An upper bound for the $$\ell _1$$ ℓ 1 -variation along the road to agreement

Dimitry Shaiderman ()
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Dimitry Shaiderman: Tel Aviv University

International Journal of Game Theory, 2021, vol. 50, issue 4, No 13, 1053-1067

Abstract: Abstract Two agents with a common prior on the possible states of the world participate in a process of information transmission, consisting of sharing posterior probabilities of an event of interest. Aumann’s Agreement Theorem implies that such a process must end with both agents having the same posterior probability. We show that the $$\ell _1$$ ℓ 1 -variation of the sequence of posteriors of each agent, obtained along this process, must be finite, and provide an upper bound for its value.

Keywords: Aumann’s Agreement Theorem; Bayesian dialogues; $$\ell _1$$ ℓ 1 -Variation; Martingales with discrete parameter; Primary 91A26; Secondary 60G42 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00182-021-00781-1

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