( 05th October 2019 )
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.
Since the early days of bitcoin in 2009 given in, blockchain technology and cryptocurrencies have caught the attention of both researchers and investors alike. The original paper on bitcoin was improved in, mostly focusing on the security analysis. In, the authors examined a common scenario in which only participants that are aware of the information can compete for some reward focussing on incentive issues within Bitcoin.
Showing an attack in which large pools can gain more than their fair share, Eyal et al. showed Bitcoin mining protocol is not incentive compatible, which was a very important work. Ron and Shamir analyzed transaction graphs, and made attempts to identify which accounts belong to the same entity. Zohar at el. examined dynamics of pooled mining and the rewards that pools manage to collect, and use cooperative game theoretic tools to analyze how pool members may share these rewards.
They showed that for some network parameters, especially under high transaction loads, it is difficult or even impossible to distribute rewards in a stable way: some participants are always incentivized to switch between pools. Furtheremore, Lewenberg et al. also suggested a modifcation to Bitcoin’s data structure, in the form of directed acyclic graphs know as DAGs, and have analyzed the game theoretic aspects quite well of their proposal. In our opinion one of the closest connected works to this paper is the work of Niyato, Vasilakos and Kun [26], which shows how to model blockchain technology as a cooperative game, in which cloud providers can cooperate. They show a novel solution of the core issues can be found using linear programming. Cooperation among agents has been widely studied in the ever growing artificial intelligence literature.
In some relatively early work like the paper by Sundholm and Lesser, the authors analyzed coalitions among self-interested agents that need to solve combinatorial optimization problems to operate effciently in the world. Further to this, Shehory and Kraus considered task allocations via agent coalition formation.
We propose a cooperative game model for analyzing Bitcoin mining pools here. Cooperative game models have been used for many real world applications, including 1. network analysis. voting. team formation. negotiation 5. pricing cloud services. auctions We have also seen the computational aspects of cooperative games being the focus of other works, most notably the work of Elkind et al. who showed that many stability-related solution concepts in weighted voting games are hard to compute.
Moreover, in the work of Aziz and De Keijzer where an algorithm for finding an optimal coalition structure for games with few player types was proposed. Cooperative games with coalition structures were introduced by Aumann and Dreze quite early. In the common practice of cooperative games with coalition structures, also known as characteristic function games, the value of each coalition is independent of nonmembers’ actions. Our model shows similarities to one proposed by Ray and Vohra in, in which the value of a coalition depends on the coalition structure. Eyal also presented a paper which explored a block withholding attack among Bitcoin mining pools — an attack that is possible in any similar system that rewards for proof of work. Such systems are gaining popularity, running most digital currencies and related services. He observes that no-pool-attacks is not a Nash equilibrium: If none of the other pools attack, a pool can increase its revenue by attacking the others.
Bitcoin is a non-renewable resource, so it is very important to mine bitcoin strategically in order to maintain the bitcoin market balance. In this paper, we consider a continuous time dynamic game model of bitcoin mining with infinite time horizon which belongs to the class of differential games. We propose two types of solutions to our model which we call optimal mining strategies, namely cooperative (social optimum) mining strategy and non-cooperative (Nash equilibrium) mining strategy. We calculate the total profit of a miner in both cases. We found that it is always beneficial to mine jointly in cooperation with other miners since it will give the miner a higher total profit compared to a miner who mines selfishly.
Also, if all the miners choose to mine according to the Nash equilibrium mining strategy, then the bitcoin will deplete much faster than if they choose to mine according to the social optimum mining strategy. Our result fits quite nicely with the common belief that mining in cooperation will be better than mining individually in a noncooperative game. We also propose a tax system which falls into a Pigovian type. This tax system is linear in the miner’s mining strategy in order to enforce social optimality in our bitcoin dynamic game model. This way, miners will be forced to behave or mine in a way that is best for social welfare of the miners.
Yorumlar