Dynamic Mechanism Collapse: A Boundary Characterization
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914222887141376 |
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| author | Zeng, Xiaopeng Cao, Erbao |
| author_facet | Zeng, Xiaopeng Cao, Erbao |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_19781 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dynamic Mechanism Collapse: A Boundary Characterization Zeng, Xiaopeng Cao, Erbao Theoretical Economics 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. |
| title | Dynamic Mechanism Collapse: A Boundary Characterization |
| topic | Theoretical Economics |
| url | https://arxiv.org/abs/2511.19781 |