The consensus among miners is that every miner who receives a block candidate with a valid fingerprint adds it to his or her own copy of the Bitcoin Blockchain (Consensus Mechanism). From a game theoretical perspective, a strategy profile where all miners add valid blocks to their own copies of the Bitcoin Blockchain is a Nash equilibrium.
If a miner believes that all other miners are acting accordingly, then it is a best response for that miner to add a valid block candidate to his or her own copy of the Bitcoin Blockchain. A deviation is not worthwhile, because it is not profitable to work on a version of the Bitcoin Blockchain that is not generally accepted.
Any reward for finding blocks on a version of the chain that is not accepted by anyone else is worthless.
Thus, although there is no authority enforcing this rule and miners are free to modify their copy of the Blockchain as they wish, there is a strong incentive to follow this rule. This self-enforcing rule allows the network to maintain consensus about the ownership of all Bitcoin units.
Mining is expensive, as the computations use large amounts of electricity and are increasingly dependent on highly specialized hardware. Moreover, valid block candidates can be found only through a trial-and-error procedure.
The consensus mechanism is therefore called “proof of work.” If a miner finds a valid fingerprint for a block candidate, then this is proof that he or she has, on average, performed a large number of costly computations.
Adding false information (e.g., illegitimate transactions) to a block candidate would render the block candidate invalid and essentially waste all the computations. Finding a valid fingerprint is therefore proof that the miner helped to maintain the Bitcoin system.