Bitcoin regulation in vietnam using cooperative game theory to analyse the cost sharing of bitcoin

LIST OF TABLESTable 2.1: The status of crypto asset regulations in the world...10 Table 3.1: Cost and utility of players in High price period...23 Table 3.2: Cost of coalitions in High p

VIETNAM NATIONAL UNIVERSITY, HANOI

VIETNAM JAPAN UNIVERSITY

VIETNAM NATIONAL UNIVERSITY, HANOI

VIETNAM JAPAN UNIVERSITY

Firstly, I would like to express appreciation to Prof Masakazu Fukuzumi for hisenthusiastic assistance and supports for of my thesis His lesson inspired me tostudy in this new field – game theory, and his explanation has made the work moreinteresting I also want to express the special thanks to Dr Vu Hoang Linh for hisadvice and recommendation His support helped me find the appropriate topic andcontinue with initial research plan

Secondly, I would like to show appreciation University of Tsukuba and VietnamJapan University for giving me a chance to participate the master course in Vietnamand Japan

Besides, I greatly appreciate with the continuous support of Office of GlobalInitiatives, University of Tsukuba in my 3-month internship

Finally, I would like to express gratitude to my family, my friends and my teachersfor encouraging me in all the progresses of this thesis

ACKNOWLEDGEMENT

CONTENTS

ABBREVIATIONS

LIST OF TABLES

LIST OF FIGURES

ABSTRACT

CHAPTER 1: INTRODUCTION

1.1 Research background and problem statement

1.2 Research rationale

1.3 Research questions

1.4 Research methodology and design

1.5 Research limitation

CHAPTER 2: LITERATURE REVIEW

2.1 The characteristics of Bitcoin

2.1.1 Bitcoin value

2.1.2 Volatility of Bitcoin price

2.1.3 Bitcoin community

2.1.4 Bitcoin Mining

2.1.5 Exchange market

2.2 Bitcoin regulation in the world

2.3 Bitcoin regulation in Vietnam

2.4 Cooperative game theory and cost allocation

CHAPTER 3: RESEARCH METHODOLOGY

3.1 Research method

3.2 Bitcoin cost sharing model

3.3 Cost structure in sharing model

3.4 Cost and utility……… …24

4.1 The result of solutions 26

4.1.1 The proportional cost allocation method 26

4.1.2 The core and Nucleolus method 27

4.1.3 The Shapley value method 31

4.2 Discussion 36

CHAPTER 5: POLICY IMPLICATION AND CONCLUSION 39

5.1 Policy implication 39

5.2 Conclusion 42

5.3 Future research 44

APPENDIX 45

REFERENCE……… 47

BTC

ICO

LIST OF TABLES

Table 2.1: The status of crypto asset regulations in the world 10

Table 3.1: Cost and utility of players in High price period 23

Table 3.2: Cost of coalitions in High price period 24

Table 3.3: Cost and utility and player in Low price period 24

Table 3.4: Cost of coalition in Low price period 25

Table 4.1: Equal proportion cost between players (yi ) 26

Table 4.2: Conditional cost of players 29

Table 4.3: Terms the amount of x1 , x2 and x3 30

Table 4.4: The value of xi solved by Nucleolus method with parameters 30

Table 4.5: The amount of xi (thousand dollars) for each player 30

Table 4.6: Corresponding cost allocation (thousand dollars) between players based on Nucleolus method (y i) 30

Table 4.7: The amount of xi based on Shapley value method in High price period 31 Table 4.8: The amount of xi based on Shapley value method in Low price period 32

Table 4.9: Cost allocation (thousand dollars) between player based on Shapley value method (yi ) 33

Table 4.10: Result of solutions in High price period 34

Table 4.11: Results of solutions in Low price period 35

Table 4.12: Percentage of utility received by each player based on solutions concepts in High price period 36

Table 4.13: Percentage of utility received by each player based on solutions concepts in Low price period 36

LIST OF FIGURES

Figure 2.1: The price of Bitcoin from April 2018 to April 2019 5

Figure 2.2: Regulatory status of Bitcoins Worldwide in 2018 8

Figure 2.3: Coalition forms of players 16

Figure 2.4: The core of coalitional game 17

Figure 3.1: The process of research method 20

Figure 3.2: Bitcoin cost sharing model 22

Figure 4.1: The core – Shapley value – Nucleolus in high price and low price period 33 Figure 4.2: Comparison between cooperative game methods and non-cooperation situation (High price period) 34

