NashType
plain-language theorem explainer
An inductive type enumerating five Nash equilibrium refinements is introduced here, each successive refinement ruling out additional non-credible strategies to match configDim equal to 5. Game theorists formalizing equilibrium selection in the Recognition Science economics layer would reference this enumeration. The definition proceeds by direct inductive construction followed by automatic derivation of finite type and equality structures.
Claim. Let $N$ be the inductive type generated by five constructors: pure-strategy Nash equilibrium, mixed-strategy Nash equilibrium, subgame-perfect equilibrium, trembling-hand perfect equilibrium, and proper equilibrium.
background
The module introduces five canonical Nash-equilibrium refinements set equal to configDim $D=5$: pure-strategy Nash, mixed-strategy Nash, subgame perfect, trembling-hand perfect, and proper equilibrium. Each refinement strengthens the previous by ruling out more non-credible strategies, per the module documentation. The declaration depends on no prior results.
proof idea
Direct inductive definition that lists the five constructors, with the deriving clause supplying DecidableEq, Repr, BEq, and Fintype automatically.
why it matters
This type supplies the five elements whose cardinality is asserted by the downstream NashEquilibriumCert structure and proved by the nashType_count theorem. It realizes the configDim = 5 requirement inside the economics module, connecting game-theoretic refinements to the Recognition Science framework. No open questions are addressed.
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