Bitcoin PoW & Game Theory Aspects

By Othman Darwish

Since the invention of Bitcoin cryptocurrency and its underlying blockchain technology, a new era of asset digitization emerge. By asset we mean anything could be owned, has a value, and could be transferred from one party to another. Asset digitization aims to provide proof of the ownership, bookkeeping of value, and streamline electronic exchanges.  Electronic transfer of asset done traditionally by the help of centralized and trusted bookkeeper/asset registrar, here the central authority acts as notary service to guarantee the validity and finality of the ownership transfer. As a result, a central entity would maintain a ledger ( bookkeeper ) of assets transfer transactions,  and keep maintaining its valid and final state. With the emergence of blockchain technology, this game changed forever; the needs for a central party that acts as a trusted intermediary to execute ownership transfer of an asset is eliminated, and replaced by blockchain security, consensus protocols from one hand and game theory from another hand. 

Blockchain from a technology perspective is a collection of already known technologies and algorithms that are in use in industries for many years ago. The invention of blockchain relay on the way that those technologies are orchestrated, to provide new distributive paradigm.  The new paradigm that enables the transfer of ownership of an asset from one party to another without needs for a central party is crucial. In this paradigm, each party ran a node and connected directly to a list of nodes forming a peer-to-peer network, where each peer (node or party) maintains a full copy of immutable tamper resistance ledger. Whenever a transfer of asset executed and finalized,  the ledger gets updated by creating of a new block, which contains a transaction referencing the asset ownership transfer, that block chained ( linked ) to previously created block, forming a chain of blocks, hence the name blockchain.          

It evident that block creation is a vital process, the  node which creates a block - miners - should prove the validity of newly proposed block, all other  nodes in the network should also have the ability to verify the correctness of any newly added block,  agreeing on newly added block done by  in fully  decentralized  manner,  and forced by security protocols and rational behavior of node operators, and here come the novelty of satoshi consensus and Bitcoin innovation. In this context, one can differentiate between two major node category, first that run node in order to execute transactions, the second to secure the network. The later -miners or validators - supposed be trustworthy nodes and not working in a way that undermines the network. Meanwhile, the protocols of the network should incentivize those nodes for there efforts in securing the network. 

Such social networking game still has a major technical problem; assuming that everyone is honest, the network will dramatically be inflated by a valid block in a short period, and thus make the consensus between nodes -that run in asynchrony processes-  impossible. Proof-Of-Work  PoW was the mechanisms that used by Bitcoin system to slow down block creation time from one hand, and shortening number of the dishonest node from another hand. PoW uses  CPUs power owned by miners to create a valid block, and guarantee that a window of time was elapsed before the ability to create a new valid block. The miners need to solve a probabilistic mathematical puzzle,  to find a proper solution that is correlated with the targeted new block. The time needed to solve a problem is bounded -approximately 10 minutes in Bitcoin - and the mathematical puzzle complexity is self-adjusted; whenever CPUs power has increased the complexity of the puzzle increased accordingly, in a way that reserve block creation time ratio around 10 minutes. By following those game rules, a block would be created every 10 minutes in Bitcoin, the winning node which find a solution before other nodes would announce the solution to the network and claim newly created coins ownership. Once a mining node receive a proposal for mined block, it will verify its validity, and if it correct, it will be confirmed as verified block, all other nodes in network would be abandoned finding a solution for this block - lose this game round -, and start over the process seeking for  next block solution for  a newly punch of transactions.   

The theoretical aspects of blockchain game theory, which assume with the existence of intelligent, rational user, that run a node to secure the network, should provide a strategy that motivates a node to play the game, and incentivize him for securing the network. The incentive would encourage nodes to stay honest, even though with existence of  a grady dishonest and "powerful" node that  able to beat all other nodes combined, such node would have to choose between using his power to defraud people and steal back his transactions, or using his power to get incentives and maximize his wealth. The rationality for such dominant player would find it more profitable to play the game rules; such rules would favor him to get incentive and rewards to maximize his wealth, rather than undermine the system and his wealth.