Wait and See: A Theory of Communication over Time

Abstract

We study a dynamic cheap talk model with multiple senders where the receiver can choose when to make her decision and communication can take place over time. Delays are wasteful, and no player can commit to any action or inaction; the receiver can choose momentary inaction only if her beliefs about the continuation play rationalize that. In contrast to the results in static versions of the model, we show that when the senders commonly know the state of nature, a perfect Bayesian equilibrium exists with instantenous, full revelation irrespective of the size and direction of the senders’ biases. We show that the equilibrium outcome is robust to the introduction of a type of small noise in the senders’ signals about the state.

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