Bitcoin Mining as a Contest

Nicola Dimitri

Ledger, 2, 31-37 (2017)

Abstract

This paper presents a simple game theoretic framework, assuming complete
information, to model Bitcoin mining activity. It does so by formalizing the activity as an
all-pay contest: a competition where participants contend with each other to win a prize by
investing in computational power, and victory is probabilistic. With at least two active
miners, the unique pure strategy Nash equilibrium of the game suggests the following
interesting insights on the motivation for being a miner: while the optimal amount of
energy consumption depends also on the reward for solving the puzzle, as long as the
reward is positive the decision to be an active miner depends only on the mining costs.
Moreover, the intrinsic structure of the mining activity seems to prevent the formation of a
monopoly, because in an equilibrium with two miners, both of them will have positive
expected profits for any level of the opponent’s costs. A monopoly could only form if the
rate of return on investment were higher outside bitcoin.