{"query": "Nash equilibrium — a fixed point", "count": 20, "results": [{"id": "card_game_nash", "title": "Nash equilibrium — a fixed point", "shelf": "codex", "surface": "secular", "snippet": "A profile where no player gains by deviating alone - a fixed point of best-response, which Nash proved always exists in mixed strategies (by Brouwer). Finding it is the solve path's converge step. Res", "authority_tier": "engine_derived", "source": "Narrow Highway — game theory", "readable": false, "generated": false}, {"id": "card_theory_game_theory", "title": "Game theory (Nash equilibrium)", "shelf": "theories", "surface": "secular", "snippet": "Game theory (Nash equilibrium) — an engine domain that can touch it: operations_research. Calibration: seals — equilibria of finite games compute. A situation where no player can do better by unilater", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_fixed_point_theorems__brouwer__kakutani", "title": "Fixed-point theorems (Brouwer, Kakutani)", "shelf": "theories", "surface": "secular", "snippet": "Fixed-point theorems (Brouwer, Kakutani) — an engine domain that can touch it: mathematics. Calibration: map-only — an existence proof, not a computation. Brouwer: any continuous map of a convex compa", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_chemical_kinetics_equilibrium", "title": "Chemical kinetics & equilibrium (Arrhenius, Le Chatelier)", "shelf": "theories", "surface": "secular", "snippet": "Chemical kinetics & equilibrium (Arrhenius, Le Chatelier) — an engine domain that can touch it: chemistry. Calibration: partial — rate constants and equilibrium shifts compute. KINETICS asks how fast,", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_haber_bosch", "title": "Haber–Bosch nitrogen fixation (bread from air)", "shelf": "theories", "surface": "secular", "snippet": "Haber–Bosch nitrogen fixation (bread from air) — an engine domain that can touch it: chemistry. Calibration: seals — stoichiometry, yield and equilibrium shifts compute. N₂ + 3H₂ ⇌ 2NH₃, run at roughl", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_supply_demand_market_equilibrium", "title": "Supply & demand / market equilibrium", "shelf": "theories", "surface": "secular", "snippet": "Supply & demand / market equilibrium — an engine domain that can touch it: economics. Calibration: seals — equilibrium points and elasticities compute. Price settles where the quantity people will buy", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_topology", "title": "Topology (what survives stretching)", "shelf": "theories", "surface": "secular", "snippet": "Topology (what survives stretching) — an engine domain that can touch it: mathematics. Calibration: map-only — specific invariants compute; the classification results are proofs, not computations. Geo", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_hardy_weinberg_equilibrium", "title": "Hardy–Weinberg equilibrium", "shelf": "theories", "surface": "secular", "snippet": "Hardy–Weinberg equilibrium — an engine domain that can touch it: genetics. Calibration: seals — allele and genotype frequencies compute exactly. In a large, randomly mating population with no selectio", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_symbiosis", "title": "Symbiosis & endosymbiosis (cooperation as a major transition)", "shelf": "theories", "surface": "secular", "snippet": "Symbiosis & endosymbiosis (cooperation as a major transition) — an engine domain that can touch it: biology. Calibration: map-only — historical and empirical. Different species living together, from m", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_evolutionary_game_theory__evolutionarily_stable_stra", "title": "Evolutionary game theory (evolutionarily stable strategies)", "shelf": "theories", "surface": "secular", "snippet": "Evolutionary game theory (evolutionarily stable strategies) — an engine domain that can touch it: biology. Calibration: map-only — stability conditions compute; the biology is empirical. Maynard Smith", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_biochemistry_enzymes", "title": "Biochemistry & enzymes (catalysis at body temperature)", "shelf": "theories", "surface": "secular", "snippet": "Biochemistry & enzymes (catalysis at body temperature) — an engine domain that can touch it: biology. Calibration: seals — reaction rates, Michaelis–Menten kinetics and energy budgets compute. An