Incentives and Proof of Work We learned about Bitcoin's consensus algorithm and the reasons it's regarded as secure in the previous part. We must recognize that technological processes and incentive engineering both account for Bitcoin's decentralization. We've mainly concentrated on the technical side up to this point, but now we'll look at incentive engineering. We previously assumed that we could choose a node at random and that the node would be trustworthy at least half the time. This assumption of honesty presents issues, though, when people have a financial incentive to undermine it. Hence, we must consider whether we can give nodes incentives to act honorably. To do this, we'll look at the illustration of the long-term consensus chain that includes a double-spend attempt. Due of nodes' lack of identities, we are unable to punish the node that originated this block. Instead, we'll give rewards to the nodes who built the blocks that eventually made it onto the consensus chain. We'll reward them by paying them in units of this decentralized digital money since we don't have node IDs. Bitcoin has two incentive mechanisms, with the first being the block reward. The node that creates each block receives a coin creation transaction that typically goes to itself. This transaction is a payment for creating the block to go onto the consensus chain. The value of this transaction halves every four years, and it's currently fixed at 25 bitcoins. However, the node only receives this reward if the block ends up on the long-term consensus branch. Therefore, this incentivizes nodes to behave honestly, or at least to create blocks that other nodes are likely to agree with. The phenomena of the total amount of bitcoins in circulation halving serves as the second incentive mechanism. Every four years, the block reward is cut in half, leaving a limited number of bitcoins. The total quantity of bitcoins, based on the pace at which new blocks are created, is 21 million. As a node creating a block, you have the opportunity to collect fees from transactions that add up to a sum for you and the address included in the block. While transaction fees are voluntary, we anticipate that they will become increasingly important as the block reward depletes. Game theory plays a significant role in how the system will evolve, which remains an area of open research in Bitcoin. If we can address a few more problems, we'll understand how Bitcoin achieves decentralization. Three remaining problems are the leap of faith, the risk of a free-for-all for nodes seeking rewards, and adversaries creating civil nodes to undermine the consensus process. Proof of Work is a solution to all these problems. Rather than selecting a random node, we choose nodes proportional to a resource that cannot be monopolized, such as computing power. This creates a competition among nodes, and the selection happens automatically in proportion to the resources used. Another way to understand proof of work is that it makes it moderately challenging to create new identities or commit civil attacks. Hash puzzles is the exact proof of work system used in Bitcoin, requiring nodes to find a nonce that satisfies a required property when hashing the entire block. The target space for this hash output is very small compared to the hash function's overall output space. This computational problem is what a node must solve to produce a block. Bitcoin's Proof-of-Work system employs a cost function that is parameterizable, as opposed to a fixed cost over time. This is made possible by the automatic recalculation of the target size of the target space as a fraction of the output space every two weeks. The nodes in the Bitcoin peer-to-peer network maintain the invariance that the average time between any two successive blocks produced globally in the overall Bitcoin network is around ten minutes. The probability that a miner, Alice, will win the next block is equal to the fraction of global hash power that she controls. Thus, if Alice's mining hardware accounts for around 0.1% of total hash power, she is likely to compute roughly one in every thousand blocks. To minimize inefficiencies and preserve the optimization advantages of being able to execute several hundred transactions in a single block, we maintain this ten-minute invariance. As the maximum block latency should not be permitted to decrease without any restrictions, the block delay should be fixed. If the majority of miners weighted by hash power are honest, many assaults on Bitcoin are impractical, according to the cost function and proof-of-work arrangement. As no one can foresee which nonce will solve the hash puzzle, its solution is probabilistic. The only method is to attempt each nuance one by one in the hopes that one will finally be successful. Since the process may be well represented by a continuous probability process known as a Poisson process, it is known mathematically as Bernoulli trials. The distribution, or probability density function, of how long it takes any node in the network to identify the next block is kept constant at an average long-term of 10 minutes. If a specific miner is interested in how quickly they're finding blocks, they can use the same equation that represents the probability density function but with a different scale on the X-axis. For a specific miner, the mean time to find a block given that they have just found a block is equal to 10 minutes divided by the fraction of hash power that they control. The variance of the time between blocks will also be very high.