The Nash Equilibrium + Blockchain Technology
The Nash Equilibrium
In 1950, an American mathematician named John Forbes Nash, Jr wrote and published a paper titled “Equilibrium points in N-person games” introducing a concept known as the Nash equilibrium. Nash was a pioneer in the study of differential geometry and partial differential equations. He won the 1994 Nobel Prize in Economics, along with two others, for his development in the mathematical foundations of game theory.
Nash equilibrium, or game theory, is concerned with situations where decisions interact. Take an intersection, for example. A car is approaching the intersection. It stops when it comes to the red light and proceeds through the intersection when the light is green. When approaching a red light, the car stops because the other vehicles will be moving through the intersection because their light is green. It is a Nash equilibrium when all the drivers behave this way.
Nash equilibrium also allows for the possibility that decision-makers follow randomized strategies. Allowing for randomization is vital for the mathematics of game theory because it guarantees that every (finite) game has a Nash Equilibrium. Randomization is also important in games such as Two-up, Rock-Paper-Scissors, poker, and tennis. Today, game theory is essential training for economists and has substantially impacted computer science, political science, sociology, and biology. *1
Game Theory and Blockchains
When people hear the word ‘blockchain,’ they think of bitcoin, decentralization, and security. Cryptocurrencies have managed to prosper despite the many attempts that have been made to disrupt their network. Game Theory is partly to credit for this. *2
Cryptocurrencies and Peer-to-Peer Networks
Crypto mining involves the process where all nodes in the network compete to find the next block, which is found by either Proof-of-Work or Proof-of-Stake mechanisms. All the miners in every cryptocurrency network help in the mining in return for that network’s cryptocurrencies, making it profitable for them. If the miner tries to mine the incorrect block by attempting to fool the network, game theory comes into play to prevent this.
Two players participate in any cryptocurrency’s existence: users and miners. Miners are responsible for validating the transactions and mining blocks, and users send and receive cryptocurrency.
Cheating and its Consequences
Miners in any network can cheat by accepting an invalid transaction to earn crypto and then continue adding more invalid blocks. Double spending is one of the most popular cheating methods. It breaks people’s faith in the network, which leads to the network’s destruction and the loss of the value of the cryptocurrency. However, this isn’t what people see happening, and it’s not because people don’t want to cheat the system it’s because the punishment is costlier than the reward for cheating.
Prisoner’s Dilemma
The police caught two criminals today. It’s brought to their attention that the two criminals have also been involved in a second crime much more severe than the one they just committed. The police interrogate them to uncover as much information about the other crime as
possible.
They are put in solitary confinement to keep the two criminals from communicating with each other. The police don’t have enough evidence of the other crime to charge them each with, and they only have enough evidence to charge the two criminals with the lesser offense. Each criminal has the opportunity to betray the other criminal by testifying against them or by staying silent and cooperating.
If 1 and 2 betray each other, they both serve two years in prison. If 1 betrays and 2 cooperates, 1 will be set free and 2 will serve three years in prison. If 2 betrays and 1 remains silent then 1 will serve three years in prison, and 2 will be set free. If both stay silent and cooperate with the police, they serve time for the lesser crime they committed.
Despite having a better strategy profile available, the players choose to betray each other as that is the best response for both players. Betrayal is the dominant strategy for both criminals.
Nash Equilibrium in Cryptocurrency Networks
In a prisoner’s dilemma game, each player selects the strategy that tries to maximize their payoffs without consideration for what the other player chooses. Mining can be considered a repeated prisoner’s dilemma game. Each node in the network functions in a way that maximizes its payoffs in the long run and improves the network’s security.
Each node in the network knows that cheating/validating illegitimate transactions will only lead them to spend a lot of computational resources mining the block and then getting ousted by the network. It’s a disincentive to the miners who plan on cheating. The Proof-of-Work mechanism causes mining to be very costly. Mining in the Proof-of-Stake mechanism also revolves around the game theory. Miners stake cryptocurrencies in a smart contract before mining begins. If the node cheats or commits wrongdoings, it results in cryptocurrencies being deducted from the staked amount. Crypto deducted from the staked amount results in a lower probability of validating transactions and earning rewards reduction. If the staked amount falls below the minimum requirement stated in the smart contract, the node(s) cannot stake at all.
As mentioned earlier, all nodes compete to get the crypto and earn higher rewards. Cheating undermines the entire community by reducing people’s faith in the crypto, which ultimately reduces and eliminates its value. Cheating is the antithesis of crypto for crypto users.
