The Inaccessible Game

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Information-Geometric Framework

The inaccessible game framework studies dynamics constrained to preserve marginal entropies.

Key Concepts:

  • Constraint manifold: States with fixed marginal entropies

  • Inaccessible region: States violating the constraint

  • Information gain: Increase in total entropy

  • Accessibility: Whether information gain is compatible with constraint

The Central Question

Given a constraint \(C(\theta) = \text{const}\) (marginal entropies fixed):

  • Which directions increase total entropy \(S(\theta)\)?

  • Which of those directions preserve the constraint?

  • What is the “inaccessible” entropy gain?

Geometric Interpretation

The dynamics follow a constrained gradient flow on the constraint manifold, using the Fisher information metric as the Riemannian structure.

See Also