  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.
