  The energy sustainability of blockchains, whose consensus protocol rests on
the Proof-of-Work, nourishes a heated debate. The underlying issue lies in a
highly energy-consuming process, defined as mining, required to validate
crypto-asset transactions. Mining is the process of solving a cryptographic
puzzle, incentivised by the possibility of gaining a reward. The higher the
number of users performing mining, i.e. miners, the higher the overall
electricity consumption of a blockchain. For that reason, mining constitutes a
negative environmental externality. Here, we study whether miners' interests
can meet the collective need to curb energy consumption. To this end, we
introduce the Crypto-Asset Game, namely a model based on the framework of
Evolutionary Game Theory devised for studying the dynamics of a population
whose agents can play as crypto-asset users or as miners. The energy
consumption of mining impacts the payoff of both strategies, representing a
direct cost for miners and an environmental factor for crypto-asset users. The
proposed model, studied via numerical simulations, shows that, in some
conditions, the agent population can reach a strategy profile that optimises
global energy consumption, i.e. composed of a low density of miners. To
conclude, can a Proof-of-Work-based blockchain become energetically
sustainable? Our results suggest that blockchain protocol parameters could have
a relevant role in the global energy consumption of this technology.
