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After a thorough look in the literature of information design like Bergemann and Morris and Kamenica and Gentzkow I am still not so sure how the utility gain or payoff of the information provider/designer (namely the sender) is modelled.

Although we have two different settings and in the Bergemann and Morris framework the payoff of the information provider is not modelled at all (only the decision rule), in Kamenica and Gentzkow the payoffs are of the following formulation

$v(a,\omega) = - (a-\omega)^2,\quad\nu(a,\omega)=a$

the first payoff function, which is continuous, stands for the utility function of the receiver and depends on her action $a\in A$ and the state of the world $\omega\in\Omega$. The second payoff function (which is also continuous), stands for the utility of the sender that depends on receiver’s action and the state of the world.

  1. My (first) question is, that since we have a game where the information provider takes part, she should receive a payoff as well, but it is not so clear to me how to model her payoff?

  2. What happens in case where we have more than one information providers?

  3. Could we introduce somehow the risk aversion parameter in this Receiver - Sender setting so as each one of them could be risk averse because neither the receiver can always be sure that the sender plays a truthful strategy nor the sender is certain about the fact that the receiver will take into account the information that she provides because she may not trust her that she tells the truth.

How to model the the payoff (or utility function) of the information provider? Could someone use the mean variance utility preferences $(u(X)=\mathbb{E}(X)-(\delta/2)\times\mathbb{V}ar(X))$

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    $\begingroup$ Kamenica & Gentzkow allow the sender's payoff function to be any jointly continuous function of the state and the receiver's action. And the sender is not a player in any game here. $\endgroup$ Jan 27, 2023 at 22:08
  • $\begingroup$ @MichaelGreinecker exactly! Is it not done because it is meaningless or because it is a difficult problem to solve? Could someone model the sender as a player in the game and hence her payoff how would differ? $\endgroup$ Jan 27, 2023 at 22:24
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    $\begingroup$ There are papers where the sender is a player, such as in the cheap-talk literature. You can, of course, change all that, but that is not an easy answer but a couple of papers. See for example this $\endgroup$ Jan 27, 2023 at 22:28
  • $\begingroup$ I didn't know the paper Michael. Thanks. So I will check it and check for competition in Bayesian Persuasion $\endgroup$ Jan 27, 2023 at 22:31

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