arbitrage detection and elimination
     
  • scaling
    • arbitrage?
    • incentives, hold-up, capital costs
  • application design
     
  • participation incentives
     
  • IO of apps
     
  • tokenization & tradFi
     
  • opportunities without pseudonimity

@financeUTM

andreas.park@rotman.utoronto.ca

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sites.google.com/site/parkandreas/

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