Abstract: This paper studies information transmission in a two-sender, multidimensional cheap talk setting where there are exogenous restrictions on the feasible set of policies for thereceiver. Such restrictions, which are present in most applications, can, by limiting the punishments available to the receiver, prevent the existence of fully revealing equilibria(FRE). We focus on FRE that are i) robust to small mistakes by the senders, in that small differences between the senders’ messages result in only small punishments by the receiver, and ii) independent of the magnitudes of the senders’ bias vectors. For convex policy spaces in an arbitrary number of dimensions, we prove that if there exists a FRE satisfying property ii), then there exists one satisfying both i) and ii). Thus the requirement of robustness is, under these assumptions, not restrictive. For convex policy spaces in two dimensions, we provide a simple geometric condition, the Local Deterrence Condition, on the directions of the senders’ biases relative to the frontier of the policy space, that is necessary and sufficient for the existence of a FRE satisfying i) and ii). We also provide a specific policy rule, the Min Rule, for the receiver that supports a FRE satisfying i) and ii) whenever one exists. The Min Rule is the anonymous rule that punishes incompatible reports in the least severe way, subject to maintaining the senders’ incentives for truthtelling, no matter how large their biases. We characterize necessary and sufficient conditions for collusion-proofness of a FRE supported by the receiver using the Min Rule and show that if such a FRE is not collusion-proof, then no other FRE satisfying ii) can be collusion-proof. We extend our existence results to convex policy spaces in more than two dimensions and to non-convex two-dimensional spaces. Finally, our necessary and sufficient condition, as well as our specific policy rule, can be easily adapted if the receiver is uncertain about the directions of the biases and/or if the biases vary with the state of the world.

中文翻译：

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多发送方廉价谈话中充分揭示的稳健性

摘要：本文研究了两个发送方、多维廉价谈话环境中的信息传输，其中对接收方的可行策略集存在外生限制。大多数应用程序中都存在这种限制，通过限制接收者可用的惩罚，可以防止完全揭示均衡（FRE）的存在。我们专注于 FRE，i) 对发送者的小错误具有鲁棒性，因为发送者消息之间的微小差异只会导致接收者受到很小的惩罚，以及 ii) 与发送者偏差向量的大小无关。对于任意维数的凸策略空间，我们证明如果存在满足性质 ii) 的 FRE，则存在满足 i) 和 ii) 的 FRE。因此，稳健性的要求是，在这些假设下，没有限制。对于二维凸策略空间，我们提供了一个简单的几何条件，即局部威慑条件，关于发送者相对于策略空间边界的偏差方向，这对于满足 i 的 FRE 的存在是必要和充分的) 和 ii) 我们还为支持满足 i) 和 ii) 的 FRE 的接收器提供了一个特定的策略规则，即最小规则。最小规则是匿名规则，以最不严厉的方式惩罚不相容的报告，但要维持发送者说真话的动机，无论他们的偏见有多大。我们使用最小规则描述了接收者支持的 FRE 的共谋证明的充分必要条件，并表明如果这样的 FRE 不是共谋证明，那么没有其他满足 ii) 的 FRE 可以是防串通的。我们将存在结果扩展到二维以上的凸策略空间和非凸二维空间。最后，如果接收者不确定偏差的方向和/或偏差随世界状况而变化，我们的充分必要条件以及我们的特定政策规则可以很容易地进行调整。