Interestingly enough, the authors propose a solution:
"Their solution to the Sybil attack is to give 0 reward to all nodes in a chain of forwards if the length of that chain is greater than H. This gives a negative incentive to create fake forwards to yourself in attempt to gain multiple rewards for a single transaction. Your best bet is to forward legitimately to other nodes and hope the transaction reaches a miner who solves it before the number of forwards is greater than H.
The paper determines optimal strategies in terms of values for H and the functions to divide the fee between nodes in the chain. But this is all modeled on directed trees (which have no cycles) rather than a random graph (which is what the Bitcoin network is like in reality) so it’s unknown how well it would work in practice. They leave work on random graphs for future research."
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