We study the guessing variants of two distributed source coding problems: the Gray-Wyner network and the Slepian-Wolf network. Building on the former, we propose a new definition of the Rényi common information as the least attainable common rate in the Gray-Wyner guessing problem under the no-excess-rate constraint. We then provide a variational characterization of this quantity. In the Slepian-Wolf setting, we follow up the work of Bracher-Lapidoth-Pfister with the case where the expected number of guesses need not converge to one but must be dominated by some given exponential.
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