Econ & Game Theory in Blockchain
What's the goal?
What's the goal?
- Demand & Supply
- Markets
- Nash Equilibrium
- Schelling Point
- ...
What's the goal?
- Consensus
- Protocol
- Tokens
- State Transition Functions
- ...
What's the goal?
Landscape
Landscape
- Systems as Games
Landscape
- Systems as Games
- Nodes/Miners/Validators as Players
Landscape
- Systems as Games
- Nodes/Miners/Validators as Players
- Protocols as Game Rules
Landscape
- Systems as Games
- Nodes/Miners/Validators as Players
- Protocols as Game Rules
- Cryptocurrencies as Points
Landscape
- Systems as Games
- Nodes/Miners/Validators as Players
- Protocols as Game Rules
- Cryptocurrencies as Points
- Rewards & Punishments as Incentives
Market Emergence
Market Emergence
"A market is a composition of systems, institutions, procedures, social relations or infrastructures whereby parties engage in exchange."
Market Emergence
Fee Market
Market Emergence
Fee Market
- Users bid with the fees
- Miners select highest fee transactions
Market Emergence
Fee Market
Market Emergence
Fee Market
- What is being exchanged is the blockspace
- Miners produce blockspace and effectively auction it to users
Market Emergence
Fee Market
- The transactions that manage to get into the blocks have fees representative of the current market equilibrium
Market Emergence
Fee Market
- In extreme cases the demand can raise so much that the fees overwhelm the network
Market Emergence
Fee Market
- In extreme cases the demand can raise so much that the fees overwhelm the network
- Most economic markets can react to growing demand with increased supply, but that is not directly possible in most blockchains
Market Emergence
Fee Market
- In extreme cases the demand can raise so much that the fees overwhelm the network
- Most economic markets can react to growing demand with increased supply, but that is not directly possible in most blockchains
Nash Equilibrium
Nash Equilibrium
- Strategy from which no player wants to deviate
- But what's the strategy for BTC mining?
Nash Equilibrium
Nash Equilibrium
Bitcoin Mining
Nash Equilibrium
- Only 2 miners
- Block reward = 2
- Difficulty scales with number of honest miners
- Miners are rational actors
- Dishonest miners do not cooperate
Nash Equilibrium
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Nash Equilibrium
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Nash Equilibrium
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Nash Equilibrium
Network Effect
"The network effect is a business principle that illustrates the idea that when more people use a product or service, its value increases."
Nash Equilibrium
Network Effect
Assumptions revisited:
- Only 2 miners
- Block reward = 2
- Difficulty scales linearly with number of honest miners
- Miners are rational actors
- Dishonest miners do not cooperate
- Token price scales quadratically with the number of honest miners
- 1 honest miner -> 1$
- 2 honest miners -> 4$
Nash Equilibrium
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Nash Equilibrium
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Nash Equilibrium
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Nash Equilibrium
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Nash Equilibrium
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Nash Equilibrium
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Nash Equilibrium
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Nash Equilibrium
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Nash Equilibrium
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Nash Equilibrium
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Nash Equilibrium
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Nash Equilibrium
What does it mean exactly to be dishonest?
There are some mainstream rules (the protocol) and if an individual miner breaks them it seems like an isolated
mistake or an attempt at cheating.
If multiple miners break the protocol in the same way, it can be seen as a new protocol deviating from the main one.
Nash Equilibrium
- Only 2 miners
- Block reward = 2
- Difficulty scales with number of honest miners
- Token price scales quadratically wih the number of honest miners
- Miners are rational actors
- Decision between which protocol to follow
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Nash Equilibrium
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Nash Equilibrium
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Nash Equilibrium
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Nash Equilibrium
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Nash Equilibrium
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Nash Equilibrium
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Nash Equilibrium
So is being honest the best strategy?
Not always. If the majority of people are honest then honesty pays off. If the majority of people are dishonest in the same way then be dishonest with them.
In fact it was proven that in PoW following the majority is the true Nash Equilibrium no matter what
strategy/protocol they are using as long as it's consistent.
Schelling Point
Schelling Point
- A solution that people tend to choose (easiest to coordinate on)
- Generally it is also a Nash Equilibrium
- How in the world can it be useful in Blockchain?
Schelling Point
Detective game
- Two partners in crime
- Detective interrogates them individually
Schelling Point
Detective game
Schelling Point
Detective game
Schelling Point
Detective game
Truthful answers are one of the easiest strategies coordinate on, so they are the Schelling Points.
Schelling Point
Oracles
Oracles are blockchain entities that provide information from the outside world to the blockchain.
