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Tragedy of the Commons
Under Proof-of-Work, it is important that there is significant computing power, in the form of miners, validating transactions and securing the blockchain. Unfortunately as block rewards decrease over, in the case of Bitcoin the coming decades (this problem is a LONG time coming), miners will have less and less incentive to stay in operation, having only the fees for sending coins as a source of revenue. Eventually, it is possible that so many miners will quit that the network hash rate could drop below safe levels.
If that happens, the network would be susceptible to several different kinds of attacks. Some of these include a 51% attack, in which a malicious miner captures the majority of the network hash rate and gains control of which transactions are allowed to be verified. Other possibility is the Finney Attack, in which a miner sends coins to a merchant, who accepts them without waiting for any confirmations, then sends an already solved block onto the blockchain, sending the coins to another address.
Various possible solutions have been put forward to prevent this kind of failure from wreaki havoc on Proof-of -Work coins. For instance, Proof-of-Stake could be added alongside P.o.W., making an attack on the network cost significantly more money for the attacker. With the attacker having to invest so significantly in the coin they wish to attack, they would also be doing significant damage to themselves with their attacks.
Another possibility is to implement demurrage, or the destruction of coins when they are spent; the percentage of which being dependent on how long they have been held. While maintaining a fixed reward for miners to incentivize them to continue mining, demurrage would allow for miners to continue being paid sufficiently while maintaining a consistent coin supply.
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