Strategic information transmission with sender’s approval: the single crossing case

Stéphan Sémirat () and Françoise Forges ()
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Stéphan Sémirat: GAEL - Laboratoire d'Economie Appliquée de Grenoble - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement - UGA - Université Grenoble Alpes - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - UGA - Université Grenoble Alpes
Françoise Forges: CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique

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Abstract: We consider a sender-receiver game, in which the sender has finitely many types and the receiver's decision is a real number. We assume that utility functions are concave, single-peaked and single-crossing. After the cheap talk phase, the receiver makes a decision, which requires the sender's approval to be implemented. Otherwise, the sender "exits". At a perfect Bayesian equilibrium without exit, the receiver must maximize his expected utility subject to the participation constraints of all positive probability types. This necessary condition may not hold at the receiver's prior belief, so that a non-revealing equilibrium may fail to exist. Similarly, a fully revealing equilibrium may not exist either due to the sender's incentive compatibility conditions.We propose a constructive algorithm that always achieves a perfect Bayesian equilibrium without exit.

Keywords: Participation constraints; Discrete Cheap talk; Single-crossing (search for similar items in EconPapers)
Date: 2022-07
New Economics Papers: this item is included in nep-gth, nep-mic and nep-upt
Note: View the original document on HAL open archive server: https://hal.science/hal-03231673v3
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Published in Games and Economic Behavior, 2022, 134, pp.242-263. ⟨10.1016/j.geb.2022.05.004⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03231673

DOI: 10.1016/j.geb.2022.05.004

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