Basics of Game Theory
Game theory is a fundamental mechanism underlying blockchain technology. It is what allows cryptocurrencies such as Bitcoin to manage and divert disruptions to the network and ensure the reliability of distributed databases.
So, what is it? Broadly, game theory uses mathematics to model human paths of behaviour within an interactive and dynamic environment. Put another way, game theory is the science of strategy that maps out the best path of play for agents to achieve a desired outcome or result. According to game theory we see three core elements of any game:
- Players: The strategic actors within a game
- Strategy: A plan of action a player will take given the circumstances that will arise
- Payoff: The result or outcome a player receives after achieving a certain state. Note that payouts are not always a dollar value but can be any quantifiable form
With these parameters, we can see ‘games’ being played out across a broad range of human activities allowing game theory to be applied to military tactics, politics, economics, evolutionary biology and computer science. Before we employ a game theoretical view of cryptocurrency, we will first see how game theory can be applied in real life.
Related article: Crypto adoption for countries is a 'high stakes' game
The Prisoner’s Dilemma
The prisoner’s dilemma is the most common scenario that is used to explain game theory modelling. In this scenario, two criminals have been arrested by police for a crime they are guilty of. The prosecutors interview the criminals separately and offer each a reduced sentence in return for a confession against the other. In this example neither criminal has the means to communicate with each other.
If prisoner A betrays prisoner B, prisoner A is released scot-free and prisoner B is sentenced to 5 years. The same applies for prisoner B (vice-versa). If both A and B betray each other they each receive 3 years. Lastly, If A and B stay silent and co-operate with each other, they will each serve only 1 year. The payoff matrix for this scenario looks like this:
The prisoner’s dilemma shows that if the prisoners pursue their own self-interest the result is sub-optimal as the best option is co-operation. Yet, as the potential consequence of co-operation is so high (5 years in prison) game theory tell us that a rational actor will opt to betray. This dynamic is often played out in real world marketplaces where an understanding of the balance between competition and co-operation can yield optimal results that are mutually beneficial.
Crypto-economics combines game theory, economics and cryptography in order to understand the incentive models underlying distributed blockchain protocols. A game theoretical understanding of rational nodes interacting within a network enhances security and sustainability of distributed peer-to-peer systems.
Since blockchain is a distributed synchronised database containing validated blocks (i.e., transactions) miners must reach consensus on which block to validate. In the case of Bitcoin, the validation of each new block is done by miners solving a computationally difficult problem. This is called a Proof of Work puzzle.
Consensus algorithms such as Proof of Work rely on game theory in order to maintain trust-less co-operation. In a competitive mining environment where solving puzzles is resource intensive, game theory tells us that rational actors are incentivised to act honestly in order to not risk losing their investment.
Bad faith actors are disincentivised to cheat — i.e., accepting invalid transactions or ‘double spending’ — as the consequence would typically involve a loss of resources.
Because of this, we can view mining as a repeated prisoner’s dilemma where each node employs a strategy that aims to maximise their payout without considering the strategy of other players. Distributed networks incentivise co-operation between nodes without relying on trust between players. It is players acting in such a way to maximise their payoffs that ensures the stability and security of the network.
Further reading: Proof of work vs. proof of stake
In the Proof of Work consensus model, we see that distributed databases rely on the behavioural interactions of rational decision makers. That is, game theory enables platform security and trust-less consensus protocols.
It is worth noting that a robust and resilient blockchain is dependent on its protocol and the number of nodes using the network. The larger a distributed network grows the more resilient it is to attacks.
Game theory allows us to understand the incentivisation of consensus models and build decentralised systems that are attack resistant. By analysing strategic interactions, we can create a distributed game that: 1) incentivises players toward desired outcomes; and 2) devises a system of trust based on code rather than human mediation.
We are approaching a future in which blockchain technology and cryptocurrency shape our everyday interactions at scale. A key element in building such a future is the underlying dynamics of game theory. Game theory and crypto-economics as a field is very much in its infancy and there is still plenty of room for contribution across a range of disciplines.
Blockchain and cryptocurrency is redefining our understanding of economic incentives and the way that humans interact. With game theory as a strategic map, we will see the social function of these technologies continue to grow.
Further reading: Blockchain: a social perspective