Uniqueness of the Equilibrium in First-Price Auctions

If the value cumulative distribution functions are log-concave at the highest lower extremity of their supports of the first-price auction in the asymmetric indepent private values model.

Uniqueness of the Equilibrium in First-Price Auctions

If the value cumulative distribution functions are log-concave at the highest lower extremity of their supports, a simple geometric argument establishes the uniqueness of the equilibrium of the first-price auction in the asymmetric independent private value model.

First-Price and Second-Price Auctions with Resale

We add a resale stage to standard auctions with two bidders. Bids are either kept secret or made public. Either the auction winner or the auction loser chooses the resale price. We characterize an infinity of equilibria of the second-price auction and a unique equilibrium of the first-price auction. For every equilibrium of an auction without bid disclosure, we construct an outcome-equivalent and, in the case of the second-price auction, “posterior implementable” equilibrium of the auction with bid disclosure. We compare the revenues from the two auctions and from the two bargaining procedures at resaleAuctions, resale

Zheng’s Optimal Mechanism with Resale and the Second-Price Auction

We show that Zheng (2002)’s optimal mechanism in the presence of resale can be interpreted as an equilibrium of an ascending-price auction and, in the two-bidder case, as an equilibrium with a no-regret property of the English and second-price auctions. We also show that it can be extended beyond Zheng (2002)’s original assumptionsZheng’s mechanism, optimality, resale, second-price auction, independent private values

Auctions with Almost Homogeneous Bidders

We deviate from the symmetric case of the independent private value model by allowing the bidders’ value distributions, which depend on parameters, to be slightly different. We show that previous results about the equality to the first-order in the parameters between revenues from the second-price auction and other auction mechanisms follow from the joint differentiability of the equilibria with respect to the parameters. We prove this differentiability for the first-price auction and obtain general formulas for the different first-order effects. From our results about the first-price auction, we analytically generate examples with continuous distributions where a stochastic improvement to a bidder’s value distribution reduces his equilibrium payoff. In another application, we show that, starting from competition among cartels of equal sizes, allowing in a small number of members from other cartels can be profitable only if the members or the synergies between them are strong enough.Independent private value model; auctions; asymmetry; first-price auction, second-price auction; differentiability; revenue equivalence theorem

First-Price, Second-Price, and English Auctions with Resale

In the independent-private-value model, we allow resale among bidders following a first-price sealed-bid, second-price sealed-bid, or English auction with two bidders. We consider two regimes with regard to the disclosure of the sealed bids: full disclosure and no disclosure. Either the auction winner or the auction loser chooses the resale mechanism. Thanks to three key properties our model shares with the common-value model, we obtain explicit formulas for the equilibria. We circumvent the “ratchet effect,” by “randomizing” every pure equilibrium under no disclosure into an equivalent behavioral equilibrium under full disclosure. We compare the auctioneer’s revenues across auctions and bargaining procedures. We present some nbidder extensions.

Early changes in diaphragmatic function evaluated using ultrasound in cardiac surgery patients: a cohort study.

Little is known about the evolution of diaphragmatic function in the early post-cardiac surgery period. The main purpose of this work is to describe its evolution using ultrasound measurements of muscular excursion and thickening fraction (TF). Single-center prospective study of 79 consecutive uncomplicated elective cardiac surgery patients, using motion-mode during quiet unassisted breathing. Excursion and TF were measured sequentially for each patient [pre-operative (D1), 1 day (D2) and 5 days (D3) after surgery]. Pre-operative median for right and left hemidiaphragmatic excursions were 1.8 (IQR 1.6 to 2.1) cm and 1.7 (1.4 to 2.0) cm, respectively. Pre-operative median right and left thickening fractions were 28 (19 to 36) % and 33 (22 to 51) %, respectively. At D2, there was a reduction in both excursion (right: 1.5 (1.1 to 1.8) cm, p < 0.001, left: 1.5 (1.1 to 1.8), p = 0.003) and thickening fractions (right: 20 (15 to 34) %, p = 0.021, left: 24 (17 to 39) %, p = 0.002), followed by a return to pre-operative values at D3. A positive moderate correlation was found between excursion and thickening fraction (Spearman's rho 0.518 for right and 0.548 for left hemidiaphragm, p < 0.001). Interobserver reliability yielded a bias below 0.1 cm with limits of agreement (LOA) of ± 0.3 cm for excursion and - 2% with LOA of ± 21% for thickening fractions. After cardiac surgery, the evolution of diaphragmatic function is characterized by a transient impairment followed by a quick recovery. Although ultrasound diaphragmatic excursion and thickening fraction are correlated, excursion seems to be a more feasible and reproducible method in this population