game. Each game action results in a game state delta broadcast to all other players in the game along with a hash of the total game state. Each player validates the change by applying the delta to their own game state and comparing the game state hashes. If the hashes do not agree then a vote is cast, and those players whose game state is in the minority are disconnected and removed from the game (known as a desync.) Another well-known approach is called MSR-type algorithms which have been used widely from computer science to control theory. [Permissionless consensus protocols] Bitcoin uses proof of work, a difficulty adjustment function and a reorganization function to achieve permissionless consensus in its open peer-to-peer network. To extend Bitcoin's blockchain or distributed ledger, miners attempt to solve a cryptographic puzzle, where probability of finding a solution is proportional to the computational effort expended in hashes per second. The node that first solves such a puzzle has their proposed version of the next block of transactions added to the ledger and eventually accepted by all other nodes. As any node in the network can attempt to solve the proof-of-work problem, a Sybil attack is infeasible in principle unless the attacker has over 50% of the computational resources of the network. Other cryptocurrencies (i.e. NEO, STRATIS, ...) use proof of stake, in which nodes compete to append blocks and earn associated rewards in proportion to stake, or existing cryptocurrency allocated and locked or staked for some time period. One advantage of a 'proof of stake' over a 'proof of work' system, is the high energy consumption demanded by the latter. As an example, Bitcoin mining (2018) is estimated to consume non-renewable energy sources at an amount similar to the entire nations of Czech Republic or Jordan. Some cryptocurrencies, such as Ripple, use a system of validating nodes to validate the ledger. This system used by Ripple, called Ripple Protocol Consensus Algorithm (RPCA), works in rounds: Step 1: every server compiles a list of valid candidate transactions; Step 2: each server amalgamates all candidates coming from its Unique Nodes List (UNL) and votes on their veracity; Step 3: transactions passing the minimum threshold are passed to the next round; Step 4: the final round requires 80% agreement Other participation rules used in permissionless consensus protocols to impose barriers to entry and resist sybil attacks include proof of