Understanding Ethereum’s Game Theory

Summary: When people invest in cryptocurrency, they frequently consider its intrinsic value as well as potential price movement. Game theory, which creates incentives in well-designed blockchain networks, is another important aspect. This article will teach you how to see the game’s “hidden rules.”

What exactly is game theory?

Game theory is an applied mathematics branch that studies human behavior in competitive or cooperative settings. It looks at how people act when they have to make hard decisions: do they work together or against each other?

Don’t be misled by the name: game theory is more about mathematics than Monopoly. The idea started in economics, but it has since spread to other fields, including blockchain.

Game theory models are used to forecast players’ potential behavior in a system as well as the outcomes of their actions. Sociologists, psychologists, and politicians, among others, can use these models.

Three key elements are distinguished by game theory:

• Players: The strategic actors in a game or environment are known as players.

• Strategy: the plan that any “rational” player would consider based on the rules of the game and the circumstances.

• Payoff: the result or outcome.

Other elements are the information available at any given point and the so-called equilibrium, which is the point in a game where all players have made their decisions and an outcome is reached.

Although we can see game scenarios in a variety of human activities, cryptocurrency is one of the most intriguing.

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

Game theory helps cryptocurrencies, like Ethereum as it moves from Proof of Work to Proof of Stake, avoid problems and make sure the blockchain is reliable.

Nash’s Equilibrium

Russell Crowe plays mathematician John Nash in the film A Beautiful Mind. He developed one of the most famous game theories, now known as the “Nash equilibrium.”

The best outcome of a game, as described in the movie clip above, is where there is no incentive to deviate from an initial strategy. Individuals can gain no advantage from changing their actions during the game if the other players stick to their strategies. There may be several Nash equilibriums in a game, or none at all.

When considering the decisions of other players, each player’s strategy is the best outcome in the Nash equilibrium. “The best outcome will be achieved if everyone in the group does what is best for themselves and the group.”

According to the Nash equilibrium, the optimal strategy for a player is to stick to the initial plan while being aware of the opponent’s strategy, and that all actors should maintain the same strategy. If no one changes their strategy, even if they are aware of the other players’ strategies, the Nash equilibrium is proven.

The Dilemma of the Prisoner

Consider another well-known example: the Prisoner’s Dilemma.

In this fictitious scenario, two criminals (A and B) have been apprehended by police and are being interrogated separately. The prosecutor who is interviewing the criminals tries to persuade them to testify against each other in exchange for a reduced sentence.

The “game’s” rules are as follows:

• If A testifies against B, he is freed while B is imprisoned for five years, and vice versa.

• If they both testify against each other, they will be imprisoned for three years.

• However, due to a lack of evidence, if both A and B remain silent and do not betray each other, they are only sentenced to one year in prison.

The payoff options are as follows:

	B betrays A	B stays quiet
A betrays B	Both A & B jailed for 3 years.	A is set free. B is jailed for 5 years.
A stays quiet	B is set free. A is jailed for 5 years.	Both A & B are jailed for 1 year.

Individually, the best scenario for A (or B) is to betray and be set free. But for that to work, the other person would have to keep quiet, and if they don’t say anything, it’s impossible to know what decision they’ll make.

In the face of a payoff, most prisoners would most likely choose to betray their self-interest.

However, if both criminals betray each other, they will be sentenced to three years in prison, which is not the best outcome.

As a result, the best solution would be for both to not betray and to receive only one year rather than three.

Assume you are one of the criminals. What would you do if you had to choose between remaining silent and betraying your partner?

Incentives, Game Theory, and Crypto

Game theory models like the Prisoner’s Dilemma are very important when building a decentralized economic system like a blockchain.

Satoshi Nakamoto created bitcoin using a combination of cryptography and game theory to create a system that does not require supervision from a centralized entity. In other words, game theory ensures that all players are working together to keep the network secure.

The use of game theory in cryptography led to the idea of cryptoeconomics, which combines cryptography, which is used to prove and verify past events, with financial incentives, which are used to get people to act in ways that are good for the whole network in the future.

Cryptoeconomics is heavily influenced by game theory because it looks at how blockchain nodes act based on the incentives given by the protocol and takes into account the most likely and rational choices.

The Ethereum blockchain, for example, is designed as a public, decentralized network of distributed nodes—servers that store the entire history of transactions. Each new block added to the chain must be agreed upon by all nodes, despite the fact that they cannot trust one another (since anyone could spin up a malicious node).

So, how does a decentralized system detect and avoid bad players?

Up until now, Ethereum has used the Proof of Work (PoW) consensus algorithm. This protects the blockchain from malicious activity by using cryptographic mechanisms (like hard math problems) that make mining time-consuming and expensive.

This encourages mining nodes to be honest, as they risk being banned, wasting valuable energy and effort. As a result, every miner makes the most rational decision to act honestly and contribute to the blockchain’s security.

As Ethereum transitions to Proof of Stake, validators must stake a minimum of 32 ETH (approximately $50,000 at the time of writing) in order to run a node. If a validator attempts to write a bad block to the new Ethereum, they may lose their staked ETH instead of wasting energy and electricity. The rules of both PoW and PoS make it in your best interest to keep the game running smoothly

How Game Theory Helps to Secure Blockchains

Given that blockchains lack a central authority to handle transactions, game theory is critical when designing a blockchain system. Instead, users have to depend on miners or block validators, who work hard to add new blocks and get paid for it.

The incentives, such as receiving ETH for running an Ethereum validator node, must align all of the players. In a self-reinforcing loop, you stake Ethereum and earn Ethereum, which makes you even more committed to securing the value of Ethereum.

However, in any PoS system, it is possible to simply “buy up” the majority of the network in what is known as a 51% attack, giving you the “voting power” to write whatever you want to the blockchain.

At today’s prices, that would require approximately $100 billion in Ethereum, which is feasible given that the largest Ethereum wallet holds more than $20 billion. But if your 51% attack works, investors will lose faith in the Ethereum network and create a new version, which will make your $100 billion worthless.

Game theory saves Ethereum yet again!

The Takeaway for Investors

In the clip above, John Nash realizes that game theory shows that the best outcome happens when we act in both our own and the group’s best interests.

The PoW consensus algorithm prevents malicious activity from mining nodes by combining game theory and cryptography. The same is true for PoS blockchains, such as the new Ethereum validator nodes.

Everyone has an incentive to follow the rules thanks to game theory models. Everyone wins in this game.