Various computer scientists have outline a number of potential solutions to the Byzantine generals problem from the allegory. The practical byzantine fault tolerance algorithm (PBFT), which is used to establish consensus in blockchain systems, is only one of those potential solutions. Three examples of blockchains that rely on the PBFT for conses are Hyperledger, Stellar, and Ripple. Very roughly and without explaining the whole algorithm (which would take a multiple page research paper), what the PBFT does is as follows: Each ‘general’ maintains an internal state (ongoing specific information or status). When a ‘general’ receives a message, they use the message in conjunction with their internal state to run a computation or operation. This computation in turn tells that individual ‘general’ what to think about the message in question. Then, after reaching his individual decision about the new message, that ‘general’ shares that decision with all the other ‘generals’ in the system. A consensus decision is determined based on the total decisions submitted by all generals.
Among other considerations, this method of establishing consensus requires less effort than other methods. However, it comes at the cost of anonymity on the system.