Equilibrium analysis of bitcoin block withholding attack: A generalized model

Abstract

Block withholding attack is an action where a miner who has found a legal block chooses not to submit it but rather directly abandons it. This attack makes the mining pool lose all bitcoin rewards contained within the block. In this paper, we construct a generalized model where two participants can choose to either cooperate with each other or employ a block withholding attack in the mining pool. To make the model more realistic, we consider both the cost of partial proof of work and the cost of cooperation. We also calculate the reward-per-time instead of profit-per-time to better measure the payoffs of each party. Further, we discuss the case where the payoff function and cost function are directly related to the computational power. The pure strategy and mixed strategy are analyzed respectively and the segmentations of the equilibrium are shown. We demonstrate that increasing the information asymmetry by utilizing information conceal mechanisms could lower the occurrence of the BWH attack.