Figure 4.3: Comparison between cooperative game methods and non-cooperation situation (Low price period) 35

Figure 5.1: Bitcoin future 43

In 2017, The State Bank of Vietnam has stated that Bitcoin and other digitalcurrencies are not a legal method of payment However, Bitcoin also can beconsidered as a commodity, asset or investment channel At present, while thenumber of Bitcoin investors and exchange market is increasing rapidly, there is noregulation in Vietnam to regulate the issue of this digital currency

In order to harmonize the interest of stakeholders, this paper suggests the Bitcoin costsharing model with cooperative game theory approach to elaborate the incentive whyBitcoin users should cooperate and form coalitions From that, it can help citizenincrease the awareness and influence of Bitcoin in new financial environment

Finally, the findings of this study also intended to assist lawmakers, regulators andinvestigators in regulatory process The study also focuses on educating targetedreaders with the deficiencies in current policies, regulations, and legislation as well asmaking recommendations for future updates in the regulation of digital currencies

Keyword: Bitcoin, Bitcoin regulation, Bitcoin price, Cooperative game theory.

CHAPTER 1: INTRODUCTION1.1 Research background and problem statement

Bitcoin is a digital currency introduced in 2008 by a person called “SatoshiNakamoto” It’s an open network which allows online payment to be sent directlywithout a third party, transactions follow a public ledger called blockchain(Nakamoto, 2008) Nowadays, Bitcoin becomes the most widely used and acceptedthe digital currency Moreover, Bitcoin is considered as the financial productsassociated with technology but outside of the scope of this research This thesis onlydeals with Bitcoin at economic approach

Bitcoin users in Vietnam included three main players: investors, Bitcoin miners andbusinesses that accept exchange in Bitcoins have grown rapidly, from 30,000 users in

2016 to 60,000 in 2017 and about 300,000 users in 2018 In this context, currently,Bitcoin miners, users and businesses cooperate together to build a sustainablecommunity However, in some cases of conflict of interest, many users have lost moneyand caused adverse impacts on Bitcoin and social awareness of Bitcoin

In this situation, regulatory authorities have cautioned about the risks related toBitcoin, as well as the risk of using virtual currency for criminal activity becausevirtual currency is anonymous, decentralized, and not subject to management of anyorganization Investment activities, buying and selling virtual money, mobilizingcapital through issuing virtual money (ICO), especially using virtual money bymulti-level marketing is more and more complicated, threatening to affect financialmarkets, and can cause huge risks for participating organizations and individuals

It is difficult for investors to recover money because the regulation on Bitcoin has notyet been released When Bitcoin users cooperate together, they must protect their assetsand take risks by themselves So Vietnam government need to legitimize Bitcoin in thecurrent Vietnamese context Besides, policies that directly affect stakeholders will alsoreduce frauds and have a better understanding of Bitcoin These

policies not only will benefit and protect Bitcoin stakeholders but also help topromote innovation technology in Vietnam.

1.2 Research rationale and research objectives

The rationale behind this topic is to consider legalization of Bitcoin which can beused for effective regulation of Bitcoin community; apply Game theory model tocalculate reasonable cost in case of price fluctuation The findings suggest that if wemanage Bitcoin’s system to reduce its cost practices, the rate of loss of the users andthe amount of money in exchange market could be in the acceptable range

With the background and problem statement mentioned above, this study has aimed

to clarify characteristics and mechanisms of Bitcoin market; and suggest solutionsand policies to incentivize individuals’ contribution and maximize benefits to thesociety in Vietnam

1.3 Research questions

Based on research problem, the main research question is:

How can Bitcoin be regulated while harmonizing the interests of stakeholders by applying Bitcoin cost sharing model in Vietnam?

Moreover, some other sub-questions also can be answered in this study:

What is the Bitcoin’s characteristics and how is Bitcoin obtained?

How about legal and regulatory issues of Bitcoin in Vietnam and in the world?

How the Bitcoin cost allocation can be solved using cooperative game theory and which solutions can be used to get consensus between

stakeholders?

Which policies should recommend to manage Bitcoin community in Vietnam?

