We address the determination of bitcoin prices and decentralized security. Users forecast the transactional and resale value of holdings, pricing the risk of malicious systemic attacks. Miners contribute resources to protect against attackers, competing for block rewards. Bitcoin’s design leads to multiple equilibria: the same technology and fundamentals are consistent with sharply different price and security levels. Bitcoin’s monetary policy can lead to welfare losses and deviations from quantity theory. Price–security feedback amplifies fundamental shocks’ volatility impact and leads to boom–busts not driven by fundamentals. We show how Bitcoin’s viability versus fiat currency depends on relative acceptability and inflation protection.