The Game Theory of Bitcoin and Cryptocurrencies

The unique properties of cryptocurrencies make them an interesting subject for game theory analysis, as they can help explain the incentives and behaviors involved in trading and investing. This article discusses the concept of the prisoner’s dilemma, cryptocurrency mining, and blockchain forks as relevant to the game theory of Bitcoin and cryptocurrencies.

Introduction to game theory and cryptocurrencies

Game theory is a mathematical framework that helps explain decision making in strategic situations. Cryptocurrencies, such as Bitcoin (BTC), have become a popular topic for game theorists due to their decentralized nature and potential to disrupt traditional financial systems.

Prisoner’s Dilemma and Cryptocurrency Mining

In the classic game theory scenario known as the prisoner’s dilemma, two parties must make a choice without knowing what the other will do. In the context of cryptocurrency mining, the prisoner’s dilemma can help explain why miners may act in their own self-interest, even if it is not in the best interests of the network as a whole.

The first miner to successfully solve a challenging mathematical equation receives fresh BTC units. Both computing power and energy use are essential requirements for mining. The tragedy of the commons, which occurs when individuals prioritize their own interests over the needs of the whole, is one of the biggest obstacles in cryptocurrency mining. By mining cryptocurrencies, miners can put their individual financial gain ahead of the overall security and stability of the network.

The prisoner’s dilemma provides a useful basis for understanding this behavior. In the scenario, two people are arrested for a crime and are offered the option of working together or turning on each other. If they both cooperate, both will have their sentences reduced. When one betrays the other, the betrayer receives a lighter sentence, while the other receives a longer sentence. Both receive a moderate punishment if they betray each other.

Related: How Does Blockchain Solve the Byzantine General Problem?

Miners face a similar decision-making process while mining cryptocurrencies. The network is safe and secure if all miners cooperate by mining honestly and making a contribution. Still, a miner may benefit more from mining maliciously or not contributing to the network if they choose to act in their own self-interest.

Let’s look at the diagram below that illustrates an example of two miners in a cryptocurrency pool to understand how the prisoner’s dilemma can be applied in the context of cryptocurrency mining.

In the diagram above, Miner A and Miner B are two miners in a cryptocurrency mining pool. They have the choice to cooperate (continue mining together) or defect (leave the pool and mine independently). The rewards and payouts are based on the classic prisoner’s dilemma scenario:

• If both miners cooperate, they both receive a reward (eg a share of the mining profit).
• If miner A fails while miner B cooperates, miner A receives a temptation payout (eg a larger share of the mining profit), while miner B receives a payout (eg a smaller share of the mining profit).
• If miner A cooperates while miner B fails, miner A gets a payout, while miner B gets a temptation.
• If both miners fail, they both receive a penalty (eg lower overall mining profit).

This diagram illustrates how the prisoner’s dilemma can be used in the context of cryptocurrency mining. It shows the potential rewards and payoffs for each combination of cooperation and defection, and can help miners make decisions about whether to stay in a pool or mine independently.

To meet this challenge, cryptocurrency networks can implement various incentives and mechanisms to encourage miners to act in the interest of the network as a whole. For example, networks can reward miners who contribute to the network with lower fees or increased mining rewards. In addition, networks can implement penalties or defensive mechanisms to discourage malicious behavior.

The game theory of blockchain forks

Blockchain forks are another scenario where game theory can help explain the decision-making process of participants. A fork occurs when a blockchain network splits into two separate lanes, often due to disagreement among participants about the direction of the network.

A fork can be considered a coordination game from the perspective of game theory. Two or more players must work together to achieve a common goal in a coordination game. Participants in a blockchain fork must work together to decide which fork to promote and which to reject.

The Bitcoin network split into two different forks in 2017: Bitcoin and Bitcoin Cash. This is one of the most famous instances of a blockchain fork. Disagreement in the Bitcoin community about how to expand the network to handle an increasing volume of transactions led to the creation of this fork.

In this case, members of the Bitcoin community had to choose between sticking with the old Bitcoin network and switching to the new Bitcoin Cash network. The choice was not easy because each fork has its own advantages and disadvantages. For example, while Bitcoin Cash offered faster transaction times and lower fees, Bitcoin had a larger network and higher acceptance.

Participants in this scenario had to take into account their personal preferences and opinions regarding the potential future value of each network in the context of game theory. Participants would be motivated to promote Bitcoin Cash even if it meant leaving the original Bitcoin network if they believed it had a stronger chance of long-term growth.

Related: How to Buy Bitcoin Cash: A Beginner’s Guide to Buying BCH

To understand how game theory can be applied in the context of blockchain forks, let’s look at the diagram below, which illustrates two miners facing the choice of adopting a new fork in the blockchain or continuing on the old fork.

The diagram above shows the strategic decision of two miners, miner A and miner B, on a blockchain, when faced with the choice of either adopting a new fork or continuing on the old fork. The rewards and punishments are based on the following assumptions:

• If both miners adopt the new fork, they both receive a reward (eg increased mining efficiency).
• If Miner A adopts the new fork while Miner B continues on the old fork, Miner A receives a penalty (eg reduced mining efficiency), while Miner B receives a reward.
• If Miner A continues on the old fork while Miner B adopts the new fork, Miner A receives a reward, while Miner B receives a penalty.
• If both miners continue on the old fork, they both receive a temptation (eg maintaining control of the blockchain).

This diagram illustrates how game theory can be applied in the context of blockchain forks. It shows the potential rewards and penalties for each combination of deploying or not deploying a new fork, and can help miners make decisions about whether to switch to a new fork or stick with the current one.

To meet this challenge, cryptocurrency networks can implement various mechanisms to ensure that forks happen as smoothly as possible. For example, networks can implement replay protection, which prevents transactions on one network from being replayed on the other.