We study the problem of designing mechanisms for \emph{information acquisition} scenarios. This setting models strategic interactions between an uniformed \emph{receiver} and a set of informed \emph{senders}. In our model the senders receive information about the underlying state of nature and communicate their observation (either truthfully or not) to the receiver, which, based on this information, selects an action. Our goal is to design mechanisms maximizing the receiver's utility while incentivizing the senders to report truthfully their information. First, we provide an algorithm that efficiently computes an optimal \emph{incentive compatible} (IC) mechanism. Then, we focus on the \emph{online} problem in which the receiver sequentially interacts in an unknown game, with the objective of minimizing the \emph{cumulative regret} w.r.t. the optimal IC mechanism, and the \emph{cumulative violation} of the incentive compatibility constraints. We investigate two different online scenarios, \emph{i.e.,} the \emph{full} and \emph{bandit feedback} settings. For the full feedback problem, we propose an algorithm that guarantees $\tilde{\mathcal O}(\sqrt T)$ regret and violation, while for the bandit feedback setting we present an algorithm that attains $\tilde{\mathcal O}(T^{\alpha})$ regret and $\tilde{\mathcal O}(T^{1-\alpha/2})$ violation for any $\alpha\in[1/2, 1]$. Finally, we complement our results providing a tight lower bound.

翻译：我们研究为 \ emph{ 信息获取} 设想设计机制的问题。 这样设置了统一的 \ emph{ receeper} 和一套知情的 emph{ renders} 之间的战略互动模式。 在我们的模型中, 发送者接收关于自然基本状态的信息, 并向接收者传达他们的观察( 不管是真实与否), 并以此信息为基础选择一个动作。 我们的目标是设计机制, 最大限度地发挥接收者的作用, 同时激励发送者真实地报告信息。 首先, 我们提供一种有效计算最优计算低的 emph{ 激励兼容} (IC) 机制。 然后, 我们集中关注接收者在未知的游戏中依次互动的问题, 目标是最大限度地减少 \ emph{ 累积遗憾} w.r. t. 最佳的 IC 机制, 以及激励兼容性约束的 。 我们调查两种不同的网络情景, 以较低 $ cal_ decal} ral de conde conversation rence.