  Low transaction throughput and poor scalability are significant issues in
public blockchain consensus protocols such as Bitcoins. Recent research efforts
in this direction have proposed shard-based consensus protocols where the key
idea is to split the transactions among multiple committees (or shards), which
then process these shards or set of transactions in parallel. Such a parallel
processing of disjoint sets of transactions or shards by multiple committees
significantly improves the overall scalability and transaction throughout of
the system. However, one significant research gap is a lack of understanding of
the strategic behavior of rational processors within committees in such
shard-based consensus protocols. Such an understanding is critical for
designing appropriate incentives that will foster cooperation within committees
and prevent free-riding. In this paper, we address this research gap by
analyzing the behavior of processors using a game-theoretic model, where each
processor aims at maximizing its reward at a minimum cost of participating in
the protocol. We first analyze the Nash equilibria in an N-player static game
model of the sharding protocol. We show that depending on the reward sharing
approach employed, processors can potentially increase their payoff by
unilaterally behaving in a defective fashion, thus resulting in a social
dilemma. In order to overcome this social dilemma, we propose a novel
incentive-compatible reward sharing mechanism to promote cooperation among
processors. Our numerical results show that achieving a majority of cooperating
processors (required to ensure a healthy state of the blockchain network) is
easier to achieve with the proposed incentive-compatible reward sharing
mechanism than with other reward sharing mechanisms.
