Forge Capsule

Game Theory: Nash Equilibria, Mechanism Design, and Auctions

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. Cooper...