nashType_count
plain-language theorem explainer
The declaration asserts that the set of Nash equilibrium types has cardinality exactly five under the configDim classification. Game theorists working on equilibrium refinements in the Recognition Science framework would cite this result to confirm the enumeration of canonical types. The proof is a one-line decision procedure that evaluates the finite cardinality from the derived Fintype instance on the inductive type.
Claim. The set of Nash equilibrium refinements has cardinality five, consisting of pure-strategy Nash equilibrium, mixed-strategy Nash equilibrium, subgame-perfect equilibrium, trembling-hand perfect equilibrium, and proper equilibrium.
background
NashType is the inductive type enumerating five refinements: purePsy for pure-strategy Nash, mixedStrategy, subgamePerfect, tremblingHandPerfect, and properEquilibrium. The module sets this enumeration equal to configDim D = 5, with each refinement strengthening the prior one by excluding additional non-credible strategies. The upstream inductive definition supplies the DecidableEq and Fintype instances required for cardinality computation.
proof idea
The proof applies the decide tactic to reduce Fintype.card NashType = 5 to a decidable equality. This succeeds immediately because the inductive definition derives DecidableEq, Repr, BEq, and Fintype, allowing the cardinality to be computed at compile time without further lemmas.
why it matters
This cardinality result supplies the five_types field in the downstream nashEquilibriumCert definition, completing the game-theoretic component of the Economics module. It directly realizes the module claim of five canonical refinements tied to configDim = 5. The supplied documentation flags no open questions or scaffolding.
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