# Beginner’s Guide to Game Theory

July 31st 2018
“Eventually, every game theory textbook will have a chapter on public blockchains.” — Naval.

Game theory is one of the most important concepts to grasp to understand blockchains/crypto, strategy, and decision making.

Game theory is the study of how and why people make decisions within a competitive situation, while keeping in mind what actions their competitors will take. You can think of it as the study of strategic decision making.

But, game theory isn’t just about games. It’s used for any situation where two people have to make decisions with rewards and consequences. The ultimate goal is find whether a “best” strategy for a given game exists.

Poker is a great example because the other players choices influences your strategy. For example, should you play tight while your opponent is playing loose? Or, should you bluff or not? Or, raise/fold?

To further understand game theory, here are some of the more important concepts:

1. Prisoner’s Dilemma — refers to a situation where two completely rational individuals might not cooperate, even if it appears that it’s in their best interests to do so. Classic choice between self-interest and mutual interest.
2. Coordination game — game in which the players benefit from working together. There’s no incentive for either party to cheat since it will result in a worse outcome than cooperating. Example: driving on the right side of the road.
3. Free Rider Problem (Tragedy of the Commons) — problem in which every individual tries to reap the greatest benefit from a given resource, which harms others who can no longer enjoy the benefits. Examples: pollution, over-fishing, and ocean garbage.
4. Zero Sum — situation in which one person or group can win something only by causing another person or group to lose it. Examples: poker and gambling
5. Principal-Agent Problem — when one person (the agent) is allowed to make decisions on behalf of another person (the principal). In this situation, the agent will not prioritize the best interest of the principal, but will instead pursue his own goals. Ex: politics
6. Nash Equilibrium — optimal outcome where no player has an incentive to deviate from his chosen strategy after considering an opponent’s choice. Ex: traffic lights
7. Grim Trigger — strategy employed in a repeated non-cooperative game where you start by cooperating and continue to cooperate as long as everyone has cooperated in the past. If someone has defected, then you defect forever.
8. Schelling Points — solution that people will tend to use in the absence of communication, because it seems natural, special, or relevant to them. Example: meeting at noon at Grand Central
9. Keynesian Beauty Contest — analogy for investing that suggests that investors may guess what other investors are going to think as opposed to what they think themselves.
10. Bounded Rationality — when given a choice, people will always follow a path that is simple and something they are used to (even if it’s not the most optimal outcome).
11. Byzantine Generals Problem — situation where parties must agree on a single strategy in order to avoid complete failure, but where some of the involved parties are corrupt and disseminating false information or are otherwise unreliable. (This problem is built around an imaginary General who makes a decision to attack or retreat, and must communicate the decision to his lieutenants. A given number of these actors are traitors & they cannot be relied upon to properly communicate orders.)

So, how does this apply to crypto? The Bitcoin blockchain was designed in a way that it is a self-enforcing Nash Equilibrium. Incentives come into play to encourage participants to maintain the protocol and avoid the Byzantine Generals Problem.

Miners are incentivized to be good actors on the network. If miners want to earn rewards, they have to abide by the rules. Otherwise, miners lose time, electricity, and processing power (costs). This is because mining has a recursive punishment system.

For example, a node controlled by a miner is free to go rogue and create an invalid block. The miner is deterred from doing this because other nodes that follow the same strategy will be punished and excluded from the system.

If a miner creates an invalid block, the other miners will simply ignore the invalid block and keep mining on the main chain. As a result, miners will choose the most stable state (Nash Equilibrium).

The system is Byzantine Fault Tolerant due to the majority of miners working in coordination to achieve and maintain the most stable state of the network at all times.

This is just one example of how game theory is incorporated into crypto but there are many others, My favorite is how white hackers “stole” \$85M to save Ethereum (incentives to cooperate).

Game theory and consensus mechanisms have successfully created incentives to coordinate people to make decisions that are in the best outcomes for the network. This is just the beginning!