# Lies and consequences

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## Abstract

I study a strategic-communication game between an informed sender and an uninformed receiver with partially aligned preferences. The receiver is endowed with the ability to probabilistically detect if the sender is lying. Specifically, if the sender is making a false claim about her type, with some commonly known probability *p* the receiver additionally observes a private signal indicating that the sender is lying. The main result is that the receiver’s stochastic lie-detection ability makes fully revealing equilibria—the best outcome for the receiver—possible, even for small *p* (less than \(\frac{1}{2}\)). Additionally, if the language consists of precise messages, fully revealing equilibria exist only for \(p=1\) and for a set of intermediate values of *p* that is bounded away from 0 and 1, making the maximal ex-ante expected equilibrium utility of the receiver non-monotone in *p*. If vague messages are allowed, full revelation can be supported for all large enough *p*, overturning the non-monotonicity and improving communication outcomes relative to the precise-language case.

## Keywords

Cheap talk Persuasion game Lie detection## JEL Classification

D83## Notes

### Acknowledgements

I have greatly benefited from comments from the associate editor, the anonymous referees and from David Ahn, Wioletta Dziuda, Haluk Ergin, Nisvan Erkal, Joseph Farrell, Johannes Hörner, Yuichiro Kamada, Maciej Kotowski, Botond Kőszegi, Matthew Leister, Simon Loertscher, Cesar Martinelli, John Morgan, Takeshi Murooka, Omar Nayeem, Santiago Oliveros, In-Uck Park, Matthew Rabin, Roberto Raimondo, Antonio Rosato, Emilia Tjernström, Steven Williams, and participants at the 2016 APET Workshop on Democracy, Public Policy, and Information at Deakin University. Any remaining errors are my own.

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