Cheap Talk by Two Senders in the Presence of Network Externalities
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We develop a model of cheap talk with two senders in the presence of network externalities, such that their utility functions are increasing in the network size. We first show that, if there is no noise in the private information received by each sender, the full information is revealed by the harshest cross-checking strategies, that is, strategies to punish the senders unless their messages exactly coincide. Then, we prove that, even with a small noise, cross-checking strategies cannot induce full revelation if the utility functions of senders are linear in the network size, whereas full revelation is possible if utility functions are strictly concave. Finally, we show that a CARA (constant absolute risk aversion) utility function of senders is the necessary and sufficient condition for the existence of a fully revealing equilibrium, which is supported by the cross-checking strategy with a positive confidence interval independent of each sender’s private information.
Abstract
We develop a model of cheap talk with two senders in the presence of network externalities, such that their utility functions are increasing in the network size. We first show that, if there is no noise in the private information received by each sender, the full information is revealed by the harshest cross-checking strategies, that is, strategies to punish the senders unless their messages exactly coincide. Then, we prove that, even with a small noise, cross-checking strategies cannot induce full revelation if the utility functions of senders are linear in the network size, whereas full revelation is possible if utility functions are strictly concave. Finally, we show that a CARA (constant absolute risk aversion) utility function of senders is the necessary and sufficient condition for the existence of a fully revealing equilibrium, which is supported by the cross-checking strategy with a positive confidence interval independent of each sender’s private information.
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