Abstract We study sender–receiver games in which a privately informed sender sends a message to N receivers, who then take an action. The sender’s type space T has finite cardinality (i.e., | T | ∞ ). We show that every equilibrium payoff vector (resp. every Pareto efficient equilibrium payoff vector) is achieved by an equilibrium in which the sender sends at most | T | + N (resp. | T | + N − 1 ) messages with positive probability. We also show that such bounds do not exist when two privately informed senders simultaneously send a message to a receiver.

中文翻译：

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论收发博弈中消息空间的基数

摘要 我们研究了发送者-接收者博弈，其中一个私下通知的发送者向 N 个接收者发送消息，然后接收者采取行动。发送者的类型空间 T 具有有限的基数（即 | T | ∞ ）。我们证明了每个均衡支付向量（分别是每个帕累托有效均衡支付向量）都是通过一个均衡实现的，其中发送方最多发送 | T | + N (resp. | T | + N − 1 ) 条具有正概率的消息。我们还表明，当两个私下通知的发送者同时向接收者发送消息时，这种界限不存在。