Game Theory
Game theory explores how individuals or groups make decisions when their choices affect one another. It uses mathematical models to map out possible moves, outcomes, and payoffs when parties face conflicts or need to cooperate, all under a defined set of rules. By considering every possible decision and outcome, game theory helps clarify what strategies lead to the best results for all involved.
Prisoner’s Dilemma
The classic prisoner’s dilemma illustrates how rational individuals might not work together, even when cooperation would benefit both. Imagine two suspects held separately by police. Each can either betray their partner or stay silent. If both betray, each gets two years in prison. Silence from both brings one year each. If one betrays while the other stays silent, the betrayer walks free while the silent one gets three years. Although mutual cooperation offers a better outcome, fear and self-interest often drive both to betray.
Another famous scenario is the Byzantine Generals Problem. Here, several generals must agree on the timing of their attack on a city, but unreliable communication risks spreading lies or confusion. Success depends on everyone acting together, but if even one general miscommunicates (accidentally or maliciously), the attack can fail. This problem reveals the challenges of reaching agreement across decentralized networks where trust and secure communication are hard to guarantee.
This dilemma has special significance for digital currencies like Bitcoin, which solve it with algorithms (specifically, Proof-of-Work) to enable decentralized groups to agree on a single version of truth—without trusting a central authority.
Nash Equilibrium
Sometimes, the best that participants can achieve is a balance, known as Nash equilibrium. This is a situation where no one can improve their outcome just by changing their own strategy while others keep theirs unchanged. Any improvement would require at least two people to act together. Studying Nash equilibria highlights how individual decisions, while optimal for one party, can sometimes lead to less-than-ideal results for the whole group.
Game theory is a powerful lens for understanding complex decision-making, revealing why people sometimes compete, sometimes cooperate, and how systems—from economics to cryptography—navigate conflict and consensus.