# Adaptive Mechanism Design using Multi-Agent Revealed Preferences

CoRR（2024）

Abstract

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.

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