We examine the classic "Beer-Quiche" game from Cho and Kreps (1987), and relax the assumption that the order placed by the sender is completely observable. Under the optimal degree of transparency, the receiver achieves a higher payoff than with full transparency. Partial obfuscation of the sender's choice encourages separation: committing to a less informative signal about the sender's choice affects the endogenous information generation process such that the receiver thereby secures himself more information.
Asriyan, Fuchs, and Green (2017) @cite_2 explores a similar problem. In their model, the @math sellers have an indivisible asset which value is private information, and have two periods in which they may trade it. In the portion of the paper relevant to this one, they ask how a planner should disclose trade behavior to maximize social welfare". As these authors note, persuasion is not the only objective, since the information policy affects the information content of trading, and hence affects trading itself.
@cite_2
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How effectively does a decentralized marketplace aggregate information that is dispersed throughout the economy? We study this question in a dynamic setting, in which sellers have private information that is correlated with an unobservable aggregate state. We first characterize equilibria with an arbitrary finite number of informed traders. A common feature is that each seller’s trading behavior provides an informative and conditionally independent signal about the aggregate state. We then ask whether the state is revealed as the number of informed traders goes to infinity. Perhaps surprisingly, the answer is no. We provide generic conditions under which the amount of information revealed is necessarily bounded and does not reveal the aggregate state. When these conditions are violated, we provide conditions under which there is coexistence of aggregating and non-aggregating equilibria. We discuss the implications for policies meant to enhance information dissemination in markets. In general, a partially revealing information policy can increase trading surplus.