A Cooperative Optimal Mining Model for Bitcoin

TL;DR

This paper introduces a game-theoretic model for Bitcoin mining that aims to optimize profits and promote decentralization by analyzing strategic interactions between pools and miners in a two-stage Stackelberg game.

Contribution

It presents a novel two-stage Stackelberg game model for Bitcoin mining that captures the strategic decision-making of pools and miners, promoting stability and decentralization.

Findings

Unique and stable Nash equilibriums in the sub-games.

The model encourages a balanced distribution of mining power.

Potential to enhance Bitcoin network stability and decentralization.

Abstract

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.