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 $$\frac{1}{2}$$12). Additionally, if the language consists of precise messages, fully revealing equilibria exist only for $$p=1$$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.

中文翻译：

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谎言和后果

我研究了知情发送者和具有部分一致偏好的不知情接收者之间的战略沟通博弈。接收者被赋予了概率检测发送者是否在说谎的能力。具体来说，如果发送者对其类型做出虚假声明，则接收者会以一些众所周知的概率 p 额外观察到表明发送者在撒谎的私人信号。主要结果是接收者的随机测谎能力使得完全揭示均衡——接收者的最佳结果——成为可能，即使对于小 p（小于 $$\frac{1}{2}$$12）也是如此。此外，如果语言由精确的消息组成，则完全揭示均衡仅存在于 $$p=1$$p=1 和一组 p 的中间值，其边界远离 0 和 1，使接收者的最大事前预期均衡效用在 p 中非单调。如果允许含糊的消息，则可以支持所有足够大的 p 的完全揭示，从而推翻非单调性并改善相对于精确语言案例的交流结果。