Evolution of Shares in a Proof-of-Stake Cryptocurrency
23 Pages Posted: 20 May 2019 Last revised: 25 Nov 2019
Date Written: November 22, 2019
Do the rich always get richer by investing in a cryptocurrency for which new coins are issued according to a Proof-of-Stake (PoS) protocol? We answer this question in the negative: Without trading, the investor shares in the cryptocurrency are martingales that converge to a Dirichlet distribution, hence are stable in the long run. This result is robust to allowing trading when investors are risk-neutral. Then, investors have no incentive to accumulate coins and gamble on the PoS protocol, but weakly prefer not to trade.
Keywords: blockchain, cryptocurrency, asset allocation, martingale, Polya urn, Dirichlet distribution
JEL Classification: C6, G11
Suggested Citation: Suggested Citation