Evolutionary Game for Consensus Provision in Permissionless Blockchain Networks with Shards

With the development of decentralized consensus protocols, permissionless blockchains have been envisioned as a promising enabler for the general-purpose transaction-driven, autonomous systems. However, most of the prevalent blockchain networks are built upon the consensus protocols under the crypto-puzzle framework known as proof-of-work. Such protocols face the inherent problem of transaction-processing bottleneck, as the networks achieve the decentralized consensus for transaction confirmation at the cost of very high latency. In this paper, we study the problem of consensus formation in a system of multiple throughput-scalable blockchains with sharded consensus. Specifically, the protocol design of sharded consensus not only enables parallelizing the process of transaction validation with sub-groups of processors, but also introduces the Byzantine consensus protocols for accelerating the consensus processes. By allowing different blockchains to impose different levels of processing fees and to have different transaction-generating rate, we aim to simulate the multi-service provision eco-systems based on blockchains in real world. We focus on the dynamics of blockchain-selection in the condition of a large population of consensus processors. Hence, we model the evolution of blockchain selection by the individual processors as an evolutionary game. Both the theoretical and the numerical analysis are provided regarding the evolutionary equilibria and the stability of the processors' strategies in a general case.