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So far, the models of Signaling Games I have seen involve two players. One player is known as the Sender and has more information. The other player is known as the Receiver and has less information.

But suppose I have two people who each don't have information about the other. Now they start sending signals and learn about the other.

Are there models of Signaling Games that cover such dynamics where both players are senders and receivers?

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  • $\begingroup$ I'm pretty sure the answer to your question is yes. Such models do exists. I don't have an example off the top of my head, but I think I remember seeing them. I'll try to remember what they were and update if I can. I suppose the general reason you don't see more of this is you usually want to show something in the simplest possible environment, so unless the phenomenon depends critically on every agent being both a sender and a receiver, it's an unnecessary complication. $\endgroup$ – Shane Feb 18 '15 at 3:42
  • $\begingroup$ Yeah, the one I have in mind requires it. Any help would be great. $\endgroup$ – Stan Shunpike Feb 18 '15 at 4:20
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A comment on the number of players in signaling games in general.

Signaling games need not have only two players. In the cheap talk literature, there are papers that study signaling games with multiple informed senders and one uninformed receiver (e.g. Krishna & Morgan, 2001), or one informed sender with multiple uninformed receivers (e.g. Farrel and Gibbons, 1989). There are no theoretical reasons to limit the number of players to two.

Is it possible to have a signaling game in which all players are both informed (about themselves) and uniformed (about other players)?

The answer is yes. For example, auctions with pre-play communication, where each bidder is informed about their own valuations of the object but not about the others'. In the communication stage, they use signals to strategically (mis-)communicate their private information, and to infer about other bidders' types from their signals (e.g. Mathews and Postlewaite, 1988). In general, mechanism design is about signaling privately observed types. But the specific model depends on what you want to do after the signaling stage, whether signals are costly, and what kind of outcome you want the model to deliver, etc.

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If you have a game where both players are sender and receiver, then there is no asymmetric information and you do not have a signalling game, but a game with uncertainty. There are a lot of these games. E.g. bayesian games, global games etc.

These types of games can also handle situations where some players no more about the state of the game than other player. E.i. they have a higer probability of being right.

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