Blockchain systems often employ proof-of-work consensus protocols to validate and add transactions into hashchains. These protocols involve competition among miners in solving cryptopuzzles (e.g. SHA-256 hash computation in Bitcoin) in exchange for a monetary reward. Here, we model mining as an all-pay auction, where miners' computational efforts are interpreted as bids, and the allocation function is the probability of solving the cryptopuzzle in a single attempt with unit (normalized) computational capability. Such an allocation function captures how blockchain systems control the difficulty of the cryptopuzzle as a function of miners' computational abilities (bids). In an attempt to reduce mining costs, we investigate designing a mining auction mechanism which induces a logit equilibrium amongst the miners with choice distributions that are unilaterally decreasing with costs at each miner. We show it is impossible to design a lenient allocation function that does this. Specifically, we show that there exists no allocation function that discourages miners to bid higher costs at logit equilibrium, if the rate of change of difficulty with respect to each miner's cost is bounded by the inverse of the sum of costs of all the miners. Additionally, we also show that it is necessary to have allocation functions that decrease with increasing number of players. As a result, it is difficult to achieve decentralization and accomplish secure blockchain systems with global block difficulty which relies only on total hash rate.
Blockchain systems have been successful in discerning truthful information from inter-agent interaction amidst possible attackers or conflicts, which is crucial for the completion of non-trivial tasks in distributed networking. However, the state-of-the-art blockchain protocols are limited to resource-rich applications where reliably-connected nodes within the network are equipped with significant computing power to run lottery-based Proof-of-Work (PoW) consensus. The purpose of this work is to address these challenges for implementation in a severely resource-constrained distributed network with Internet-of-Things (IoT) devices. The contribution of this work is a novel lightweight alternative, called Weight-based Reputation (WBR) scheme, to classify new transactions via modeling blockchain decisions as a distributed machine-learning task. WBR identifies network nodes that are willing to cooperate towards securing ground-truth, showing robustness to adversarial subnetworks that are greater than 50% and reducing collaboration error by 50% compared to other similar schemes. This two-step approach of reputation plus transaction classification for generating blockchain data is treated as a novel method of preventing fraud and double-spending attacks in blockchain networks. To capture adversary influence, a Bayesian game is formulated and implemented to show superior performance to the state-of-the-art along with resource consumption metrics.