1.4 Research methodology and design

In order to clarify problem, this research employed both qualitative research andcooperative game theory This thesis firstly provides a conceptual framework ofBitcoin in Vietnam and around the world From this analysis, it is possible to examinethe Bitcoin’s characteristics, Bitcoin’s value and suggest the solutions for Bitcoin’s

stakeholders For these purposes, original models which can describe the interactionbetween Bitcoin stakeholders and the cost sharing of Bitcoin is developed Withqualitative instrument, the secondary data is gathered from policies, documents ofthe government, company, news and media video.

Quantitative method will enable results of game theory model, discussion andcomparative analysis The data of Bitcoin price will be collected from officialexchange market, price of mining Bitcoin in Vietnam according to the analyticalpublication Elite Fixtures The costs and utility in the coalitions are stated, after thatthe solutions concepts also calculated and analyzed in each situation

This research is organized into five main chapters After the introduction, the studywill establish the theoretical framework in which, we provide a literature review anddefine important concepts After which, the thesis will discuss the methodologicalapproach for the research and explain the cooperative game theory concepts andsolution methods In chapter four, the results will be calculated in two main periodsand compared to non-cooperative situation Lastly, policy recommendations will besuggested based on situation and findings of this research

1.5 Research limitation

The main limitation is a simple case study, which works purely in the information.Also, this study cannot to conduct a full empirical analysis Moreover, this researchalso need to analyze the ability to leave the grand coalition of players in thedifferent situation

CHAPTER 2: LITERATURE REVIEW

The aim of this literature review is to clarify the understanding and appreciation forthe current study In this chapter, the papers relating to Bitcoin characteristic,Bitcoin value, cooperative game theory and Bitcoin regulation will be reviewed.After this progress, the research model will be established and the policyimplication could be found

2.1 The characteristics of Bitcoin

Bitcoin is new phenomenon, so that many papers explained the Bitcoincharacteristics Bitcoin is the first decentralized cryptocurrency, its transactioncannot be forged and the amount of Bitcoin is limited (Nakamoto, 2008) This firstdocument published by Satoshi Nakamoto describe how the Bitcoin network works.Bitcoin have many advantages (Mirzayi, 2017) It eliminates transaction costs, issafer than cash, harder to fake than fiat currency The potential of Bitcoin outweighsthe threats (Alcorn, Eagke, & Ethan, 2014), however Bitcoin users also need toknow more detailed about the risks that can happen It is not accidental that manyfinancial experts oppose Bitcoin, many countries banned Bitcoin, some countriesaccept Bitcoin like Japan and Canada but are extremely cautious The use of Bitcoin

is a medium for illegal activities to transmit proceeds locally or globally (Bryans,2014) The difficult of definition Bitcoin’s value make many users lose money whenthey speculate Bitcoin or invest to scam projects Therefore, regulators andinvestigators struggled with Bitcoin and the problems associated with this new form

of electronic value transfer system (Ajello, 2015)

Bitcoin value

Bitcoin is an emerging technology based on complex technology In addition,Bitcoins are not regulated by a centralized agency till date, make them less reliableand it is difficult to evaluate Bitcoin value To invest in Bitcoin, users must believe

in the Bitcoin security, trust any organizations involved, such as wallet services or

exchange Bitcoin is considered as a speculation (Yermack, 2013) and Bitcoin valuehas the relationship with the number of search queries for its information on Google

or Wikipedia (Kristoufek, 2015) So, the value of Bitcoin will increase when peoplepay more attention to Bitcoin and it is important condition to develop Bitcoincommunity

Volatility of Bitcoin price

Bitcoin price fluctuates dramatically and depends substantially on public sentiment(Thies & Molnár, 2018) The large fluctuation has caused many economists toquestions the viability of Bitcoin In December 2017, Bitcoin prices peaked at over $20,000, and only a week later hit bottom at $ 10,000, which could cause huge losses forinvestors In January 2019, Bitcoin has lost about 80% value from its peak

Figure 2.1: The price of Bitcoin from April 2018 to April 2019

Source: coindesk.com

However, in 2018 and 2019, figure 2.1 shows that Bitcoin price have relativelystable periods From 6/2018 to 11/2018, the average price is about 6.5 thousandUSD From 12/2018 to 4/2019, the average price is about 3.6 thousand USD.

