Blockchains are distributed ledgers, operated within peer-to-peer networks. We model the proof-of-work blockchain protocol as a stochastic game and analyze the equilibrium strategies of rational, strategic miners. Mining the longest chain is a Markov perfect equilibrium, without forking, in line with Nakamoto (2008). The blockchain protocol, however, is a coordination game, with multiple equilibria. There exist equilibria with forks, leading to orphaned blocks and persistent divergence between chains. We also show how forks can be generated by information delays and software upgrades. Last we identify negative externalities implying that equilibrium investment in computing capacity is excessive.Received May 31, 2017; editorial decision July 6, 2018 by Editor Itay Goldstein.

ABSTRACT We present a theory of optimal transparency when banks are exposed to rollover risk. Disclosing bank‐specific information enhances the stability of the financial system during crises, but has a destabilizing effect in normal economic times. Thus, the regulator optimally increases transparency during crises. Under this policy, however, information disclosure signals a deterioration of economic fundamentals, which gives the regulator ex post incentives to withhold information. This commitment problem precludes a disclosure policy that provides ex ante optimal insurance against aggregate shocks, and can result in excess opacity that increases the likelihood of a systemic crisis.

ABSTRACT We offer a general equilibrium analysis of cryptocurrency pricing. The fundamental value of the cryptocurrency is its stream of net transactional benefits, which depend on its future prices. This implies that, in addition to fundamentals, equilibrium prices reflect sunspots. This in turn implies multiple equilibria and extrinsic volatility, that is, cryptocurrency prices fluctuate even when fundamentals are constant. To match our model to the data, we construct indices measuring the net transactional benefits of Bitcoin. In our calibration, part of the variations in Bitcoin returns reflects changes in net transactional benefits, but a larger share reflects extrinsic volatility.