The Gap Game
Itay Tsabary, Technion
Headline result: miners in PoW are incentivized to shut off their hardware occasionally.
Proof of Work
- Find a value for which a protocol-defined condition holds
- In Bitcoin, hash(block) < K
- Memory-less process
- PoW is very expensive
- First incentive is the minting of new currency (i.e., inflation)
- Second incentive is transaction fees
- The sum of transaction fees within mempool = your mining incentive
- You choose the optimal subset of these transactions
- Because mining is a memory-less process, this is fine.
- Miners are willing to mine when their expected reward is above their
The Gap Game
- If transaction fees are most of the mining incentive, what happens?
- Note: this is what happens in Bitcoin as block reward approaches 0, and as contention for block space increases
- The longer you wait, the more transaction fees accumulate
- But if transaction fees at time T are below your operating cost as a miner, it's not rational to mine
- Therefore, a rational miner will wait to turn on their miner until the best possible block in the mempool is above their mining cost
- These gaps are called Mining Gaps
- These gaps in mining were first formalized by Carlsten, et al in 2016.
- Carlsten also uses a simplified model with unbounded block size
Gap Game Setup
- Create a game theoretic model of cryptocurrencies
- Incentives + expenses
- Players, strategies, etc.
What's a miner's expected profit?
- Composition of three steps:
- Block time probability distribution function
- Conditional expected profit (assuming a block time)
- Expected profit using law of total expectation
- Create a set of random miners
- Sample a miner and have them randomly change strategy at each tick
- Wait until they reach equilibrium
- Bunch of simulated rollouts
- Long story short: rational miners turn off their machines
- The fewer miners in the system, the larger the mining gap should be
- The more dominant the fees, the larger the gap
- Assuming all parameters stay the same as today, but minting reward halves twice
- In 10 years, we'll have an average 20% mining gap
- When PoW block rewards approach 0, mining security goes down
- Miners will be incentivized to turn off their machines (or point them at different chains) until enough profitable transactions accumulate
- This is bad!