Institutions Are Strict Extensions of the Game

Repeated interaction routinely produces structure absent from the one-shot game: reputations, norms, conventions, and other institutions. The problem is to say what this structure is, when the bare game predicts play, and where the extra structure comes from. This paper argues that the institutional content of repeated play is a strict extension of the stage game: a refinement with genuinely new predictive distinctions not definable as a function of the game's own vocabulary. The argument uses a finite, fully explicit repeated-game laboratory, with mathematical claims verified by exact finite recomputation and reproducible validators, and a pre-registered re-analysis of a published human repeated Prisoner's Dilemma dataset. The institutional state studied here has a canonical form: the coarsest predictive summary of history, equivalent to a predictive-sufficiency or causal-state construction. On the finite carrier this object is non-definable from the game itself, and the predictive failure of stage-vocabulary models is priced exactly by a conditional mutual information. The quantitative constants governing institutional collapse are reproducible within declared protocols but resist shortcut: across a declared formula class and three frozen out-of-sample transfer attempts, no tested low-complexity shortcut transfers across families. In the human data, the corresponding predictive-residue hypothesis is confirmed out of sample under a protocol registered before any data access, while a more specific pre-registered timing hypothesis fails in the reverse direction: history-dependence grows with experience. Claims are scoped to the declared finite carrier, declared run families and protocols, and analyzed dataset; broader framework theorems are imported and cited, not re-proved here.