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Rationalizable Outcome Distributions: A Markov Characterization

    Olivier Gossner and Rafael Veiel
    SSRN preprint, 2022

    Abstract: We study (interim correlated) rationalizability in a game with in- complete 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 hi- erarchies 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 gen- erate every outcome distribution induced by general common prior information structures. Using this result, we characterize the set of rationalizable distributions as a convex polyhedron.