Monetary Dynamics with Proof of Stake

In recent years blockchain consensus mechanisms based on Proof of Stake gained increasing attention as an alternative to Proof of Work, which requires high energy consumption. In its original version Proof of Stake hinges on the idea that, for a user, the likelihood to confirm the next block is positively related to the amount of currency units held in the wallet, and possibly also on the time length which the money has been unspent for. In a simple framework with risk neutral users we provide some early insights on the monetary equilibrium of Proof of Stake based platforms. In particular, we find that the aggregate demand and supply of currency may not coincide, which implies that users could hold suboptimal quantities of the currency. Furthermore, we also discuss how symmetric stationary states of the system could be implausible. As a consequence, a long run uniform distribution of money would seem unlikely unless appropriate measures are introduced.