Strategic Information Design in Quadratic Multidimensional Persuasion Games with Two Senders

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. However, if the objectives of the information providers are different from that of the estimator, this might result in interesting strategic interactions. In this work, we consider a hierarchical signaling game between two 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 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. While we show that full revelation of the state is always an equilibrium, we propose an algorithm to achieve non trivial equilibria. Through simulations we show that misalignment between senders' objectives is beneficial for the receiver.