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How to replace public communication with private one

Author

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  • Āzacis, Helmuts
  • Vida, Péter

Abstract

A sender wants to make a public announcement to three receivers but she cannot. The Byzantine agreement communication protocol (Lamport et al., 1982) prescribes that the sender instead sends the same private message to the receivers who in turn forward to each other the message they have received from the sender. Let the receivers consider the (bitwise) majority of their received messages as a pseudo public message of the sender. We show that this protocol, besides being 1-resilient, substitutes public communication in a very strong sense: every player can consistently believe (Kreps and Wilson, 1982), no matter what messages they have sent or received, that all the receivers hold the same pseudo public message which coincides with the (bitwise) majority of the messages sent by the sender. It follows that the set of sequential equilibrium outcomes of any game (with at least four players) is weakly larger with private communication than with public communication.

Suggested Citation

  • Āzacis, Helmuts & Vida, Péter, 2026. "How to replace public communication with private one," Games and Economic Behavior, Elsevier, vol. 159(C), pages 483-491.
    • Handle: RePEc:eee:gamebe:v:159:y:2026:i:c:p:483-491
    DOI: 10.1016/j.geb.2026.07.008
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    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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