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We propose a measure of strategic complexity for strategy-proof mechanisms in terms of the contingent reasoning they require agents to engage in to recognize their dominant strategy. Our rankings are consistent with the coarser ones implied by the solution concepts of (strong) obvious strategy-proofness (Li, 2017b; Pycia and Troyan, 2023b). The added flexibility of our approach allows a designer to balance a mechanism’s implicity with other objectives: We characterize the Ausubel (2004) auction as the simplest way to implement the VCG outcome in multi-unit allocation problems with transfers, and provide novel rankings of mechanisms that implement stable outcomes in matching problems.
