Paper 2018/780

Bitcoin Mining: A Game Theoretic Analysis

Rajani Singh and Ashutosh Dhar Dwivedi and Gautam Srivastava

Abstract

Bitcoin is a decentralized cryptocurrency payment system, working without a single administrator or a third party bank. A bitcoin is created by miners, using complex mathematical "proof of work" procedure by computing hashes. For each successful attempt, miners get rewards in terms of bitcoin and transaction fees. Miners participate in mining to get this reward as income. Mining of cryptocurrency such as bitcoin becomes a common interest among the miners as the bitcoin market value is very high. Bitcoin is a non-renewable resource, since the reward of mining a bitcoin decreases over time, obvious questions that arise are what will be the incentive for miners in bitcoin mining over time? Moreover, how will balance be maintained in the bitcoin mining market as time goes on ? From the fact that at any time only one miner will be rewarded (the one who will win the mining game by first creating and updating the blocks and the remaining miners effort will be wasted at that time), it is better for them to mine strategically. However, this strategy could be a plan of action designed to achieve a long-term goal, either Cooperative--- where miners can benefit by cooperating and binding agreements or Non-Cooperative-- where miners do not make binding agreements and compete against each other. In this paper we create a game theoretic model where we consider bitcoin mining as a continuous time dynamic game which is played an infinite number of times. We propose two different types of game theory solutions: Social optimum: (Cooperative) when the miners altogether maximize their total profit and Nash equilibrium: (Non-Cooperative) when each miner behaves selfishly and individually wants to maximize his/her total profit. Note that in our game theory model, a player represents a single "miner" or a single "mining pool" who is responsible to create a block in the blockchain. Our work here found that the bitcoin is never sustainable and depleted very fast for the Nash equilibrium even if it is sustainable for the Social optimum. Our result is quite intuitive to the common belief that mining in cooperation will give the higher payoff or profit to each miner than mining individually. Finally, to retain the bitcoin market at equilibrium we also propose a linear tax system which is of Pigovian type in order to enforce social optimality in our bitcoin dynamic game model.