Schelling Point
Oracles
Oracles are blockchain entities that provide information from the outside world to the blockchain.
External Information Examples:
- What's the temperature in Berkeley?
- Who won the election?
- What's the exchange rate of USD to BTC?
Schelling Point
Oracles
Schelling Point
Oracles
Schelling Point
Oracles
Schelling Point
Oracles
- Honest participants are naturally coordinated
- Attackers could try to coordinate and lie
Schelling Point
Oracles
Schelling Point
Oracles
If they go unpunished they can repeat the attack until successful
Schelling Point
Oracles
If they go unpunished they can repeat the attack until successful
Or even worse, they can make a million fake identities and spam incorrect votes
Incentives
Incentives
"Something that encourages a person to do something."
In our case we want to shape incentives that motivate the users to submit honest values.
Incentives
Oracles
If they go unpunished they can repeat the attack until successful
Or even worse, they can make a million fake identities and spam incorrect votes
Incentives
Oracles
What to do with attackers?
If they go unpunished they can repeat the attack until successful
Or even worse, they can make a million fake identities and spam incorrect votes
If they go unpunished they can repeat the attack until successful
Incentives
Oracles
Common problem in blockchain.
If deploying on a chain, an easy solution is to make users lock some funds.
Incentives
Oracles
What to do with attackers?
If they go unpunished they can repeat the attack until successful
Or even worse, they can make a million fake identities and spam incorrect votes
Incentives
Oracles
We already laid out the foundation for punishments.
Our solution for de-sybiling users makes them lock funds.
If such a user would vote incorrectly, we can slash their funds.
If such a user would vote incorrectly, we can slash their funds.
Incentives
Oracles
Did we forget about something?
Why would anyone participate in this system?
Incentives
Oracles
No user wants to participate
Getting information from the real world is an effort and they voters are doing the protocol a service
Incentives
Oracles
If users are doing the protocol a service they need to be rewarded
One way to do it is to mint some token rewards for well-behaved voters
Or distribute them from a previously acquired pool of rewards
Incentives
Oracles
Can we distribute fixed value rewards for correct votes?
Correct vote = 10$
No.
We should base rewards on the size of the voter's stake.
Incentives
In summary:
- Make it easy to honest users and hard for attackers
- Service to the protocol needs to be rewarded
- Destructive or interfering actions need to be punished
- De-Sybiling the users can help defend against spam
Misaligned Incentives
Misaligned Incentives
Ethereum State Storage Issue
Misaligned Incentives
Ethereum State Storage Issue
State Storage Replication
Whenever we store something on chain (like a smart contract) it needs to be at least partially replicated among the nodes.
Multiple nodes store the same data.
Misaligned Incentives
Ethereum State Storage Issue
State Storage Replication Costs
Ethereum deals with the burden of replication by charging more gas for submitting bulky data.
All of that is ON TOP OF any computation gas costs.
Misaligned Incentives
Ethereum State Storage Issue
State Storage Duration
This particular part of the state might be relevant for future state transitions so nodes cannot simply discard it.
Full nodes need to keep ALL the data.
Misaligned Incentives
Ethereum State Storage Issue
Meet Bob
Bob happily deploys his awesome smart contract in Ethereum. He paid a hefty gas fee but so be it.
Misaligned Incentives
Ethereum State Storage Issue
The Problem
Bob decided to become a musician or just no longer likes programming.
He doesn't care about his smart contract anymore.
Misaligned Incentives
Ethereum State Storage Issue
The Problem Made Worse
Many others like Bob follow suit.
Some of them continue developing but, why bother removing old data? They already paid for it.
Misaligned Incentives
Ethereum State Storage Issue
"Why Bother?"
Getting data on chain is expensive, but there is no incentive to clean it up.
This is a core misalignment of incentives that lead to Ethereum state size growing out of control.
Misaligned Incentives
Ethereum State Storage Issue
The Goal
Design new protocol rules that shape the behavior of the users in a way that they start cleaning up the state.
Misaligned Incentives
Ethereum State Storage Issue
The Solution
State Storage Gas Refunds
Pay a hefty fee when deploying data to state, but get some of it refunded when removing it.
Misaligned Incentives
Ethereum State Storage Issue
behavior Before
Misaligned Incentives
Ethereum State Storage Issue
behavior After
Opportunity Cost
Opportunity Cost
"The loss of other alternatives when one option is chosen."
Opportunity Cost
Ethereum State Storage
The Real Cost
Instead of having the funds locked in the storage deposit/refund scheme, Bob could have invested them somewhere else and gain some profit.
