A Nucleolus-Based Quota Allocation Model for the Bitcoin-Refunded Blockchain Network

Abstract

The Bitcoin operates in a Blockchain network under which a group of participants are responsible for adding new blocks into the chain. These participants are called miners and the ones that successfully add a block into the network receive a reward for their work. As the technology evolved over the years, this "mining" process has become more challenging with miners facing long periods without positive cash flow, while still having costs associated. This resulting business architecture has driving participants away from the technology, jeopardizing its operations, and defying its progression. In order to cope with this issue, an alternative to provide miners' financial sustainability is to join a mining pool, which main purpose is to mitigate this cash flow sparsity by sharing the (more-recurrent) rewards obtained by the group. Therefore, in this work, we propose a reward sharing methodology for mining pools based on the Nucleolus of a stochastic cooperative game. A risk-averse value functional based on the Conditional Value-at-Risk (CVaR) is used to characterize the game's certainty equivalent. Two numerical experiments were conducted in this work: (i) one based on a small, illustrative network; and (ii) one derived from real data of the Bitcoin-refunded Blockchain network. The focus of the experiments is on the incremental value of the proposed methodology over using intuitive allocations (uniform and based on computational power) and in what extent the relative increase in the mining likelihood by playing as a group benefits the pool stability. Finally, we discuss and numerically analyze a nested procedure based on the proposed Nucleolus-based allocation seeking for higher "fairness" in sharing the pool rewards.