Rationalizable Outcome Distributions: A Markov Characterization

Rationalizable Outcome Distributions: A Markov Characterization — SSRN preprint, 2022
Authors

Olivier Gossner

Rafael Veiel

Abstract

We study (interim correlated) rationalizability in a game with incomplete information. We characterize the recursive set of possible rationalizable hierarchies through a finite automaton, and provide a revelation principle that characterizes the distributions over these hierarchies that arise from any common prior. We show that a simple and finitely parametrized class of information structures, Stationary Common Automaton Markov Priors (SCAMP), is sufficient to generate every outcome distribution induced by general common prior information structures. Using this result, we characterize the set of rationalizable distributions as a convex polyhedron.

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SSRN preprint, 2022

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BibTeX citation:
@report{gossner2022,
  author = {Gossner, Olivier and Veiel, Rafael},
  title = {Rationalizable {Outcome} {Distributions:} {A} {Markov}
    {Characterization}},
  date = {2022},
  url = {https://gossner.me/papers/rationalizable-outcome-distributions-a-markov-characterization.html},
  langid = {en},
  abstract = {We study (interim correlated) rationalizability in a game
    with incomplete information. We characterize the recursive set of
    possible rationalizable hierarchies through a finite automaton, and
    provide a revelation principle that characterizes the distributions
    over these hierarchies that arise from any common prior. We show
    that a simple and finitely parametrized class of information
    structures, Stationary Common Automaton Markov Priors (SCAMP), is
    sufficient to generate every outcome distribution induced by general
    common prior information structures. Using this result, we
    characterize the set of rationalizable distributions as a convex
    polyhedron.}
}
For attribution, please cite this work as:
Gossner, Olivier, and Rafael Veiel. 2022. “Rationalizable Outcome Distributions: A Markov Characterization.” In SSRN Preprint. https://gossner.me/papers/rationalizable-outcome-distributions-a-markov-characterization.html.