  Crypto-currencies are digital assets designed to work as a medium of
exchange, e.g., Bitcoin, but they are susceptible to attacks (dishonest
behavior of participants). A framework for the analysis of attacks in
crypto-currencies requires (a) modeling of game-theoretic aspects to analyze
incentives for deviation from honest behavior; (b) concurrent interactions
between participants; and (c) analysis of long-term monetary gains. Traditional
game-theoretic approaches for the analysis of security protocols consider
either qualitative temporal properties such as safety and termination, or the
very special class of one-shot (stateless) games. However, to analyze general
attacks on protocols for crypto-currencies, both stateful analysis and
quantitative objectives are necessary. In this work our main contributions are
as follows: (a) we show how a class of concurrent mean-payoff games, namely
ergodic games, can model various attacks that arise naturally in
crypto-currencies; (b) we present the first practical implementation of
algorithms for ergodic games that scales to model realistic problems for
crypto-currencies; and (c) we present experimental results showing that our
framework can handle games with thousands of states and millions of
transitions.
