Название: Bitcoin: A Game-Theoretic Analysis
Автор: Micah Warren
Издательство: De Gruyter
Год: 2023
Страниц: 344
Язык: английский
Формат: pdf (true)
Размер: 10.2 MB

The definitive guide to the game-theoretic and probabilistic underpinning for Bitcoin’s security model. The book begins with an overview of probability and game theory. Nakamoto Consensus is discussed in both practical and theoretical terms.

The question of how one party can transfer money to another party without physically exchanging money is an old problem. The most common solution, available for hundreds of years, is to use a trusted third party, like a bank. If a bank is mutually trusted and has custody of one person’s money, this person can write a check or by some other means direct the bank to pay their counterparty. A check can be thought of as simply instructions for the money’s custodian to do something with the money.

Such relationships require trust. If the two parties do not use the same bank, there must be a relationship between the banks. If the banks are in different jurisdictions, this can be an obstacle.

For many reasons, individuals may want to transmit money without the use of a trusted third party. They may want to do this at a distance. They may also want to do this with some level of anonymity. Suppose a network of individuals forms around this goal: to be able to send money to each other, without doing so in person. Keeping in mind the notion of a bank cashing a check, there are issues that must be overcome:

– There must be a way for everyone involved in the network to know what money is good, at any given time.
– Parties must be able to “sign” payments in a verifiable way. That is, there must be some way to verify that the instructions to transfer money are coming from the owner of the money.
– There must be a way to ensure that a payment is not reused repeatedly.

Cryptography (a subdiscipline of number theory) solves the second issue quite handily. A blockchain attempts to solve the other two problems, with probabilistic assurances. The goal of this text is to offer some accessible game-theoretic background for analysis of proof-of-work blockchains. Much of the current game-theoretic understanding is found in podcasts, videos, blog posts, and uncurated forum discussions and is poorly formalized. On the other hand, quite a bit of academic research exists, but much is esoteric and not written with immediate applications in mind. This textbook is a brazen attempt to bridge this gap. Deeper game-theoretic issues are discussed at length with the goal that an undergraduate student can understand their applicability.

Cooperative and non-cooperative game theory are distinct. In the former, players are assumed to have the ability to negotiate, form coalitions, and enter into binding agreements with other players. This leads to different dynamics: The idea of a Nash equilibrium is no longer applicable; a player should consider not only the effects of changing their own strategy but also what would happen if they changed their strategy in concert with other players. Immediately the dynamics of games such as stag hunt and the prisoners’ dilemma change. If two players in a prisoners’ dilemma can agree to be bound to cooperate, certainly they will cooperate; this is preferred over each defaulting to the less optimal Nash equilibrium (the question of how such binding agreements are enforced in practice is a separate question). Cooperative game theory studies the behavior of players not only as individuals but also potentially as coalitions.

The background material provided in the first three chapters includes an overview of how proof of work functions, followed by an overview of basic concepts from probability theory and relevant notions from game theory. In the remainder we will discuss the implication for Bitcoin.

This volume:

Describes attacks and exploits with mathematical justifications, including selfish mining.
Identifies common assumptions such as the Market Fragility Hypothesis, establishing a framework for analyzing incentives to attack.
Outlines the block reward schedule and economics of ASIC mining.
Discusses how adoption by institutions would fundamentally change the security model.
Analyzes incentives for double-spend and sabotage attacks via stock-flow models.
Overviews coalitional game theory with applications to majority takeover attacks
Presents Nash bargaining with application to unregulated environments

This book is intended for students or researchers wanting to engage in a serious conversation about the future viability of Bitcoin as a decentralized, censorship-resistant, peer-to-peer electronic cash system.