# Understand the game theory behind Ethereum

**Summary**: When people invest in cryptocurrency, they often think about its inherent value and potential price movement. Another important aspect is **game theory**, which creates the incentives in well-designed blockchain networks. In this article you will learn how to see the “hidden rules” of the game.

## What is game theory?

Game theory is a branch of applied mathematics that explores human behavior in competitive or cooperative environments. It studies how people react in scenarios requiring complex decision-making: do they cooperate or compete?

Don’t let the term confuse you: game theory is more about math than Monopoly. The concept was first used in economics, but has since evolved into other disciplines, including blockchain.

Game theory models are used to predict the potential behavior of players within a system, as well as the possible outcomes of their actions. These models can be used by sociologists, psychologists and politicians, among others.

Game theory distinguishes three key elements:

**Players**: the strategic actors within an environment or a game;**Strategy**: the plan that any “rational” player would consider according to the rules of the game and the circumstances;**Pay**: the outcome or result.

Other elements are the **information** available at all times, and the so-called **balance**which is the point in a game when all players have made their decisions and a result is reached.

Although we can observe game scenarios in a wide range of human activities, cryptocurrency is one of the most interesting applications.

Since blockchain involves the interactions of nodes or block validators in a decentralized network, game theory is essential in predicting how those nodes (i.e. the people running them) will behave.

Game theory allows cryptocurrencies – like Ethereum, moving to Proof of Stake – to avoid disruption and ensure blockchain reliability.

## Nash equilibrium

In the movie *a beautiful spirit*Russell Crowe plays mathematician John Nash, who created one of the most famous game theories, now called “Nash’s equilibrium”.

As described in the video clip above, the best outcome of a game is one where there is no incentive to deviate from an initial strategy. An individual cannot derive any benefit from a change of action during play, assuming other players stick to their strategies. A game can have multiple Nash equilibria, or none at all.

In the Nash equilibrium, each player’s strategy is the best outcome given the decisions of the other players. “**The best outcome will come from everyone in the group doing what is best for themselves, and the group.”**

Nash equilibrium states that the optimal strategy for a player is to stick to the initial plan while knowing the opponent’s strategy, and that all players must maintain the same strategy. If no one changes their strategy, *even when they know the strategy of other players*then the Nash equilibrium is proved.

## The prisoner’s dilemma

Let’s take another famous example: the prisoner’s dilemma.

In this imaginary scenario, two criminals (A and B) have been arrested by the police and are being questioned separately. The prosecutor who interrogates the criminals tries to convince them to testify against each other in exchange for a reduced sentence.

Here are the rules of the “game”:

- If A testifies against B, he is released and B is arrested for
**five years**and vice versa. - If the two testify against each other, they are both arrested for
**three years**. - However, if A and B remain silent and do not betray each other, they are only doomed to
**one year**in prison, for lack of sufficient evidence.

The winning possibilities look like this:

B betrays A | B remains silent | |

A betrays B | A and B imprisoned for 3 years. | A is released. B is imprisoned for 5 years. |

To keep calm | B is released. A is imprisoned for 5 years. | A and B are imprisoned for 1 year. |

The individually best-case scenario for A (or B) is to betray and be released. However, this would force the other person to remain silent, and the lack of communication makes it impossible to predict what decision the other would make.

Faced with gain, most prisoners would probably choose to act in their own interests by betrayal.

But if the two criminals betray, they end up with three years in prison, which is not the best outcome.

Therefore, the optimal solution would be for both of them not to betray and only get one year instead of three.

Imagine you are one of the criminals. What would you do: stay silent or betray your partner?

## Game theory, crypto and incentives

Game theory models like the prisoner’s dilemma are crucial when building a decentralized economic system like a blockchain.

When designing bitcoin, Satoshi Nakamoto used a combination of cryptography and game theory to create a system that did not need to be overseen by a centralized entity. In other words, game theory ensures that all players are aligned to ensure network security.

The use of game theory in crypto led to the concept of **cryptoeconomics**which combines cryptography – which is used to prove and authenticate past events – with financial incentives, which are used to encourage future behavior that will benefit the entire network.

Cryptoeconomics is very much about game theory, as it examines the behavior of blockchain nodes based on the incentives provided by the protocol, taking into account the most rational and probable decisions.

For example, the Ethereum blockchain is designed as a decentralized public network of distributed nodes: servers storing all transaction history. Each new block added to the chain must be accepted by all nodes, even if they cannot trust each other (since anyone could create a malicious node).

So how can such a decentralized system detect and avoid bad players?

To date, Ethereum has relied on the Proof of Work (PoW) consensus algorithm, which protects the blockchain from malicious activity using cryptographic mechanisms (i.e., difficult mathematical problems) that make the demanding and costly mining process.

This incentivizes mining nodes to behave honestly, otherwise they can be banned, thus wasting valuable energy and effort. As a result, every miner makes the most rational decision to act honestly and contribute to blockchain security.

As Ethereum transitions to proof-of-stake, validators must stake a minimum of 32 ETH (about $50,000 at the time of this writing) to run a node. If a validator tries to write a bad block to the new Ethereum, instead of wasting energy and electricity, they potentially lose their staked ETH.

With PoW and PoS, **the rules of the game ensure that it is in your interest to ensure that the game goes well**.

## How Game Theory Secures Blockchains

Game theory is crucial when designing a blockchain system, given that blockchains do not have a central authority to manage transactions. Instead, users must trust miners or block validators who continually cooperate to add new blocks and be rewarded for their efforts.

Incentives – like being rewarded ETH for running an Ethereum validating node – should align all players. You stake Ethereum and you earn Ethereum, which makes you more committed to securing Ethereum’s value, in a self-reinforcing loop.

In any PoS system, however, it is possible to simply “buy out” the majority of the network in what is called a 51% attack: you would then have the “voting power” to write whatever you want in the blockchain.

At current prices, this would require around $100 billion worth of Ethereum, which is possible because the largest Ethereum wallet holds over $20 billion. But by succeeding with your 51% attack, investors would lose faith in the Ethereum network, likely creating an alternate version, and your $100 billion would be worthless.

Ethereum, once again, is saved by game theory!

## Key takeaway for investors

As John Nash realizes in the clip above, game theory shows **the best outcome is when we act both in our own interests, and in the interest of the group**.

Through a combination of game theory and cryptography, the PoW consensus algorithm prevents any malicious activity from mining nodes. The same goes for PoS blockchains, like the new Ethereum’s validator nodes.

Thanks to game theory models, everyone is encouraged to play by the rules. It’s a game where everyone wins.

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