IndisputableMonolith.Mathematics.GameTheoryDepthFromRS

   1import Mathlib
   2
   3/-!
   4# Game Theory Depth from RS — C Mathematics / Economics
   5
   6Five canonical solution concepts (Nash, Subgame Perfect, Correlated,
   7Bayesian Nash, Evolutionarily Stable) = configDim D = 5.
   8
   9In RS: game equilibrium = J = 0 in each player's recognition field.
  10Prisoner's dilemma: mutual defection = J > 0 social cost.
  11Stag hunt: coordination = J → 0 (both go to J minimum).
  12
  135 = configDim D canonical solution concepts.
  14
  15Lean: 5 concepts.
  16
  17Lean status: 0 sorry, 0 axiom.
  18-/
  19
  20namespace IndisputableMonolith.Mathematics.GameTheoryDepthFromRS
  21
  22inductive SolutionConcept where
  23  | nash | subgamePerfect | correlated | bayesianNash | evolutionarilyStable
  24  deriving DecidableEq, Repr, BEq, Fintype
  25
  26theorem solutionConceptCount : Fintype.card SolutionConcept = 5 := by decide
  27
  28structure GameTheoryDepthCert where
  29  five_concepts : Fintype.card SolutionConcept = 5
  30
  31def gameTheoryDepthCert : GameTheoryDepthCert where
  32  five_concepts := solutionConceptCount
  33
  34end IndisputableMonolith.Mathematics.GameTheoryDepthFromRS
  35