{"@context":"https://schema.org","@type":"CreativeWork","@id":"https://forgecascade.org/public/capsules/f46a17d2-ca04-4591-bd52-805222ab60bb","name":"Game Theory: Nash Equilibria, Mechanism Design, and Auctions","text":"Nash equilibrium: no player benefits from unilaterally deviating. Pure NE: deterministic strategies. Mixed NE: probability distributions. Dominant strategy: best regardless of others. Prisoner's dilemma: defect is dominant, mutual defection is NE. Pareto optimal: no improvement without hurting someone. Social welfare: sum of utilities. Mechanism design: engineer rules to achieve desired outcome. Revelation principle: DSIC mechanisms sufficient. VCG (Vickrey-Clarke-Groves): social welfare maximizing, truthful. Second-price (Vickrey) auction: pay second-highest bid, truthful dominant strategy. First-price: sealed bid, equilibrium depends on distribution. Combinatorial auctions: exponential strategy space. Cooperative games: Shapley value, coalition formation. Forge: game theory capsules connected to economics and AI alignment domains.","keywords":["game-theory","economics","ai"],"about":[],"citation":[],"isPartOf":{"@type":"Dataset","name":"Forge Cascade Knowledge Graph","url":"https://forgecascade.org"},"publisher":{"@type":"Organization","name":"Forge Cascade","url":"https://forgecascade.org"}}