We consider a setting of non-cooperative communication where a receiver wants to recover randomly generated sequences of symbols that are observed by a strategic sender. The sender aims to maximize an average utility that may not align with the recovery criterion of the receiver, whereby the signals it sends may not be truthful. The rate of communication is defined as the number of reconstructions corresponding to the sequences recovered correctly while communicating with the sender. We pose this problem as a sequential game between the sender and the receiver with the receiver as the leader and determine strategies for the receiver that attain vanishing probability of error and compute the rates of such strategies. We show the existence of such strategies under a condition on the utility of the sender. For the case of the binary alphabet, this condition is also necessary, in the absence of which, the probability of error goes to one for all choices of strategies of the receiver. We show that for reliable recovery, the receiver chooses to correctly decode only a $\textit{subset}$ of messages received from the sender and deliberately makes an error on messages outside this subset. Despite a clean channel, our setting exhibits a non-trivial $\textit{maximum}$ rate of communication, which is in general strictly less than the capacity of the channel. This implies the impossibility of strategies that correctly decode sequences of rate greater than the maximum rate while also achieving reliable communication. This is a key point of departure from the usual setting of cooperative communication.

翻译：我们考虑一种非合作通信场景，其中接收方希望恢复由战略发送方观测到的随机生成符号序列。发送方旨在最大化可能与接收方恢复准则不一致的平均效用，因此其发送的信号可能不真实。通信速率定义为在与发送方通信过程中正确恢复序列所对应的重建数量。我们将此问题建模为发送方与接收方之间的序贯博弈（接收方为领导者），并确定使错误概率趋于零的接收方策略，同时计算此类策略的速率。我们证明了在发送方效用满足特定条件时此类策略的存在性。对于二进制字母表情形，该条件同样是必要的——若不满足，则无论接收方采用何种策略，错误概率均趋于一。研究表明，为实现可靠恢复，接收方仅选择正确解码从发送方接收消息的一个子集，并对此子集外的消息故意产生错误。尽管信道无噪声，我们的设定仍展现出非平凡的最大通信速率，该速率通常严格小于信道容量。这意味着不存在能同时实现可靠通信且以高于最大速率的速率正确解码序列的策略。这是与常规合作通信场景的关键区别所在。