Cryptocurrency is accounting coordination: Selfish mining and double spending in a simple mining game

The fundamental monetary innovation embedded into cryptocurrencies is accounting coordination. Decentralized management of digital money’s accounting by a network of computers is achieved as a Nash equilibrium of a coordination game among the network’s nodes: the so called miners. Equilibrium analysis demands allowing miners to secretly update their accounting, i.e., to privately build multiple blocks of transactions and to deviate from the longest chain rule. We formalize such reasoning by proposing an accounting coordination game inspired on the Bitcoin design. In particular, by proposing a model that explicitly tells apart mining costs related to energy consumption from those related to computational capacity, we are able to study how symmetric equilibrium existence depends on well known parameters, like the average time for updating accounting records and the rewards collected from mining (accounting) activities. It is shown that the (off-equilibrium) possibility of double spending makes the attractiveness of the equilibrium strategy a decreasing function of the average time for updating accounting records.