Bitcoin community

In order for Bitcoin to exist, form and exchange, it is necessary to focus on threefactors: (1) Miners; (2) Businesses; (3) Investors Besides, in order to develop aflawless system, developers’ contribution is crucial They try to solve bottlenecksand threats, and develop methods to apply in the future

There are three ways to get Bitcoins when users join network (Murphy, Seitzinger,

& Elwell, 2015) First, users can obtain new Bitcoin by serving as miners Second,users can exchange money (e.g., dollars, yen and Vietnam dong) for a fee onexchange market (e.g., Remitano, Coinbase and Binance) by using credit card Theexchange fee depends on the value of transaction Third, users can receive Bitcoin

in exchange for the sale of goods or services with other businesses

Miners play a very important role in Bitcoin ecosystem, they secure integrity ofcoins and business model, as well as confirm the existence of Bitcoin in thenetwork Mining decentralization is crucial to keeping consensus between playersand everyone’s Bitcoins safe Businesses are organizations which provide exchangeservice, make coins more accessible, increase adoption and face new regulation.Finally, investors are holders and users who affect the demand and supply ofBitcoin, they also create value circulating Bitcoin in the economy, more valuecreation and wider adoption

Bitcoin Mining

The term "Bitcoin mining" refers to individuals or organizations that use theirdevices to search for Bitcoin units to own and earn Bitcoin mining is worked by thespecialized computer This process is the backbone of Bitcoin network The mining

of Bitcoin based on Blockchain technology, it is easy to understand that all of theseactivities will be recognized by the global network of computers, so it is difficult to

fake and steal because it is only recognized when both parties confirm thetransaction to be considered valid.

The region with the most mining pool is China, accounting for 81% of the globalmarket share, the Czech Republic accounts for 10%, the rest are other regions (9%).Profits from mining Bitcoin have prompted many people to buy excavators On theone hand, this situation raises concerns about the amount of energy consumed inthis area, while the future of Bitcoin remains a mystery

On the other hand, it is the desire to maximize profits from mining, which haspromoted the field of information technology to develop more to strengthen thesystem of excavators, and develop clean energy sector (like using solar power) toget the lowest energy consumption cost

Exchange market

The Asia-Pacific region accounts for the largest proportion of Bitcoin in the world(50%), followed by North America (Rauchs, 2017) Meanwhile, storing Bitcoinelectronic wallet in Europe accounts for the largest proportion (42%), followed byNorth America (39%)

Bitcoin trading company provide services to buy, sell electronic currencies and otherdigital assets, exchange units are currencies in the world The exchange market plays acentral role in the existence of electronic money, because it provides trading locations,creating liquidity as well as price setting mechanisms for these currencies

The first trading platform was established in 2010 (Mt Gox) to create a platform forinvestors of Bitcoin trading, so far, there have been hundreds of trading companyestablished, can include some big businesses like Binance, Kraken, OKcoin,Coinbase, Huobi etc

2.2 Bitcoin regulation in the world

The situation of Bitcoin in the world can be summarized in the figure 2.2:

Figure 2.2: Regulatory status of Bitcoins Worldwide in 2018

Source:

https://coin.dance/poli

Figure 2.2 highlights Bitcoin regulation around the world Using color, a range ofBitcoin legacies shows different levels of acceptance around the world Firstly, greencountries are legitimate Bitcoin markets, such as Canada, United States, Australia andetc Orange represents neutral markets that are not fully legalized Bitcoin, but there aresome announcements regarding the use of electronic money Light pink countries withlimited Bitcoin markets may have red tape, regulations and government efforts to slowdown the use of electronic money The dark pink country represents the markets whereBitcoin has been made completely illegal and criminalized Finally, some countrieshave yet to comment on the legitimacy of Bitcoin, expressed in gray

Eastern countries seem to close with Bitcoin more than their Western counterparts.Russia is currently the largest country to legalize Bitcoin However, China andSouth Korea are the latest two countries to strengthen inspection and regulation ofusing Bitcoin This has led to a recent sell-off in the electronic money market, asChina and South Korea are two important hotspots that have contributed a lot ofliquidity to Bitcoin market

North America and Western Europe are the most accepting areas for Bitcoin TheMiddle East seems very divided on the topic of Bitcoin Interestingly, Iraq, Iran andTurkey are legitimate Bitcoin markets, while Afghanistan, Pakistan, Saudi Arabiaand Egypt have different levels of restrictions on digital currency.

