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On the cardinality of the message space in sender–receiver games

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  • Heumann, Tibor

Abstract

We study sender–receiver games in which a privately informed sender sends a message to N receivers, who then take an action. The sender’s type space T has finite cardinality (i.e., |T|<∞). We show that every equilibrium payoff vector (resp. every Pareto efficient equilibrium payoff vector) is achieved by an equilibrium in which the sender sends at most |T|+N (resp. |T|+N−1) messages with positive probability. We also show that such bounds do not exist when two privately informed senders simultaneously send a message to a receiver.

Suggested Citation

  • Heumann, Tibor, 2020. "On the cardinality of the message space in sender–receiver games," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 109-118.
    • Handle: RePEc:eee:mateco:v:90:y:2020:i:c:p:109-118
    DOI: 10.1016/j.jmateco.2020.07.001
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    References listed on IDEAS

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    Cited by:

    1. Eilat, Ran & Neeman, Zvika, 2023. "Communication with endogenous deception costs," Journal of Economic Theory, Elsevier, vol. 207(C).

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