This paper constructs an algorithmic framework for adaptively achieving the mechanism design objective, finding a mechanism inducing socially optimal Nash equilibria, without knowledge of the utility functions of the agents. We consider a probing scheme where the designer can iteratively enact mechanisms and observe Nash equilibria responses. We first derive necessary and sufficient conditions, taking the form of linear program feasibility, for the existence of utility functions under which the empirical Nash equilibria responses are socially optimal. Then, we utilize this to construct a loss function with respect to the mechanism, and show that its global minimization occurs at mechanisms under which Nash equilibria system responses are also socially optimal. We develop a simulated annealing-based gradient algorithm, and prove that it converges in probability to this set of global minima, thus achieving adaptive mechanism design.

翻译：本文构建了一个自适应实现机制设计目标的算法框架，即在无需知晓智能体效用函数的情况下，寻找能诱发社会最优纳什均衡的机制。我们考虑一种探测方案，其中设计者可迭代实施机制并观察纳什均衡响应。首先，我们推导出存在使经验纳什均衡响应达到社会最优的效用函数的充要条件，该条件以线性规划可行性形式呈现。进而，我们利用这一结论构造了关于机制的损失函数，并证明其全局极小值恰出现在能使纳什均衡系统响应也达到社会最优的机制处。我们开发了基于模拟退火的梯度算法，并证明该算法依概率收敛于这一全局极小值集合，从而实现了自适应机制设计。