A General Statistical Framework for Designing Strategy-proof Assignment Mechanisms

We develop a statistical framework for the design of a strategy-proof assignment mechanism that closely approximates a target outcome rule. The framework can handle settings with and without money, and allows the designer to employ techniques from machine learning to control the space of strategy-proof mechanisms searched over, by providing a rule class with appropriate capacity. We solve a sample-based optimization problem over a space of mechanisms that correspond to agent-independent price functions (virtual prices in the case of settings without money), subject to a feasibility constraint on the sample. A transformation is applied to the obtained mechanism to ensure feasibility on all type profiles, and strategy-proofness. We derive a sample complexity bound for our approach in terms of the capacity of the chosen rule class and provide applications for our results.