Game Theory and Blockchain

Game theory explores how rational people make strategic decisions in different scenarios. Although often conflated with general logic, game theory is based in purely mathematical terms and has applications in any domain where people must coordinate or compete with each other.

Given blockchain mechanics of network interdependence, it should be no surprise that game theoretical thinking is critical for designing cryptocurrencies via its influence on cryptoeconomics.

The goal of game theory for cryptocurrency is to model human reasoning to build networks that need no oversight yet have positive outcomes for the greater good. Unfortunately, planning for unpredictable human decisions first requires that we understand what motivates people, which is easier said than done.

Game theory and cryptoeconomics

Game theory comes into the cryptoeconomic picture on the economic side, by incentivizing rational actors to behave a certain way.

Cryptoeconomics is the combination of cryptography (securely communicating with people) and designing economic incentives in order to build systems that have certain desired characteristics. This newly popularized discipline provides the tools to build strong, safe, peer-to-peer networks.

Thus, cryptography is used to prove past events — such as the authenticity of messages, while economic incentives are used to encourage desired future behavior. With backward looking security mechanisms, and forward looking incentivization, cryptoeconomics allows us to build robust decentralized protocols, opening up new ways to organize and govern ourselves.

Bitcoin: Best behaviour

Bitcoin, for example, incentivizes miners to use their computing power to secure the network by rewarding them with bitcoins — an economic incentive. Consensus among the nodes is reached by Proof-of-Work (PoW), which reflects the real, quantifiable resources it took to get there.

The creators of cryptocurrencies like Bitcoin have to ensure that when they allow the entire world onto their blockchains, people behave and follow protocol rules. As such, protocol creators design games to reward or punish participating nodes depending on their behaviour.

Bitcoin’s genius lies in intentionally making mining difficult and inefficient, thus making it costly for malicious actors. In this way, the network works to ensure that nodes don’t deviate from protocol, lest they incur steep costs in the process and ultimately fail to receive block rewards.

This game theoretical thinking of promoting good behaviour and deter bad exists in daily life, as we’ve built societies to reward work we value and deter behaviour we don’t. It may cost society money to pay police officers, judges, etc., but the system is designed to cost criminals more.

Ethereum: Just add punishment

Ethereum takes it a step further and not only rewards good behaviour, but punishes bad through it’s new proof system. As opposed to PoW, consensus is secured through Proof-of-Stake (PoS), which, as the name hints, requires some skin in the game so that they can punish bad actors.

You can see how PoS affects game design differently than PoW by examining real world behaviour. It’s likely most of us don’t rob banks because we fear going to jail, not because it may preclude us from our bonus at work.

Combining punishments with rewards strengthens the protocol security features. The strength of these features is represented by the cryptoeconomic security margin, which states the cost (in tokens or fiat currency) that is required to thwart the network.

In cryptoeconomics, you can indeed do bad stuff, you just have to pay for it.

Security model assumptions

All games must make certain assumptions about the players and the playing field. In game theory, we rely on assuming a model of human interaction and of each player’s utility function (what they value).

The choice of model is fundamentally a question on participants being coordinated or uncoordinated. The model seeks to understand if people make individual choices, or if they will instead coordinate and work together? In daily life there are clearly cases where both exist, and this holds true in cryptoeconomics.

In a coordinated model, Bitcoin, for example, can be subject to a takeover attack by a coalition of malicious miners. However, a defense mechanism rests partly upon a game theory principle called a Grim Trigger equilibrium, which suggests in this case that if miners were successful in ‘defeating’ the honest nodes, a new swarm of attackers will soon follow, and there will be an endless cycle of attackers, jeopardizing Bitcoin itself, and hurting everybody.

Importantly, the desire for nodes to coordinate doesn’t necessarily mean they are capable to do so. With a handful of players, it can be easy to coordinate your peers; however, with millions of participants, coordination becomes much more difficult.

Coordination can, of course, be used to incentivize good behaviour. An example would be increasing payments to miners as network quality increases — as measured by decentralization. Currently, however, the reward stays the same if the mining pool gets more concentrated, which is not necessarily a desirable property.

Utility assumptions

Some models don’t rely on economics for security, but rather may assume that a majority of participants on the network are honest. In this regard, as long as honest nodes control the most CPU power on the network, they can generate the longest chain and outpace any attackers.

Although considered naive by some, this leads to an important point of what actually motivates people from the start. In economics and game theory, we call this a utility function: how much use, or value, someone receives from a given outcome. Usually we assume some basic factors, such as people liking money, and preferring more to less.

In practice, though, it’s not as easy to specify different players’ utilities, and this becomes one of the most difficult challenges in designing games. For this reason, sometimes we perceive others as acting irrationally when they might just have a different utility function than we expected.

In the end, many protocols and security questions still rest on human judgement calls. Nonetheless, cryptoeconomics and game theory have accomplished the impressive task of modeling human decision making to build systems that align participant goals with socially desirable outcomes for the network.

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