In the classical communication setting multiple senders having access to the same source of information and transmitting it over channel(s) to a receiver in general leads to a decrease in estimation error at the receiver as compared with the single sender case. However, if the objectives of the information providers are different from that of the estimator, this might result in interesting strategic interactions and outcomes. In this work, we consider a hierarchical signaling game between multiple senders (information designers) and a single receiver (decision maker) each having their own, possibly misaligned, objectives. The senders lead the game by committing to individual information disclosure policies simultaneously, within the framework of a non-cooperative Nash game among themselves. This is followed by the receiver's action decision. With Gaussian information structure and quadratic objectives (which depend on underlying state and receiver's action) for all the players, we show that in general the equilibrium is not unique. We hence identify a set of equilibria and further show that linear noiseless policies can achieve a minimal element of this set. Additionally, we show that competition among the senders is beneficial to the receiver, as compared with cooperation among the senders. Further, we extend our analysis to a dynamic signaling game of finite horizon with Markovian information evolution. We show that linear memoryless policies can achieve equilibrium in this dynamic game. We also consider an extension to a game with multiple receivers having coupled objectives. We provide algorithms to compute the equilibrium strategies in all these cases. Finally, via extensive simulations, we analyze the effects of multiple senders in varying degrees of alignment among their objectives.

翻译：在经典通信设置中，多个发送者获取同一信息源并通过信道将其传输给接收者，通常会导致接收者的估计误差较单个发送者情形有所降低。然而，若信息提供者的目标与估计者的目标不一致，则可能引发有趣的战略互动与结果。本文考虑一个多层信号博弈，涉及多个发送者（信息设计者）与单个接收者（决策者），各方拥有各自可能不一致的目标。发送者通过同时承诺各自的信息披露策略来主导博弈，该过程在非合作纳什博弈框架内进行，随后接收者做出行动决策。在高斯信息结构及所有参与者的二次型目标（依赖于潜在状态与接收者行动）下，我们证明均衡通常不唯一。因此，我们识别出一组均衡，并进一步证明线性无噪声策略可实现该集合中的最小元素。此外，我们表明与发送者合作相比，发送者间的竞争对接收者更有利。进一步地，我们将分析扩展至有限时域且信息演化服从马尔可夫过程的动态信号博弈，证明线性无记忆策略可实现该动态博弈的均衡。我们还考虑了具有耦合目标的多个接收者博弈的扩展情形。针对所有这些情形，我们提供了计算均衡策略的算法。最后，通过大量仿真，我们分析了多个发送者在其目标对齐程度不同时的影响。