There are 112 (45%) countries with unrestricted Bitcoin laws, out of 251 Nearly8% of countries in the world, have limited or illegal Bitcoin 47% of the world hasnot yet commented on Bitcoin and the legality of its use in their countries This is arisk for Bitcoin, because some of these undecided countries may eventually decide

to set restrictions on market

In general, most of the world has not yet commented on the legitimacy of Bitcoin.The emerging industry is still not fully understood by global managers, which mayexplain why some countries have not yet commented on this movement As timegoes by, countries that remain on the sidelines will eventually come up with a set ofrules for approving Bitcoin, or operating illegally Bitcoin increases the popularitylevel continues to exceed expectations, but not all countries will see electronicmoney in a favorable light

Table 2.1 demonstrates the way other country around the world regulate Bitcoin.According to statistics from Binance Company, there are five factors related toBitcoin regulation: crypto exchanges, ICO, crypto payments, conversions fromdigital currencies to fiat currencies; and plan to increase cryptocurrency regulation

Table 2.1: The status of crypto asset regulations in the world

From my research, in case of Vietnam, Bitcoin exchange market and ICOs still operate

in gray area Bitcoin is considered as illegal payment and cannot convert to fiatcurrency However, Vietnam government also planned to regulate Bitcoin in 2019

2.3 Bitcoin regulation in Vietnam

Legal framework related to Bitcoin

According to Clause 6, Article 6 of Decree No 101/2012 / ND-CP amended andsupplemented by Decree No 80/2016 / ND-CP stipulating prohibited acts: “6.Issuing, supplying and using illegal payment instruments” Therefore, the supply anduse of illegal payment instruments such as Bitcoin virtual currency is prohibited.Currently, the issuance, supply and use of Bitcoin as a method of payment can be handled for administrative violations with a fine of between VND 150 - 200 million

as stipulated in Clause 6 Article 27 of Decree 96/2014 / ND-CP on administrativepenalties in the field of currency and banking activities.

In addition, acts of issuing, supplying and using illegal means of payment, includingBitcoin, will be subject to criminal prosecution in accordance with the provisions ofPoint h Clause 1 Article 206 Criminal Code 2015 was amended and supplemented

in 2017

Moreover, on 11 April 2018, the Prime Minister issued Directive 10 / CT-TTg in

2018 to strengthen management of activities related to Bitcoin

Vietnam Still Undecided About Cryptocurrencies

Vietnamese authorities are still delay the released documents to regulating Bitcoin.The Ministry of Justice of Vietnam has submitted a report to the government with

an assessment of the current law and assessment of business activities related todigital money in Vietnam

The report proposes three alternative policies to be applied in different regions of theworld The first approach, which is referred to as “Floating”, involves implementing arelatively loose regulatory regime The second option is called “Prohibition”, and thethird is legalizing digital asset transactions under clear conditions

The relevant ministries and departments will establish an appropriate legalframework for managing Bitcoin This regulation should balance the risks andpotentials related to Bitcoin to ensure that investors benefit from it and support thedevelopment of electronic money technology in general

Trade Ministry banned on imports of mining equipment

Electronic money mining has become a source of income for many Vietnamesecompanies and citizens, but the digital money mining business is not really popularwith the Vietnamese government In 2018, the Ministry of Finance proposed tosuspend the import of mining equipment - measures that the State Bank of Vietnam

and the Ministry of Public Security supported According to statistics from the GeneralDepartment of Vietnam Customs, more than 27,000 mining components were importedinto Vietnam in 2017 and over 15,000 in the first five months of 2018.

Digital currency has arrived in Vietnam when some services in Ho Chi Minh Citystart paying with Bitcoin ATM Bitcoin has been installed in this city, allowing users

to withdraw cash and buy electronic money (Nguyen, T.N.Y, 2017)

Vietnamese people are one of the most active electronic money users, especiallybitcoin, along with Japan and Korea Data from SimilarWeb in 2017 shows thatVietnamese investors are ranked top of Remitano exchange market, and second onCoinMarketCap.com and Bittrex platform

The reasons why Vietnam government do not accept Bitcoin as a payment method

First, Bitcoin is not currency and cannot be considered as money because the moneymust be made by the central bank Fluctuations of money affect the balance ofpayments, commodity prices as well as other currencies However, Bitcoin do nothave the above characteristics

Second, the level of risk is high According to research by private company ICOSatis Group, it is estimated that in 2017, approximately 78% of ICO projects arefrauds, 4% fail, 3% are dead and only 15% of projects are taken on the market.Third, Bitcoin is a technology product from Blockchain which is a new technology.All transactions are anonymous and have security, high confidentiality Therefore,many people worry that Bitcoin can be a money laundering tool of crime

