Tullock Contest: A Model of Proof-of-Work Mining in Cryptocurrencies

This paper presents an N-player Tullock contest where players purchases shares in a lottery at a fixed common cost. Once all players have purchased their shares, a common value reward is raffled off. The model has some similarities to all-pay auctions, however the assignment mechanism differs. This difference ensures that, unlike all-pay auctions, the N-player Tullock contest has an unique pure strategy Nash equilibrium. This article presents also a new kind of Tullock contest that integrates the main mechanism behind proof-of-work mining of cryptocurrencies such as Bitcoin. The application of the model is expanded to analyze some topics of proof-of-work protocols, such as concentration of hashing power, double-spending attacks and environmental externalities.