enzy", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_labor_economics", "title": "Labor economics (minimum wage, overtime law)", "shelf": "theories", "surface": "secular", "snippet": "Labor economics (minimum wage, overtime law) — an engine domain that can touch it: labor. Calibration: seals — wage, hour and overtime calculations compute exactly. Labour is bought and sold, but not ", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_mechanism_design___auction_theory", "title": "Mechanism design & auction theory", "shelf": "theories", "surface": "secular", "snippet": "Mechanism design & auction theory — an engine domain that can touch it: economics. Calibration: partial — auction outcomes and incentive conditions compute. Game theory run BACKWARDS: instead of askin", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_floor_game_theory", "title": "Game theory — equilibrium, dilemmas, and strategy", "shelf": "codex", "surface": "secular", "snippet": "The mathematics of strategic choice. A Nash equilibrium is a fixed point where no one gains by deviating alone; the prisoner's dilemma shows rational players reaching a worse outcome than cooperation;", "authority_tier": "engine_derived", "source": "Narrow Highway — game theory", "readable": false, "generated": false}, {"id": "card_floor_physical_chemistry", "title": "Physical chemistry — rate, equilibrium, acid-base, redox", "shelf": "codex", "surface": "secular", "snippet": "Deeper in chemistry: the laws that make it predictive. Kinetics (how fast), equilibrium (the balance point, Delta G = -RT ln K), acid-base (pKa + pKb = 14), and electrochemistry (the cell potential). ", "authority_tier": "engine_derived", "source": "Narrow Highway — physical chemistry", "readable": false, "generated": false}, {"id": "card_bridge_theory_supply_demand_market_equilibrium__chemical_kinetics_equilibrium", "title": "Bridge: Supply & demand / market equilibrium  ↔  Chemical kinetics & equilibrium (Arrhenius, Le Chatelier)", "shelf": "bridges", "surface": "secular", "snippet": "Supply & demand / market equilibrium and Chemical kinetics & equilibrium (Arrhenius, Le Chatelier) are the same form in different domains. Le Chatelier's principle and market response are one form: pe", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_bridge_theory_quantum_mechanics__game_theory", "title": "Bridge: Quantum mechanics (Schrödinger equation)  ↔  Game theory (Nash equilibrium)", "shelf": "bridges", "surface": "secular", "snippet": "Quantum mechanics (Schrödinger equation) and Game theory (Nash equilibrium) are the same form in different domains. a MIXED STRATEGY and a QUANTUM MIXED STATE are the same object: a probability distri", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_bridge_theory_game_theory__linear_programming_duality", "title": "Bridge: Game theory (Nash equilibrium)  ↔  Linear programming & duality", "shelf": "bridges", "surface": "secular", "snippet": "Game theory (Nash equilibrium) and Linear programming & duality are the same form in different domains. von Neumann's minimax theorem for zero-sum games and LP strong duality are equivalent -- each is", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_bridge_theory_coase_theorem__supply_demand_market_equilibrium", "title": "Bridge: The Coase theorem (law & economics)  ↔  Supply & demand / market equilibrium", "shelf": "bridges", "surface": "secular", "snippet": "The Coase theorem (law & economics) and Supply & demand / market equilibrium are the same form in different domains. bargaining drives allocation to the efficient market outcome — law meeting economic", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_bridge_theory_pharmacokinetics__chemical_kinetics_equilibrium", "title": "Bridge: Pharmacokinetics (dosing, clearance, half-life)  ↔  Chemical kinetics & equilibrium (Arrhenius, Le Chatelier)", "shelf": "bridges", "surface": "secular", "snippet": "Pharmacokinetics (dosing, clearance, half-life) and Chemical kinetics & equilibrium (Arrhenius, Le Chatelier) are the same form in different domains. first-order clearance and chemical first-order dec", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}], "house": {"door": "FIND", "kind": "cards", "trail": "results", "seal": null, "next_step": {"do": "open the top card", "door": "FIND", "tool": "card_get", "params": {"id": "card_game_nash"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}