Game Theory and Cryptocurrencies

Game theory is the study of human conflict and cooperation within a competitive environment. It can be used to analyze a wide variety of situations, from chess tournaments to economic markets. Game theory and cryptocurrencies are two areas that have seen a lot of overlap in recent years.

What Is Game Theory?

Game theory is a branch of mathematics that studies the behavior of rational decision-makers in interactive settings. In-game theory, players (also called agents) are assumed to be rational, meaning they will always choose the course of action that is most likely to lead to their desired outcomes.

A game theory has been present in the field of economics since the early 20th century, but it wasn’t until the 1950s that game theory began to be widely used in other disciplines such as political science and sociology.

One of the most famous game theory models is the prisoner’s Dilemma, which was first formulated by mathematicians Merrill M. Flood and Melvin Dresher in 1950.

Game theory and cryptocurrencies have been associated with each other since the early days of Bitcoin. In 2013, researcher Nick Szabo proposed using game theory to explain why people would choose to use Bitcoin instead of traditional fiat currencies.

Key Concepts of Game Theory

Game theory has an interactive environment in which the agents in the game react to each other.

The key concepts of game theory are:

Rationality: Each player is assumed to be rational and will always choose the course of action that is most likely to lead to their desired outcomes.
Interaction: The players in the game interact with each other, affecting each other’s chances of winning.
Equilibrium: A game reaches equilibrium when each player has no incentive to change their dominant strategy.

It is important to note that game theory does not always lead to equilibrium. In fact, game theory can be used to analyze situations in which players do not have the same objectives.

Applications of Game Theory

There are a lot of ways how you can apply Game Theory.

Business World: In the business world, game theory is often used to understand how companies can maximize their profits. For example, game theory can be used to analyze how two companies might compete against each other in the marketplace.
Politics: Game theory is also commonly used in political science. It can be used to understand how different countries might interact with each other or how different political parties might negotiate with each other.
Economics: Game theory is widely used in economics. It can be used to understand how different market participants might interact with each other or how different economic policies might affect the economy as a whole.
Cryptocurrencies: Cryptocurrencies are a relatively new application of game theory. Due to their decentralized nature, cryptocurrencies are often described as “trustless” systems. This means that there is no need for a central authority to oversee the transactions taking place on the bitcoin network. Instead, game theory is used to incentivize users to participate in the network and to ensure that the system remains secure.

Game theory can be applied in a variety of ways to cryptocurrencies. For example, game theory can be used to understand how different miners might compete against each other for rewards or how different users might trade with each other in the market.

Game Theory Model

There are many types of game theory models that you can use as tools to analyze different situations. The most famous and well-known model is the Prisoner’s Dilemma.

Here is a list of some other game theory models that you may come across:

Nash Equilibrium: A Nash equilibrium is a set of strategies in which each player’s strategy is the best response to the other players’ strategies.
Cooperative Game Theory: Cooperative game theory is a branch of game theory that studies the effects of cooperation and collaboration between players.
Stackelberg Game: In game theory, the Stackelberg model is a strategic form of the game in which one player, called the leader, makes their decisions before the other player, called the follower, does.
Bayesian Game: A Bayesian game is a game in which players have incomplete information about the other players.
Zero-sum Games: A zero-sum game is a game in which the total gains of the players sum to zero.
Non-zero-sum Games: A non-zero-sum game is a game in which the total gains of the players do not sum to zero.
Sequential Games: A sequential game is a game in which the players take turns making decisions.
Simultaneous Games: A simultaneous game is a game in which all of the players make their decisions at the same time.

These are some of the game theory models that you may come across while reading about game theory or while analyzing a situation using game theory.

The Prisoner’s Dilemma

Prisoner’s Dilemma was initiated by Albert W. Tucker in 1950s game theory studies. The Dilemma was later formalized by Merrill M. Flood and Melvin Dresher while working at Rand Corporation. The model is a classic example of a game that does not have a Nash equilibrium in pure strategies.

The prisoner’s Dilemma is considered a classic example of a game theory model that illustrates how rational decision-makers can end up with suboptimal outcomes.

The prisoner’s Dilemma is a famous game theory model that illustrates the problem of cooperation.

The Prisoner’s Dilemma goes as follows:

Two prisoners are each in separate cells and cannot communicate with each other according to the game rules.

The prosecutor offers both prisoners the following deal:

If one prisoner confesses and the other does not, the confessor will go free, and the non-confessor will get a 10-year sentence.

If both prisoners confess, then both will get a 5-year sentence.

If neither prisoner confesses, then both will only get a 1-year sentence.

What should each prisoner do?

The game theory analysis of this situation shows that the prisoners should confess because it is in their best interest to do so. However, if both prisoners confess, then they will both end up with a worse outcome than if neither had confessed.

This is an example of how game theory can be used to study human behavior based on interactive situations.

What is the best course of action for each prisoner?

The answer to this question depends on the preferences of the prisoners.

If the prisoners are risk-averse, then they should not confess because there is a chance that they will get a 10-year sentence if the other prisoner confesses.

If the prisoners are risk-neutral, then they should confess because the expected sentence is five years if they both confess.

If the prisoners are risk-seeking, then they should confess because there is a chance that they will go free if the other prisoner does not confess.

How Does Game Theory Relate to Cryptocurrencies?

The game theory model that is most relevant to cryptocurrencies is the Prisoner’s Dilemma.

The reason why the Prisoner’s Dilemma is relevant to cryptocurrencies is because of the way that Bitcoin and other cryptocurrencies are created.

Bitcoins are created through a process called mining. Mining is a process where people use their computers to solve complex mathematical problems.

When a problem is solved, a new Bitcoin is created.

The people who solve the problems are called miners.

Mining Competition

Mining is a competition. The first miner to solve the problem gets the new Bitcoin. The incentive to mine is that the more Bitcoins you have, the more valuable they are.

The problem with mining is that it requires a lot of energy and money to run the computers that do the mining.

As more people start mining, the problems become harder and harder to solve, and the amount of energy and money required to mine new Bitcoins increases.

This creates a dilemma for miners.

Payoff Metrix

There is a certain amount of risk losing involved in mining.

The payoff matrix for mining is as follows:

If a miner does not mine, then they will not get any Bitcoins.
If a miner mines and nobody else solves the problem first, then the miner will get the new Bitcoin.
If the miner mines and somebody else solve the problem first, then the miner will not get the new Bitcoin.

To avoid double spending, miners need to be sure that they are the first to solve the problem. This requires them to invest in expensive computers and pay for a lot of electricity.

The game theory tells the analysis of this situation shows that miners should mine because it is in their best interest to do so according to their strategic decision-making skills. However, if all miners mine, then they will all end up with a worse outcome than if nobody mined.

Conclusion

Game theory is a powerful tool that can be used to analyze a wide variety of situations. In the business world, game theory is often used to analyze competition between businesses. In the world of cryptocurrencies, game theory can be used to understand the incentives of miners and how they affect the overall supply of Bitcoin.