Direct Representations for Interim Correlated Rationalizability
We study direct representations of information for interim correlated rationalizability. For a fixed finite payoff structure, each type induces a hierarchy of surviving action sets. Pushing the common prior through this map projects the information structure onto the solution concept’s output language. When best-response regions are convex, this representation is direct: the solution concept applied to the hierarchy seen as a type is the identity. The induced distributions are characterized by level-by-level obedience constraints. Terminal ICR sets alone do not have this property. For arbitrary finite payoff structures, we refine each hierarchy level with a tag identifying a convex cell of its best-response region. Augmented hierarchies provide a direct representation and project onto the ordinary hierarchy. Full augmented hierarchies may form a continuum, but retaining only the tags at the boundaries of constant stretches of the ordinary hierarchy yields an exact countable representation with finitely many obedience constraints per type. Finite-type models are dense in terminal rationalizability outcome distributions.
arXiv:2607.21851, 2026
Citation
@report{gossner2026,
author = {Gossner, Olivier and Veiel, Rafael},
publisher = {arXiv},
title = {Direct {Representations} for {Interim} {Correlated}
{Rationalizability}},
number = {2607.21851},
date = {2026},
url = {https://arxiv.org/abs/2607.21851},
doi = {10.48550/arXiv.2607.21851},
langid = {en},
abstract = {We study direct representations of information for interim
correlated rationalizability. For a fixed finite payoff structure,
each type induces a hierarchy of surviving action sets. Pushing the
common prior through this map projects the information structure
onto the solution concept’s output language. When best-response
regions are convex, this representation is direct: the solution
concept applied to the hierarchy seen as a type is the identity. The
induced distributions are characterized by level-by-level obedience
constraints. Terminal ICR sets alone do not have this property. For
arbitrary finite payoff structures, we refine each hierarchy level
with a tag identifying a convex cell of its best-response region.
Augmented hierarchies provide a direct representation and project
onto the ordinary hierarchy. Full augmented hierarchies may form a
continuum, but retaining only the tags at the boundaries of constant
stretches of the ordinary hierarchy yields an exact countable
representation with finitely many obedience constraints per type.
Finite-type models are dense in terminal rationalizability outcome
distributions.}
}