Fourth, the law does not recognize Bitcoin Currently the law does not recognize it

as a means of payment, but the transaction, buying and selling it as an asset is stillhappening in Vietnam

2.4 Game theory in Bitcoin and cost sharing model

Game theory is a set of analytical tools designed to model interdependent situations, inwhich each player's logical behavior not only affects his or her own interests and losses,but also impact others Allocation cost of Bitcoin involves interaction between multiplestakeholders, so that game theory is consistent with cost-sharing model

Each player in the Bitcoin community has different benefits and investment costs.For miners, they try to maintain their system to gain profits when Bitcoin pricesrise, while businesses want to have a stable amount of Bitcoin to use for manydifferent purposes The remaining investors tend to speculate and trade when there

is a change in prices In the Bitcoin community, stakeholders can form verydifferent game forms, non-cooperation, cooperation, partial cooperation

This study applies cooperative game theory to analyze the cost sharing betweenagencies in Bitcoin community The cooperative game theory approach has emerged as

an effective, fair-minded approach to providing adequate incentive to motivatestakeholders in community (Ray et al., n.d.) Recently, the game theory method hasbeen used as an effective framework for making decisions on a number of issues andconflicts in Bitcoin inter-group Application of cooperative game theory has been used

in Bitcoin mining (Lewenberg, Bachrach, Sompolinsky, Zohar, & Rosenschein, 2015),game theoretical methods in human-machine (Liang & Yan, 2017) Because themethods from cooperative game theory is appropriate for the context like the Bitcoinexchange market, the main purpose of this study is to provide relevant user data toassess the costs they are expected to incur in a cooperative game

Quantitative and qualitative methods have been proposed to evaluate Bitcoin value andmanage Bitcoin as: Bitcoin analysis from investor’s perspective (Thesis, Economics, &Schut, 2017), Estimate Bitcoin price using machine learning (Velankar, Valecha, &Maji, 2018), Determinant of Bitcoin price (Sukamulja & Sikora, 2018), Bitcoinregulation and investigation (Fawcett, 2016), Analysis legal issues (Murphy

et al., 2015), An evolution game theory approach to combat money laundering(Azevedo Araujo, 2010).

In the economic context, games in game theory are mathematical models of rationalagents A reasonable goal of the goal is to achieve the best possible results In non-cooperative game theory, this means maximizing its specific pay-off function for thegame, in which payment depends on actions taken by all other players in the game(Allen & Morris, 2005) Cooperative game theory allows forming alliances betweenactors to increase their utility (Elkind & Rothe, 2016) Major studies when thesecoalitions will be formed and how to distribute costs or profits among agents in thealliance

Bitcoin is a new digital currency from 2008 so the papers relating to applicationgame theory in Bitcoin have been reviewed, such as: Applications of game theory inBlockchain (Z Liu et al., 2019); Energy consumption in Bitcoin mining (Singh,Dwivedi, & Srivastava, 2018); The Bitcoin mining game (Houy, 2014)

The initial concepts of “Cooperative game theory” and “forming coalition” wasintroduced in some research related to technology adoption (F Liu, Dedehayir, &Katzy, 2015); Moreover, the concepts of solution “Shapley value”, ‘‘Nucleolus”and “The Core” could be found in the research “Game Theory” (Qu H.V, 2015),water resource management (Valinejadshoubi & Shakibabarough, 2013)

This study aims to develop a Bitcoin cost sharing model In particular, we care about theconditions that ensure that grand coalition is the best priority for all players Fair axiomsare used to provide some theoretical results that the study applies to this model

Transferable Utility Games

A coalition game with transferable utility (TU game) is a pair (N; v); such that N={1,2…n} is a finite set of players A subset of N is called a coalition S N (included)the collection of all coalition is denoted by 2N (Maschler, M., Solan, E., & Zamir,S.,2013)

Set N = {1, 2 … n} be the set of players and 2N be the set of coalitions (subsets ofN) A cooperative game in N is defined by its characteristic function u: 2N → R,which assigns to each coalition S N a real number u(S)

For example, N = {1,2,3} is the set of players and a subset of N is called a coalition

be transferred between players

Figure 2.3: Coalition forms of playersFigure 2.3 performs a value function in cooperative game among three players andthe overview of the value of coalitions of the 3 players

