A game theoretic analysis of resource mining in blockchain

Abstract

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. Keywords Blockchain Á Bitcoin mining Á Dynamic game theory Á Differential game Á Hamilton-Jacobi-Bellman equation Á Social optimum Á Nash equilibrium Á Myopic Nash equilibrium Á Pigovian tax

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