  We analyze Bitcoin mining from the perspective of a game and propose an
optimal mining model that maximizes profits of pools and miners. The model is a
two-stage Stackelberg game in which each stage forms a sub-game. In stage I,
pools are the leaders who assign a computing power to be consumed by miners. In
stage II, miners decide of their power consumption and distribution. They find
themselves in a social dilemma in which they must choose between mining in
solo, therefore prioritizing their individual preferences, and participating in
a pool for the collective interest. The model relies on a pool protocol based
on a simulated game in which the miners compete for the reward won by the pool.
The solutions for the stage I sub-game and the simulated protocol game are
unique and stable Nash equilibriums while the stage II sub-game leads to a
stable cooperative equilibrium only when miners choose their strategies
according to certain criteria. We conclude that the cooperative optimal mining
model has the potential to favor Bitcoin decentralization and stability.
Mainly, the social dilemma faced by miners together with the balance of
incentives ensure a certain distribution of the network computing power between
pools and solo miners, while equilibriums in the game solutions provide
stability to the system.

Computer Science and Game Theory;Cryptography and Security;Distributed, Parallel, and Cluster Computing;Multiagent Systems