Simple Mechanisms for a Subadditive Buyer and Applications to Revenue Monotonicity

We study the revenue maximization problem of a seller with n heterogeneous items for sale to a single buyer whose valuation function for sets of items is unknown and drawn from some distribution D. We show that if D is a distribution over subadditive valuations with independent items, then the better of pricing each item separately or pricing only the grand bundle achieves a constant-factor approximation to the revenue of the optimal mechanism. This includes buyers who are k-demand, additive up to a matroid constraint, or additive up to constraints of any downwards-closed set system (and whose values for the individual items are sampled independently), as well as buyers who are fractionally subadditive with item multipliers drawn independently. Our proof makes use of the core-tail decomposition framework developed in prior work showing similar results for the significantly simpler class of additive buyers [LY13, BILW14]. In the second part of the paper, we develop a connection between approximately optimal simple mechanisms and approximate revenue monotonicity with respect to buyers' valuations. Revenue non-monotonicity is the phenomenon that sometimes strictly increasing buyers' values for every set can strictly decrease the revenue of the optimal mechanism [HR12]. Using our main result, we derive a bound on how bad this degradation can be (and dub such a bound a proof of approximate revenue monotonicity); we further show that better bounds on approximate monotonicity imply a better analysis of our simple mechanisms.Comment: Updated title and body to version included in TEAC. Adapted Theorem 5.2 to accommodate \eta-BIC auctions (versus exactly BIC

Fear and the Response to Terrorism: An Economic Analysis

This paper offers a rational approach to the economics and psychology of fear and provides empirical evidence that supports our theory. We explicitly consider both the impact of danger on emotions and the distortive effect of fear on subjective beliefs and individual choices. Yet, we also acknowledge individuals' capacity to manage their emotions. Though costly, people can learn to control their fear and economic incentives affect the degree to which they do so. Since it does not pay back the same returns to everyone, people will differ in their reaction to impending danger. We then empirically examine the response of Israelis to terror incidents during the "Al-Aqsa" Intifada. Consistent with our theory, the overall impact of attacks on the usage of goods and services subject to terror attacks (e.g. bus services, coffee shops) reflects solely the reactions of occasional users. We find no impact of terrorist attacks on the demand for these goods and services by frequent users. Education and the exposure to media coverage also matters. We find a large impact of suicide attacks during regular media coverage days, and almost no impact of suicide attacks when they are followed by either a holiday or a weekend, especially among the less educated families and among occasional users.Economics, psychology, education

Innovation in Isolation: Labor-Management Partnerships in the United States

In the United States, as in other advanced industrial countries, worker participation in management has taken on increasing importance, placing pressures on employers and unions to change how they deal with employees/members, and with each other. This paper examines two of the most impressive cases in the U.S.: the partnerships between General Motors (G.M.) and the United Autoworkers union (U.A W.) at Saturn and between BellSouth and the Communication Workers union (C.W.A.). We outline the evolution and the basic features of these innovations, as well as highlighting certain ongoing problems. These problems, we argue, confront the parties to employment relations in the U.S. more generally, reflecting profound ambivalence about such experiments, and their continued isolation as ‘islands of excellence ’. As such, these cases both illustrate the vast potential for labor-management partnerships as well as the dampening effect of the employment relations context in the U.S

Optimal Single-Choice Prophet Inequalities from Samples

We study the single-choice Prophet Inequality problem when the gambler is given access to samples. We show that the optimal competitive ratio of $1/2$ can be achieved with a single sample from each distribution. When the distributions are identical, we show that for any constant $\varepsilon > 0$, $O(n)$ samples from the distribution suffice to achieve the optimal competitive ratio ($\approx 0.745$) within $(1+\varepsilon)$, resolving an open problem of Correa, D\"utting, Fischer, and Schewior.Comment: Appears in Innovations in Theoretical Computer Science (ITCS) 202

Privacy Localism

Privacy law scholarship often focuses on domain-specific federal privacy laws and state efforts to broaden them. This Article provides the first comprehensive analysis of privacy regulation at the local level (which it dubs “privacy localism”), using recently enacted privacy laws in Seattle and New York City as principal examples. Further, this Article attributes the rise of privacy localism to a combination of federal and state legislative failures and three emerging urban trends: the role of local police in federal counterterrorism efforts; smart city and open data initiatives; and demands for local police reform in the wake of widely reported abusive police practices. Both Seattle and New York City have enacted or proposed (1) a local surveillance ordinance regulating the purchase and use of surveillance equipment and technology by city departments, including the police, and (2) a law regulating city departments’ collection, use, disclosure, and retention of personal data. In adopting these local laws, both cities have sought to fill two significant gaps in federal and state privacy laws: the public surveillance gap, which refers to the weak constitutional and statutory protections against government surveillance in public places, and the fair information practices gap, which refers to the inapplicability of the federal and state privacy laws to government records held by local government agencies. Filling these gaps is a significant accomplishment and one that exhibits all of the values typically associated with federalism such as diversity, participation, experimentation, responsiveness, and accountability. This Article distinguishes federalism and localism and shows why privacy localism should prevail against the threat of federal and—more importantly—state preemption. This Article concludes by suggesting that privacy localism has the potential to help shape emerging privacy norms for an increasingly urban future, inspire more robust regulation at the federal and state levels, and inject more democratic control into city deployments of privacy-invasive technologies

Brunnian links are determined by their complements

If L_1 and L_2 are two Brunnian links with all pairwise linking numbers 0, then we show that L_1 and L_2 are equivalent if and only if they have homeomorphic complements. In particular, this holds for all Brunnian links with at least three components. If L_1 is a Brunnian link with all pairwise linking numbers 0, and the complement of L_2 is homeomorphic to the complement of L_1, then we show that L_2 may be obtained from L_1 by a sequence of twists around unknotted components. Finally, we show that for any positive integer n, an algorithm for detecting an n-component unlink leads immediately to an algorithm for detecting an unlink of any number of components. This algorithmic generalization is conceptually simple, but probably computationally impractical.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-7.abs.htm

Euler characteristic and quadrilaterals of normal surfaces

Let $M$ be a compact 3-manifold with a triangulation $\tau$. We give an inequality relating the Euler characteristic of a surface $F$ normally embedded in $M$ with the number of normal quadrilaterals in $F$. This gives a relation between a topological invariant of the surface and a quantity derived from its combinatorial description. Secondly, we obtain an inequality relating the number of normal triangles and normal quadrilaterals of $F$, that depends on the maximum number of tetrahedrons that share a vertex in $\tau$.Comment: 7 pages, 1 figur