Mining Pool Manipulation in Blockchain Network Over Evolutionary Block Withholding Attack

In the current blockchain network, many participants rationally migrate the pool to receive a better compensation according to their contribution in situations where the pools they engage encounter undesirable attacks. The Nash equilibria of attacked pool has been widely analyzed, but the analysis of practical methodology for obtaining it is still inadequate. In this paper, we propose an evolutionary game theoretic analysis of Proof-of-Work (PoW) based blockchain network in order to investigate the mining pool dynamics affected by malicious infiltrators and the feasibility of autonomous migration among individual miners. We formulate a revenue model for mining pools which are implicitly allowed to launch a block withholding attack. Under our mining game, we analyze the evolutionary stability of Nash equilibrium with replicator dynamics, which can explain the population change with time between participated pools. Further, we explore the statistical approximation of successful mining events to show the necessity of artificial manipulation for migrating. Finally, we construct a better response learning based on the required block size which can lead to our evolutionarily stable strategy (ESS) with numerical results that support our theoretical discoveries.