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Agent-based Modelling of Bitcoin Consensus without Block Rewards

Trust is key to the efficient functioning of any fiat or crypto-currency and so is for the consensus algorithm behind the functioning of blockchain systems. By an arbitrary design choice, Bitcoin and most Proof-of- Work (PoW) blockchains have a limited supply. Once block rewards vanish, only transaction fees will remain as an incentive for miners to partake in the verification process. In this paper, we analyse the impact that miners bargaining over block composition has on consensus in the absence of block rewards: in this situation, competing blocks at the same height may be more attractive to peers by including less transactions (i.e. sharing the mempool). The mining and acceptance of blocks can be modelled as an Ulti-matum Game, where miners' strategies represent their fairness sentiment. Extending previous Literature, our study focuses on the effect of the transaction arrival rate on global consensus in the system and whether local consensus is formed under certain assumptions about the strategies of miners. We find that consensus is threatened when the supply of transactions is low and stable consensus only emerges when the amount of unconfirmed transactions remains sufficient. In addition, when miners are set with randomised strategies, it is more difficult for the system to achieve consensus. Our research suggests that transitioning from a block reward incentive to a transaction fee incentive may weaken and even destroy the consensus of PoW-based systems.