Auctions with Severely Bounded Communication

We study auctions with severe bounds on the communication allowed: each bidder may only transmit t bits of information to the auctioneer. We consider both welfare- and profit-maximizing auctions under this communication restriction. For both measures, we determine the optimal auction and show that the loss incurred relative to unconstrained auctions is mild. We prove non-surprising properties of these kinds of auctions, e.g., that in optimal mechanisms bidders simply report the interval in which their valuation lies in, as well as some surprising properties, e.g., that asymmetric auctions are better than symmetric ones and that multi-round auctions reduce the communication complexity only by a linear factor

Single Parameter Combinatorial Auctions with Partially Public Valuations

We consider the problem of designing truthful auctions, when the bidders' valuations have a public and a private component. In particular, we consider combinatorial auctions where the valuation of an agent $i$ for a set $S$ of items can be expressed as $v_if(S)$, where $v_i$ is a private single parameter of the agent, and the function $f$ is publicly known. Our motivation behind studying this problem is two-fold: (a) Such valuation functions arise naturally in the case of ad-slots in broadcast media such as Television and Radio. For an ad shown in a set $S$ of ad-slots, $f(S)$ is, say, the number of {\em unique} viewers reached by the ad, and $v_i$ is the valuation per-unique-viewer. (b) From a theoretical point of view, this factorization of the valuation function simplifies the bidding language, and renders the combinatorial auction more amenable to better approximation factors. We present a general technique, based on maximal-in-range mechanisms, that converts any $\alpha$-approximation non-truthful algorithm ($\alpha \leq 1$) for this problem into $\Omega(\frac{\alpha}{\log{n}})$ and $\Omega(\alpha)$-approximate truthful mechanisms which run in polynomial time and quasi-polynomial time, respectively

Expressiveness and Robustness of First-Price Position Auctions

Since economic mechanisms are often applied to very different instances of the same problem, it is desirable to identify mechanisms that work well in a wide range of circumstances. We pursue this goal for a position auction setting and specifically seek mechanisms that guarantee good outcomes under both complete and incomplete information. A variant of the generalized first-price mechanism with multi-dimensional bids turns out to be the only standard mechanism able to achieve this goal, even when types are one-dimensional. The fact that expressiveness beyond the type space is both necessary and sufficient for this kind of robustness provides an interesting counterpoint to previous work on position auctions that has highlighted the benefits of simplicity. From a technical perspective our results are interesting because they establish equilibrium existence for a multi-dimensional bid space, where standard techniques break down. The structure of the equilibrium bids moreover provides an intuitive explanation for why first-price payments may be able to support equilibria in a wider range of circumstances than second-price payments

Fixed Price Approximability of the Optimal Gain From Trade

Bilateral trade is a fundamental economic scenario comprising a strategically acting buyer and seller, each holding valuations for the item, drawn from publicly known distributions. A mechanism is supposed to facilitate trade between these agents, if such trade is beneficial. It was recently shown that the only mechanisms that are simultaneously DSIC, SBB, and ex-post IR, are fixed price mechanisms, i.e., mechanisms that are parametrised by a price p, and trade occurs if and only if the valuation of the buyer is at least p and the valuation of the seller is at most p. The gain from trade is the increase in welfare that results from applying a mechanism; here we study the gain from trade achievable by fixed price mechanisms. We explore this question for both the bilateral trade setting, and a double auction setting where there are multiple buyers and sellers. We first identify a fixed price mechanism that achieves a gain from trade of at least 2/r times the optimum, where r is the probability that the seller's valuation does not exceed the buyer's valuation. This extends a previous result by McAfee. Subsequently, we improve this approximation factor in an asymptotic sense, by showing that a more sophisticated rule for setting the fixed price results in an expected gain from trade within a factor O(log(1/r)) of the optimal gain from trade. This is asymptotically the best approximation factor possible. Lastly, we extend our study of fixed price mechanisms to the double auction setting defined by a set of multiple i.i.d. unit demand buyers, and i.i.d. unit supply sellers. We present a fixed price mechanism that achieves a gain from trade that achieves for all epsilon > 0 a gain from trade of at least (1-epsilon) times the expected optimal gain from trade with probability 1 - 2/e^{#T epsilon^2 /2}, where #T is the expected number of trades resulting from the double auction

Efficiency of scalar-parameterized mechanisms

We consider the problem of allocating a fixed amount of an infinitely divisible resource among multiple competing, fully rational users. We study the efficiency guarantees that are possible when we restrict to mechanisms that satisfy certain scalability constraints motivated by large scale communication networks; in particular, we restrict attention to mechanisms where users are restricted to one-dimensional strategy spaces. We first study the efficiency guarantees possible when the mechanism is not allowed to price differen- tiate. We study the worst-case efficiency loss (ratio of the utility associated with a Nash equilibrium to the maximum possible utility), and show that the proportional allocation mechanism of Kelly (1997) minimizes the efficiency loss when users are price anticipating. We then turn our attention to mechanisms where price differentiation is permitted; using an adaptation of the Vickrey-Clarke-Groves class of mechanisms, we con- struct a class of mechanisms with one-dimensional strategy spaces where Nash equilibria are fully efficient. These mechanisms are shown to be fully efficient even in general convex environments, under reasonable assumptions. Our results highlight a fundamental insight in mechanism design: when the pricing flexibility available to the mechanism designer is limited, restricting the strategic flexibility of bidders may actually improve the efficiency guarantee.National Science FoundationArmy Research OfficeDARPA - Next Generation Internet InitiativeNational Science Foundation Graduate Research Fellowshi

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