Dual Reductions and the First-Order Approach for Informationally Robust Mechanism Design

The guarantee of a mechanism is the lowest objective value for the designer, across all information structures and equilibria. Brooks and Du (2024) proposed a “first-order” approach to characterizing guarantee-maximizing mechanisms by maximizing a particular lower bound on the guarantee: the expected lowest strategic virtual objective. In this paper, we show that for any mechanism M, there is an associated “dual reduction” mechanism M1 for which the expected lowest strategic virtual objective of M1 (and hence the guarantee of M1) is greater than the guarantee of M. This provides a rigorous foundation for the use of the strategic virtual objective in designing informationally robust mechanisms. A parallel result, based on dual reductions of information structures, justifies Brooks and Du’s (2024) first-order approach to characterizing information structures with the lowest potential, in terms of those that minimize the expected highest informational virtual objective.