Abstract
Godfrey-Smith advocates for linking deception in sender-receiver games to the existence of undermining signals. I present games in which deceptive signals can be arbitrarily frequent, without this undermining information transfer between sender and receiver.
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Notes
There is another option (suggested to me by an anonymous reviewer): denying that M 1—which, as we have seen, has a tautologous propositional content—has meaning at all. It would be, perhaps, rather a non-message. This is, I think, a good illustration of the way in which Skyrms' informational contents are more explanatory than propositional contents, at least in the context of these games: if M 1 was just a non-message one would expect the receiver to respond to it by producing A 3 alone; after all, non-messages, presumably, are communicatively inert, and A 3 is the best response to the mix of two-thirds of S 1 and one third of S 2 that the unconditional probabilities of these states produce. In fact, the receiver responds by mixing four fifths of A 1 and one fifth of A 3 —that is, by correctly adapting its response to the information that M 1 carries about world states. This provides evidence that M 1 is meaningful.
Both here and in the game discussed in Sect. 6 the receiver resorts to partial pooling. This could be taken to imply that the receiver's responsiveness to the sender is decreasing: in the receiver's final response, A 2 carries less information about the message sent by the sender than it did in the original Nash equilibrium. On the other hand, A 3 carries more information about the message sent by the sender than it did in the Nash equilibrium: the receiver, one might say, is increasing its responsiveness to the faithful messages that the sender is still sending.
This conclusion, as I have said, is based on data gathered randomly from the space of all cheap-talk 3 × 3 × 3 games. It remains an open question whether restricting the data-gathering to biologically salient regions of this space (i.e., regions in which games can be used to model actual sender–receiver interactions in nature) would show deceptive, not non-maintaining messages to be less (or more, or equally) prevalent.
There are at least two other respects in which this numerical exploration should be supplemented by further work: first, although casual inspection does not reveal salient common features among the 251 games in the sample that have deceptive, not non-maintaining signals, it is possible (perhaps likely) that more systematic exploration might uncover such similarities in the payoff structure of these games. Second, in this paper I am using Nash equilibria as the target equilibrium concept. This should be complemented with a study of how accessible to evolution, and how dynamically stable, those equilibria are.
Although this is not pooling in the strict sense, I will grant that this response counts as pooling for the purposes of the definition of non-maintaining message: the game does not allow for a pooling, always-buy strategy, and this is as close as the receiver can get to such a strategy.
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Acknowledgments
I would like to thank Peter Godfrey-Smith and two anonymous reviewers for their helpful comments to earlier drafts. Research for this paper was supported by the Spanish government via research grants MCINN FFI2011-26853 and CSD2009-0056 (CONSOLIDER INGENIO).
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Martínez, M. Deception in Sender–Receiver Games. Erkenn 80, 215–227 (2015). https://doi.org/10.1007/s10670-014-9623-z
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DOI: https://doi.org/10.1007/s10670-014-9623-z