A game theoretic analysis of resource mining in blockchain

Blockchain and cryptocurrency are a hot topic in today’s digital world. In this paper, we create a game theoretic model in continuous time. We consider a dynamic game model of the bitcoin market, where miners or players use mining systems to mine bitcoin by investing electricity into the mining system. Although this work is motivated by BTC, the work presented can be applicable to other mining systems similar to BTC. We propose three concepts of dynamic game theoretic solutions to the model: Social optimum, Nash equilibrium and myopic Nash equilibrium. Using the model that a player represents a single “miner” or a “mining pool”, we develop novel and interesting results for the cryptocurrency world.

[1]  T. Başar,et al.  Dynamic Noncooperative Game Theory , 1982 .

[2]  John D. Wilson,et al.  A theory of interregional tax competition , 1986 .

[3]  Richard Thompson Ainsworth,et al.  Blockchain, Bitcoin, and VAT in the GCC: The Missing Trader Example , 2017 .

[4]  H. T. Mouftah,et al.  Fairness-Aware Game Theoretic Approach for Service Management in Vehicular Clouds , 2017, 2017 IEEE 86th Vehicular Technology Conference (VTC-Fall).

[5]  Aron Laszka,et al.  When Bitcoin Mining Pools Run Dry - A Game-Theoretic Analysis of the Long-Term Impact of Attacks Between Mining Pools , 2015, Financial Cryptography Workshops.

[6]  Jonathan Harvey-Buschel,et al.  Bitcoin Mining Decentralization via Cost Analysis , 2016, ArXiv.

[7]  Somdip Dey,et al.  A Proof of Work: Securing Majority-Attack in Blockchain Using Machine Learning and Algorithmic Game Theory , 2018, International Journal of Wireless and Microwave Technologies.

[8]  Athanasios V. Vasilakos,et al.  Resource and Revenue Sharing with Coalition Formation of Cloud Providers: Game Theoretic Approach , 2011, 2011 11th IEEE/ACM International Symposium on Cluster, Cloud and Grid Computing.

[9]  Jeffrey S. Rosenschein,et al.  Bitcoin Mining Pools: A Cooperative Game Theoretic Analysis , 2015, AAMAS.

[10]  Karl J. O'Dwyer,et al.  Bitcoin mining and its energy footprint , 2014 .

[11]  J. Krawczyk,et al.  Games and Dynamic Games , 2012 .

[12]  A. Sandmo.  Optimal taxation: An introduction to the literature , 1976 .

[13]  Geraldo Nunes Silva,et al.  On the value function for nonautonomous optimal control problems with infinite horizon , 2007, Syst. Control. Lett..

[14]  Kim-Kwang Raymond Choo,et al.  Cracking Bitcoin wallets: I want what you have in the wallets , 2019, Future Gener. Comput. Syst..

[15]  Emin Gün Sirer,et al.  Majority Is Not Enough: Bitcoin Mining Is Vulnerable , 2013, Financial Cryptography.

[16]  Aggelos Kiayias,et al.  Blockchain Mining Games , 2016, EC.

[17]  Murat Yuksel,et al.  Profit Maximization for Bitcoin Pool Mining: A Prospect Theoretic Approach , 2017, 2017 IEEE 3rd International Conference on Collaboration and Internet Computing (CIC).

[18]  A. Wiszniewska-Matyszkiel,et al.  Linear quadratic game of exploitation of common renewable resources with inherent constraints , 2018 .

[19]  Thar Baker,et al.  A Profitable and Energy-Efficient Cooperative Fog Solution for IoT Services , 2020, IEEE Transactions on Industrial Informatics.

[20]  Jerzy Zabczyk,et al.  Mathematical control theory - an introduction , 1992, Systems & Control: Foundations & Applications.

[21]  Satoshi Nakamoto.  Bitcoin : A Peer-to-Peer Electronic Cash System , 2009 .

[22]  Meni Rosenfeld,et al.  Analysis of Hashrate-Based Double Spending , 2014, ArXiv.

[23]  Nancy L. Stokey,et al.  Recursive methods in economic dynamics , 1989 .

[24]  H. T. Mouftah,et al.  Multiagent/multiobjective interaction game system for service provisioning in vehicular cloud , 2016, IEEE Access.

[25]  Rajani Singh,et al.  Discontinuous Nash Equilibria in a Two-Stage Linear-Quadratic Dynamic Game With Linear Constraints , 2019, IEEE Transactions on Automatic Control.

[26]  Nicolas Houy,et al.  The Bitcoin Mining Game , 2014, Ledger.

[27]  Yaser Jararweh,et al.  Privacy Management in Social Internet of Vehicles: Review, Challenges and Blockchain Based Solutions , 2019, IEEE Access.

[28]  Jacob Engwerda,et al.  LQ Dynamic Optimization and Differential Games , 2005 .

[29]  Thar Baker,et al.  Cloud-Based Multi-Agent Cooperation for IoT Devices Using Workflow-Nets , 2019, Journal of Grid Computing.

[30]  Moayad Aloqaily,et al.  A Blockchain Framework for Securing Connected and Autonomous Vehicles , 2019, Sensors.

[31]  Adam S. Hayes.  Bitcoin price and its marginal cost of production: support for a fundamental value , 2018, Applied Economics Letters.