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Dynamic Mechanism Collapse: A Boundary Characterization

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  • Xiaopeng Zeng
  • Erbao Cao

Abstract

When are dynamics valuable? In Bayesian environments with public signals and no intertemporal commitment, we study a seller who allocates an economically single-shot resource over time. We provide necessary and sufficient conditions under which the optimal dynamic mechanism collapses to a simple terminal design: a single public experiment at date 0 followed by a posterior-dependent static mechanism executed at a deterministic date, with no further disclosure. The key condition is the existence of a global affine shadow value that supports the posterior-based revenue frontier and uniformly bounds all history-dependent revenues. When this condition fails, a collapse statistic pinpoints the dates and public state variables that generate genuine dynamic value. The characterization combines martingale concavification on the belief space with an affine-support duality for concave envelopes.

Suggested Citation

  • Xiaopeng Zeng & Erbao Cao, 2025. "Dynamic Mechanism Collapse: A Boundary Characterization," Papers 2511.19781, arXiv.org, revised Dec 2025.
    • Handle: RePEc:arx:papers:2511.19781
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    References listed on IDEAS

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