# Nash Equilibrium **Domain:** Game Theory / Economics / Governance **Doc Type:** Canonical Theory Node **Maturity:** Foundational ## Definition A **Nash equilibrium** is a strategy profile in which no participant can improve its own payoff by changing strategy unilaterally while the other participants' strategies remain fixed. For finite games, an equilibrium exists when mixed strategies are allowed. Existence does not imply uniqueness, fairness, efficiency, cooperation, resilience or moral legitimacy. ## Governance Context [[articles/John Nash's Unparalleled Legacy in Societal Transformation|John Nash's Unparalleled Legacy]] extends game-theoretic language into climate negotiation, reparative systems and AI-mediated coordination. [[articles/The Algorithmic State and Nash Equilibrium of Planetary Governance|The Algorithmic State]] adds the necessary warning: deployed models usually optimize local objectives under institutional constraints rather than discovering one impartial planetary optimum. A harmful arrangement may be stable because every actor is trapped by the expected actions of others. A fairer arrangement may require changing incentives, information, enforcement, bargaining power or available strategies. [[wiki/Equilibrium Engineering|Equilibrium Engineering]] names that institutional task. ## AI Boundary AI can search strategy spaces, simulate responses and identify candidate equilibria. It does not become morally neutral by performing those calculations. The payoff structure, represented actors, omitted harms and admissible actions are prior political and ethical choices. ## Key Insight **Nash equilibrium explains resistance to unilateral change; it does not tell civilization which stable world it ought to inhabit.** ## See Also [[wiki/Game Theory|Game Theory]], [[wiki/Non-Cooperative Games|Non-Cooperative Games]], [[wiki/John Nash|John Nash]], [[wiki/Objective Function|Objective Function]], [[wiki/Reparative Justice|Reparative Justice]]