Mechanism Design for Perturbation Stable Combinatorial Auctions

Motivated by recent research on combinatorial markets with endowed valuations by (Babaioff et al., EC 2018) and (Ezra et al., EC 2020), we introduce a notion of perturbation stability in Combinatorial Auctions (CAs) and study the extend to which stability helps in social welfare maximization and mechanism design. A CA is $\gamma\textit{-stable}$ if the optimal solution is resilient to inflation, by a factor of $\gamma \geq 1$, of any bidder's valuation for any single item. On the positive side, we show how to compute efficiently an optimal allocation for 2-stable subadditive valuations and that a Walrasian equilibrium exists for 2-stable submodular valuations. Moreover, we show that a Parallel 2nd Price Auction (P2A) followed by a demand query for each bidder is truthful for general subadditive valuations and results in the optimal allocation for 2-stable submodular valuations. To highlight the challenges behind optimization and mechanism design for stable CAs, we show that a Walrasian equilibrium may not exist for $\gamma$-stable XOS valuations for any $\gamma$, that a polynomial-time approximation scheme does not exist for $(2-\epsilon)$-stable submodular valuations, and that any DSIC mechanism that computes the optimal allocation for stable CAs and does not use demand queries must use exponentially many value queries. We conclude with analyzing the Price of Anarchy of P2A and Parallel 1st Price Auctions (P1A) for CAs with stable submodular and XOS valuations. Our results indicate that the quality of equilibria of simple non-truthful auctions improves only for $\gamma$-stable instances with $\gamma \geq 3$

The evolution of fetal protection policies

This article examines the evolution of fetal protection policies (FPPs) by detailing their historical legacy and a range of contemporary social forces that have contributed to their maintenance. It is based on a case study of the 1977 U.S. Department of Labor, Occupational Safety and Health Administration (OSHA) hearings to revise the industrial lead standard, the 1991 U.S. Supreme Court decision that such policies are unconstitutional ( United Auto Workers v. Johnson Controls , 1991), and the case law preceding that decision. A primary issue is the notion that women and fetuses are disproportionately susceptible to lead. This study reveals the ways in which this belief is framed, disputed, and appropriated by various parties to the fetal protection policy debate. Implications of this case study for family health policy are also discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44656/1/10834_2006_Article_BF02353687.pd