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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. Article Note: Bruno Biais is at HEC Paris. Christophe Bisière, Matthieu Bouvard, and Catherine Casamatta are at Toulouse School of Economics, Université Toulouse Capitole (TSM-Research). Albert J. Menkveld is at Vrije Universiteit Amsterdam. Many thanks for helpful comments to the editor, Stefan Nagel, the Associate Editor, two referees, as well as Will Cong, Patrick Fève, René Garcia, Co-Pier Georg, Alexander Guembel, Zhiguo He, Michael Kumhof, Nour Meddahi, Eric Mengus, Julien Prat, George Tauchen, Harald Uhlig, Boris Vallée, Stefan Voigt, Yu Wang and conference and seminar participants in the 2018 BIS Research Network meeting, the 2018 Becker Friedman Institute Conference on Blockchains and Cryptocurrencies, the 2018 Ridge Forum, the 2018 EuroFIT Conference at UCL, the 2019 WEF Davos, the 2019 Toronto FinTech Conference, the 2019 Tokenomics Conference, the 2019 Sustainable Finance Center Conference and Financial Econometrics Conference at TSE, the 2019 ESSFM in Gerzensee, the 2019 CEBRA Annual Meeting, the 2019 EFA Meeting, the 2020 AFA meeting, the 2021 AFFI meeting, Autorité des Marchés Financiers, Banque Centrale du Luxembourg, Banque de France, Cambridge University, CEIBS Shanghai, Central European University, Fudan University, HEC Paris, HEC Liège, Imperial College, Said Business School, University of Chile FEB, University of New South Wales, University Paris Dauphine, University of Technology Sydney and University of Vienna. We gratefully acknowledge support from the Jean-Jacques Laffont Digital Chair, the Norwegian Finance Initiative (NFI), the Netherlands Organization for Scientific Research (NWO Vici grant), the ANR (grant ANR-17-EURE-0010), EconPol Europe, and the European Research Council (grant 882375, WIDE). We have read The Journal of Finance disclosure policy and have no conflicts of interest to disclose. CAPTION(S): Appendix S1: Internet Appendix. Replication Code. Byline: BRUNO BIAIS, CHRISTOPHE BISIÈRE, MATTHIEU BOUVARD, CATHERINE CASAMATTA, ALBERT J. MENKVELD

We study consensus in a protocol capturing in a simplified manner the major features of the majority of Proof of Stake blockchains. A committee is formed; one member proposes a block; and the others can check its validity and vote for it. Blocks with a majority of votes are produced. When an invalid block is produced, the stakes of the members who voted for it are "slashed." Profit-maximizing members interact with adversaries seeking to disrupt consensus. When slashing is limited, free-riding and moral-hazard lead to invalid blocks in equilibrium. We propose a protocol modification producing only valid blocks in equilibrium. Authors have furnished an Internet Appendix , which is available on the Oxford University Press Web site next to the link to the final published paper online. [ABSTRACT FROM AUTHOR]

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.jfineco.2015.03.004 Byline: Bruno Biais, Thierry Foucault, Sophie Moinas Abstract: High speed market connections improve investors' ability to search for attractive quotes in fragmented markets, raising gains from trade. They also enable fast traders to obtain information before slow traders, generating adverse selection, and thus negative externalities. When investing in fast trading technologies, institutions do not internalize these externalities. Accordingly, they overinvest in equilibrium. Completely banning fast trading is dominated by offering two types of markets: one accepting fast traders, the other banning them. Utilitarian welfare is maximized with (i) a single market type on which fast and slow traders coexist and (ii) Pigovian taxes on investment in the fast trading technology. Author Affiliation: (a) Toulouse School of Economics (CNRS-CRM and FBF IDEI Chair on Investment Banking and Financial markets), Manufacture des Tabacs, 21 allees de Brienne, 31000 Toulouse, France (b) HEC, Paris, 1 rue de la Liberation, 78351 Jouy en Josas, France (c) Toulouse School of Economics, University of Toulouse 1 Capitole and FBF IDEI Chair on Investment Banking and Financial markets, Manufacture des Tabacs, 21 allees de Brienne, 31000 Toulouse, France Article History: Received 8 February 2013; Revised 3 September 2014; Accepted 23 September 2014 Article Note: (footnote) [star] Many thanks for helpful comments to the referee, Alex Guembel, Terrence Hendershott, Carolina Manzano, Albert Menkveld, Anna Obizhaeva, Emiliano Pagnotta, Rafael Repullo, Ailsa Roell, Xavier Vives and participants in the High Frequency Conference (Madrid, 2012), the 2012 SFS Cavalcade, the 2013 AFA meeting, and the 2014 SED meeting. Moinas acknowledges the support of the ANR (Grant 09-JCJC-0139-01). Biais acknowledges the support of the ERC (Grant 295484 - TAP).