gameTypeCount
plain-language theorem explainer
Recognition Science encodes exactly five canonical game types as an inductive enumeration. Game theorists working within the RS framework cite this result when fixing the dimension of the strategy space for deriving Nash equilibria from the J-cost minimum. The proof is a decision procedure that counts the constructors of the inductive game type definition.
Claim. The finite set of canonical game types, consisting of zero-sum, cooperative, non-cooperative, symmetric, and repeated games, has cardinality five.
background
The module derives game theory from Recognition Science by equating Nash equilibrium to the vanishing of the J-cost functional, so that no unilateral deviation improves a player's outcome. The inductive definition enumerates five game types: zero-sum, cooperative, non-cooperative, symmetric, and repeated, each carrying a Fintype instance. This count is identified with configDim D = 5, providing the RS derivation of Nash's theorem.
proof idea
The proof is a one-line wrapper applying the decide tactic to the cardinality equality for the inductive game type. The tactic evaluates the finite set cardinality by enumerating the five constructors and confirms the result.
why it matters
This declaration provides the count of game types for the downstream game theory certificate, which packages the RS derivation including Nash equilibrium at J = 0 and positive J-cost off equilibrium. It completes the step in the module that five types realize configDim D = 5, thereby embedding classical game theory into the Recognition Science framework via the J-cost functional.
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