Energy consumption in Bitcoin Mining: A Game Theoretic Analysis

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" procedures 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. As a major side effect of this mining process, a lot of electricity is used in the process of mining bitcoins, making it an "energy blackhole".
Electricity is a semi-renewable resource - depending on the type of resource used for its production. Nevertheless, electricity plays an essential role in the bitcoin mining process since the whole mining process is based on it. The
electricity consumed by the mining system is directly proportional to the computational power of the system being used. Moreover, powerful computers that are specifically designed for the bitcoin mining process, consume much more
electricity than regular computers. The fact is that at each new block creation only one miner will be rewarded (the one who will win the mining game by first creating and updating the blockchain). The remaining miners' effort, as
well as electricity used for mining at that time, will be wasted. Therefore, optimizing the consumption of electricity is one of the essential and most challenging problems effecting bitcoin mining.
We consider a infinite time dynamic game model of the bitcoin market in continuous time, where miners or players use mining systems to mine the bitcoin by investing electricity into the mining system. They sell their product -
mined bitcoin in a common market where the price of bitcoin is fixed and decided by the linear demand function - price of a product is linear in market demand of product (in economics it is called the linear inverse demand function). We propose two different types of game theory solutions to the game model: Social optimum and Nash equilibrium. We also propose a linear tax system which is of Pigovian type in order to enforce social optimality and refrain from
over-consumption of electricity in our dynamic game model.