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Equilibrium Existence in First‐Price Auctions With Private Values

Wojciech Olszewski et al.

Econometrica2026https://doi.org/10.3982/ecta22570article
FT50AJG 4*ABDC A*
Weight
0.37

Abstract

We provide sufficient conditions for equilibrium existence in first‐price auctions with private values that accommodate non quasi‐linear utilities and value‐distributions that contain atoms and exhibit positive or negative correlation. These conditions show that equilibrium existence often turns on properties of a single statistic of the joint distribution of values, namely, the minimum value in the support of the high‐value distribution (the mHV). We also show that modifying the standard tie‐breaking rule only at the mHV is enough to guarantee equilibrium existence without our sufficient conditions. Our results also apply to Bertrand price competition when each firm's constant marginal cost is private information.

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https://doi.org/https://doi.org/10.3982/ecta22570

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@article{wojciech2026,
  title        = {{Equilibrium Existence in First‐Price Auctions With Private Values}},
  author       = {Wojciech Olszewski et al.},
  journal      = {Econometrica},
  year         = {2026},
  doi          = {https://doi.org/https://doi.org/10.3982/ecta22570},
}

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Equilibrium Existence in First‐Price Auctions With Private Values

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Evidence weight

0.37

Balanced mode · F 0.40 / M 0.15 / V 0.05 / R 0.40

F · citation impact0.16 × 0.4 = 0.06
M · momentum0.53 × 0.15 = 0.08
V · venue signal0.50 × 0.05 = 0.03
R · text relevance †0.50 × 0.4 = 0.20

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