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# Haseeb-Qureshi/gap_game.md

Created Oct 11, 2018
The Gap Game @ CESC

# 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

# Mining incentives

• 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

# Mining Gap

• 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

# Results

• 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
• Estimate:
• Assuming all parameters stay the same as today, but minting reward halves twice
• In 10 years, we'll have an average 20% mining gap

# Summary

• 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!
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