The Framework of Consensus Equilibria for Mining-Pool Games and Related Stability of Gap Games Behaviors in Blockchain Ecosystems

40 Pages Posted: 3 Apr 2020

See all articles by George Xianzhi Yuan

George Xianzhi Yuan

Soochow University; Business School, Sun Yat-sen University; School of Fintech, Shanghai Lixin University of Accounting and Finance; BBD Technology Co., Ltd. (BBD)

Date Written: March 10, 2020

Abstract

The goal of this paper is to establish the general framework of consensus equilibria for Mining-Pool Games in Blockchain Ecosystems, and in particular to explain the stable in the sense for the existence of consensus equilibria related to mining gap game’s behaviors by using one new concept called “consensus games (CG)” in Blockchain Ecosystems, here, the Blockchain ecosystem mainly means the economic activities by taking into the account of three types of different factors which are expenses, reward mechanism and mining power for the work on blockschain by applying the key consensus called “Proof of Work” due to Nakamoto in 2008.

In order to do so, we first give an outline how the general existence of consensus equilibria for Mining-Pool Games is formulated, and then used to explain the stable for Gap Games for Bitcoin in the sense by the existence of consensus equilibria under the framework of Blockchain consensus, we then establish a general existence result for consensus equilibria of general mining gap games by using the profit functions for miners as the payoffs in game theory. As applications, the general existence results for consensus equilibria of Gap games are established, which not only help us to claim the existence for the general stability for Gap games under the general framework of Blockchain ecosystems, but also allow us to illustrate a number of different phenomenons on the study of mining- pool games with possible impacts due to miners’ gap behaviors with scenarios embedded in Bitcoin economics. Our study on the explanation for the stability of mining gap game for Blockchain ecosystems shows that the concept of consensus equilibria may play a important role for the development of fundamental theory for consensus economics.

Keywords: Consensus Equilibrium, Nakamoto Consensus, Proof of Work, Stability, Blockchain Ecosystems, Mining-Pool Game, Mining Gap Games, Longest Chain Rules (LCR), Incentive Compatibility, Cooperative and Non-Cooperative Games, Hybird Solution

JEL Classification: C73, D82, D89, G20, G28, G39, L13, L86, O31

Suggested Citation

Yuan, George Xianzhi, The Framework of Consensus Equilibria for Mining-Pool Games and Related Stability of Gap Games Behaviors in Blockchain Ecosystems (March 10, 2020). Available at SSRN: https://ssrn.com/abstract=3551829 or http://dx.doi.org/10.2139/ssrn.3551829

George Xianzhi Yuan (Contact Author)

Soochow University ( email )

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Business School, Sun Yat-sen University ( email )

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School of Fintech, Shanghai Lixin University of Accounting and Finance ( email )

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China
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BBD Technology Co., Ltd. (BBD) ( email )

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No. 199 Tianfu Avenue
Chengdu, Sichuan 610093
China
15010983759 (Phone)

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