Griefing Factors and Evolutionary In-Stabilities in Blockchain Mining Games

We revisit the standard game-theoretic model of blockchain mining and identify two sources of instabilities for its unique Nash equilibrium. In our first result, we show that griefing, a practice according to which participants of peer-to-peer networks harm other participants at some lesser cost to themselves, is a plausible threat that may lead cost-efficient miners to allocate more resources than predicted. The proof relies on the evaluation of griefing factors, ratios that measure network losses relative to an attacker’s own losses and leads to a generalization of the notion of evolutionary stability to non-homogeneous populations which may be of independent game-theoretic interest. From a practical perspective, this finding provides explains the over-dissipation of mining resources, consolidation of power and high entry barriers that are currently observed in many mining networks. We, then, turn to the natural question of whether dynamic adjustments of mining allocations may, in fact, lead to the Nash equilibrium prediction. By studying two common learning rules, gradient ascent and best response dynamics, we provide evidence for the contrary. Thus, along with earlier results regarding in-protocol attacks, these findings paint a more complete picture about the various inherent instabilities of permissionless mining networks.