Proof-of-Stake in Algorand


 In the last few years, a number of blockchain-based online platforms decided to use consensus procedures other than Proof of Work (PoW), originally adopted by Bitcoin. An alternative protocol, which attracted much attention, is the so-called Proof-of-Stake (PoS), which unlike PoW consensus is not based on solving an energy-consuming cryptopuzzle, but rather on the amount of currency units owned by a user. Different platforms adopted alternative versions of PoS. In this article, we investigate a version of PoS inspired by Algorand, which embodies a number of specific features. Indeed, to confirm a new block in the chain Algorand introduces three steps:
 proposal, selection
 , and
 confirmation
 of a block. Each step is performed by randomly selected users, where draws are based on PoS. We find explicit solutions for individual money demand, under the main simplifying assumption that a user is rewarded by the system only for the first role that she's drawn for. We do so by considering both
 exogenous
 and
 endogenous
 money supply. We also discuss the monetary equilibrium of the system, an important element in the analysis because a long-lasting disequilibrium of the economy may cause disappointment and induce some users to leave the system. Our findings suggest that an equilibrium seems to be more likely to take place if users have heterogeneous, rather than homogeneous, preferences.