Just locking your funds is sort of a punishment by itself.
Opportunity Cost
Extra Examples
- Creating invalid blocks in Bitcoin never gets directly punished even if the block is rejected by the network. The real cost is the opportunity cost, as the miner could have mined a valid block instead.
- Polkadot native token DOT is inflationary (~7.5% per year) but it can be staked to earn rewards (~15% per year). Not staking DOT has an opportunity cost which incentives staking to secure the network.
Externalities
Externalities
"A consequence of an economic activity that is experienced by unrelated third parties."
Externalities
Ethereum State Storage
The clogging of the chain with useless data is a negative externality that affects all the users of the chain.
As protocol designers we need to be aware of such externalities and we can try and limit their effects by pricing them in.
Externalities
Ethereum State Storage
Negative Externality Cost
In the Ethereum State Storage problem we priced in the negative externality as the opportunity cost of locking your funds.
Externalities
Oracles
Positive Externality
Providing the voting services in the Oracle scheme can be seen as a positive externality for the network that can further use this extra information.
The voters are providing a valuable service to the protocol.
Externalities
Oracles
The voters are providing a valuable service to the protocol.
So if they submit the vote on chain through a transaction, should they pay any fees?
Externalities
Oracles
Beneficial Transactions
Such a transaction can be totally free.
But make sure it cannot be spammed!
Free Transactions
There are other free transactions that are not necessarily positive externalities.
Inherent Transactions
- Block rewards in BTC
- Any logic that needs to be executed for every block (is inherent to the block)
Complete vs Partial Information Games
Complete vs Incomplete Information Games
Do players know everything about the game state?
Do players NEED to know everything about the game state?
Complete vs Incomplete Information Games
Polkadot Approval Voting (Simplified)
Complete vs Incomplete Information Games
Polkadot Approval Voting (Simplified)
Approval Checkers
In Polkadot when new blocks are validated, not everyone does the work. Only some randomly chosen validators - called Approval Checkers - are selected to validate candidate blocks.
Complete vs Incomplete Information Games
Polkadot Approval Voting (Simplified)
Attackers
We assume that attackers can DDoS some but not ALL Validators.
Being DDoS'ed makes them unable to vote in time.
Complete vs Incomplete Information Games
Polkadot Approval Voting
Default Scenario
- Randomly select 3 Approval Checkers and announce them
- Approval Checkers publish votes if they are selected
- If all the votes received confirm the block is fine it passes
Complete vs Incomplete Information Games
Polkadot Approval Voting
Default Scenario
- Randomly select 3 Approval Checkers and announce them
- Approval Checkers publish votes if they are selected
- Attackers use the information and DDoS the selected before they publish the vote (except their insider)
- If all the votes received confirm the block is fine it passes
Complete vs Incomplete Information Games
Polkadot Approval Voting
What was the Problem?
- Attackers learned everything about the game
- Attackers could use this information before the validators could respond
How do we fix it?
- Limit the information the attackers have access to so they cannot plan ahead
Complete vs Incomplete Information Games
Polkadot Approval Voting
Improved Scenario
- Each validator uses a VRF to generate a random number
- Validators with a sufficiently small number will have the right to be Approval Checkers
- Approval Checkers reveal themselves by showing their low numbers and publish a vote at the same time
- If all the votes received confirm the block is fine it passes
Complete vs Incomplete Information Games
Polkadot Approval Voting
What can the Attackers do?
- They no longer know who the Approval Checkers are so they have to guess
- If they don't guess correctly they get heavily slashed
Complete vs Incomplete Information Games
Extra Examples
- BABE is a Polkadot mechanism for selecting new block producers (further covered in Polkadot module). It also uses a similar VRF scheme to generate random assignments
Shifting Assumptions
Shifting Assumptions
- Number of players
- Available actions
- Access to information
- etc
Shifting Assumptions
Shifting Assumptions
Restaking
The incentive game will be vastly different and the capital will effectively be leveraged (double risk and double rewards).
Shifting Assumptions
Restaking
Restaking consequences are still not fully understood and the research is ongoing.
Speaker Notes ("S") for further reading.
Summary
- Markets - Fee Markets
- Nash Equilibrium - BTC Mining
- Schelling Point - Oracles
- Incentivization - Oracles
- Opportunity cost - Ethereum State Storage Refunds
- Externalities - Ethereum State Storage and Oracles
- Complete vs Incomplete Information Games - Polkadot Approval Voting
- Assumptions - Restaking