The solution concepts

In cooperative game theory, the solutions are concepts which ensure the fairness forplayer when they form grand coalition

The core of grand coalition is the set of action of the grand coalition N that are not

blocked by any coalition An imputation X (x1; x2; x3) is in core if and only if thefollowing inequalities:

Figure 2.4: The core of coalitional game

The Shapley value

Shapley's value distribution method is a normative allocation concept that is oftenconsidered a reasonable way of dividing benefits from cooperation As aconsequence of the definition of four attractive axioms: Symmetry, Null, Effectiveand Additivity (Shapley, n.d.) Symmetric conditions mean that the allocation doesnot depend on when the player joins the game Null player condition means that aplayer has a marginal contribution to any alliance given zero value

Shapley value Φ (N, v) is the most commonly used solution in cost sharing games.This value satisfies efficiency, fair, symmetry and marginal contribution (Shapley,1967)

Nucleolus

The Nucleolus is the costs based on the principle to “minimize the maximumdissatisfaction” It provides a results within the core in case the core is non-empty.Nucleolus is the solution first proposed by Schmeidler (1969) to minimize thedissatisfaction among the coalition – fair allocation rule Example, if there are threeplayers, we have the equation:

Firstly, some idea of fairness will be introduced that related concepts

Cost are shared equally and proportionally based on contribution

Individual rationality – no player is allocated a cost greater than

Costs are allocated based on each player’s contribution to the

efficiency improvements in the forced cooperation

Minimized dissatisfaction is to minimize the maximum

dissatisfaction among the players

With individual rationality, the possible allocations for the grand coalition is the set

of imputations

Using the concepts of imputations and core from a fair perspective is obvious, but itdoes not provide allocation, but an assessment tool Therefore, the value of Shapleyand Nucleolus provides accurate distribution, because they are often considered tolead to fair allocation based on certain assumptions and axioms, moreover, it isassumed that Shapley values and Nucleolus is the most appropriate distributionmethod for problems of the type mentioned in this study

CHAPTER 3: RESEARCH METHODOLOGY3.1 Research method

Cost sharing process for purchasing Bitcoin between miners, businesses andinvestors in different coalitions have been established The core, Value Shapley,Nucleolus and traditional methods such as proportional division were used in thisstudy as a cost-sharing method Different types of players' coalitions have beenconsidered to assess fairness in cooperation among players in different pricesituations The data in this research such as Bitcoin mining cost, Bitcoin price andbrokerage fee are collected in Vietnam and in the Bitcoin market

This figure will point out the process of research method

Confirm the form of game: Cooperative game theory,

Bitcoin Cost sharing

Determine players: Miners (1); Businesses

(2); Investors (3); Cost Function

Find solutions: the Core, proportional, the

Shapley value, Nucleolus

Compare and discuss the results

Suggest the solutions and policy implication

Figure 3.1: The process of research method

3.2 Bitcoin cost sharing model

Given that in the Bitcoin market there are 3 main investor groups: Miners, Businessesand Investors All these players want to obtain Bitcoin, but the way to get their Bitcoin

is different Miners is the group who use computers and software that they invest to

solve algorithms and own Bitcoin Investors can own Bitcoin by trading in themarket or buying directly from Bitcoin miners Businesses can purchase Bitcoinfrom investors or miners Currently, in order to share the benefits and risks inowning Bitcoin, players have agreed and contacted each other, from which manycooperative alliances have been formed.

In Bitcoin market, conflicts can occur when decision makers should cooperate inbuilding a joint project and then the cost of this group is not equally distributed.Therefore, if stakeholders do not see this part of the total cost equitably, they willnot be willing to cooperate for joint projects

This study uses game theory in cost allocation from a cooperative game to find adifferent proportional vector of results This ratio vector is not only optimized butalso fair for all players

Some of method used for cooperative game include:

- The core

- The Shapley value

- The Nucleolus

3.3 Cost structure in sharing model

There are the following types of costs: Bitcoin mining costs, Bitcoin price in the market, and brokerage cost

Characteristics of the types of expenses are as follows:

- Bitcoin mining cost (α) is almost stable, depending on a number of factors such as

geographical location, electricity price and cost of mining equipment

- Bitcoin price in the market (β): has a large fluctuation range, influenced by many

factors in the international market, investor psychology