Computer-aided verification in mechanism design

In mechanism design, the gold standard solution concepts are dominant strategy incentive compatibility and Bayesian incentive compatibility. These solution concepts relieve the (possibly unsophisticated) bidders from the need to engage in complicated strategizing. While incentive properties are simple to state, their proofs are specific to the mechanism and can be quite complex. This raises two concerns. From a practical perspective, checking a complex proof can be a tedious process, often requiring experts knowledgeable in mechanism design. Furthermore, from a modeling perspective, if unsophisticated agents are unconvinced of incentive properties, they may strategize in unpredictable ways. To address both concerns, we explore techniques from computer-aided verification to construct formal proofs of incentive properties. Because formal proofs can be automatically checked, agents do not need to manually check the properties, or even understand the proof. To demonstrate, we present the verification of a sophisticated mechanism: the generic reduction from Bayesian incentive compatible mechanism design to algorithm design given by Hartline, Kleinberg, and Malekian. This mechanism presents new challenges for formal verification, including essential use of randomness from both the execution of the mechanism and from the prior type distributions. As an immediate consequence, our work also formalizes Bayesian incentive compatibility for the entire family of mechanisms derived via this reduction. Finally, as an intermediate step in our formalization, we provide the first formal verification of incentive compatibility for the celebrated Vickrey-Clarke-Groves mechanism

Budget feasible mechanisms on matroids

Motivated by many practical applications, in this paper we study budget feasible mechanisms where the goal is to procure independent sets from matroids. More specifically, we are given a matroid =(,) where each ground (indivisible) element is a selfish agent. The cost of each element (i.e., for selling the item or performing a service) is only known to the element itself. There is a buyer with a budget having additive valuations over the set of elements E. The goal is to design an incentive compatible (truthful) budget feasible mechanism which procures an independent set of the matroid under the given budget that yields the largest value possible to the buyer. Our result is a deterministic, polynomial-time, individually rational, truthful and budget feasible mechanism with 4-approximation to the optimal independent set. Then, we extend our mechanism to the setting of matroid intersections in which the goal is to procure common independent sets from multiple matroids. We show that, given a polynomial time deterministic blackbox that returns -approximation solutions to the matroid intersection problem, there exists a deterministic, polynomial time, individually rational, truthful and budget feasible mechanism with (3+1) -approximation to the optimal common independent set

Sequential Posted Price Mechanisms with Correlated Valuations

We study the revenue performance of sequential posted price mechanisms and some natural extensions, for a general setting where the valuations of the buyers are drawn from a correlated distribution. Sequential posted price mechanisms are conceptually simple mechanisms that work by proposing a take-it-or-leave-it offer to each buyer. We apply sequential posted price mechanisms to single-parameter multi-unit settings in which each buyer demands only one item and the mechanism can assign the service to at most k of the buyers. For standard sequential posted price mechanisms, we prove that with the valuation distribution having finite support, no sequential posted price mechanism can extract a constant fraction of the optimal expected revenue, even with unlimited supply. We extend this result to the the case of a continuous valuation distribution when various standard assumptions hold simultaneously. In fact, it turns out that the best fraction of the optimal revenue that is extractable by a sequential posted price mechanism is proportional to ratio of the highest and lowest possible valuation. We prove that for two simple generalizations of these mechanisms, a better revenue performance can be achieved: if the sequential posted price mechanism has for each buyer the option of either proposing an offer or asking the buyer for its valuation, then a Omega(1/max{1,d}) fraction of the optimal revenue can be extracted, where d denotes the degree of dependence of the valuations, ranging from complete independence (d=0) to arbitrary dependence (d=n-1). Moreover, when we generalize the sequential posted price mechanisms further, such that the mechanism has the ability to make a take-it-or-leave-it offer to the i-th buyer that depends on the valuations of all buyers except i's, we prove that a constant fraction (2-sqrt{e})/4~0.088 of the optimal revenue can be always be extracted.Comment: 29 pages, To appear in WINE 201

The Core of the Participatory Budgeting Problem

In participatory budgeting, communities collectively decide on the allocation of public tax dollars for local public projects. In this work, we consider the question of fairly aggregating the preferences of community members to determine an allocation of funds to projects. This problem is different from standard fair resource allocation because of public goods: The allocated goods benefit all users simultaneously. Fairness is crucial in participatory decision making, since generating equitable outcomes is an important goal of these processes. We argue that the classic game theoretic notion of core captures fairness in the setting. To compute the core, we first develop a novel characterization of a public goods market equilibrium called the Lindahl equilibrium, which is always a core solution. We then provide the first (to our knowledge) polynomial time algorithm for computing such an equilibrium for a broad set of utility functions; our algorithm also generalizes (in a non-trivial way) the well-known concept of proportional fairness. We use our theoretical insights to perform experiments on real participatory budgeting voting data. We empirically show that the core can be efficiently computed for utility functions that naturally model our practical setting, and examine the relation of the core with the familiar welfare objective. Finally, we address concerns of incentives and mechanism design by developing a randomized approximately dominant-strategy truthful mechanism building on the exponential mechanism from differential privacy

Elastic-plastic solutions for expanding cavities embedded in two different cohesive-frictional materials

An analytical solution of cavity expansion in two different concentric regions of soil is developed and investigated in this paper. The cavity is embedded within a soil with finite radial dimension and surrounded by a second soil, which extends to infinity. Large-strain quasi-static expansion of both spherical and cylindrical cavities in elastic-plastic soils is considered. A non-associated Mohr–Coulomb yield criterion is used for both soils. Closed-form solutions are derived, which provide the stress and strain fields during the expansion of the cavity from an initial to a final radius. The analytical solution is validated against finite element simulations, and the effect of varying geometric and material parameters is studied. The influence of the two different soils during cavity expansion is discussed by using pressure–expansion curves and by studying the development of plastic regions within the soils. The analytical method may be applied to various geotechnical problems, which involve aspects of soil layering, such as cone penetration test interpretation, ground-freezing around shafts, tunnelling, and mining

Bespoke Biomolecular Wires for Transmembrane Electron Transfer: Spontaneous Assembly of a Functionalized Multiheme Electron Conduit.

Shewanella oneidensis exchanges electrons between cellular metabolism and external redox partners in a process that attracts much attention for production of green electricity (microbial fuel cells) and chemicals (microbial electrosynthesis). A critical component of this pathway is the outer membrane spanning MTR complex, a biomolecular wire formed of the MtrA, MtrB, and MtrC proteins. MtrA and MtrC are decaheme cytochromes that form a chain of close-packed hemes to define an electron transfer pathway of 185 Å. MtrA is wrapped inside MtrB for solubility across the outer membrane lipid bilayer; MtrC sits outside the cell for electron exchange with external redox partners. Here, we demonstrate tight and spontaneous in vitro association of MtrAB with separately purified MtrC. The resulting complex is comparable with the MTR complex naturally assembled by Shewanella in terms of both its structure and rates of electron transfer across a lipid bilayer. Our findings reveal the potential for building bespoke electron conduits where MtrAB combines with chemically modified MtrC, in this case, labeled with a Ru-dye that enables light-triggered electron injection into the MtrC heme chain

Summer and winter differences in zooplankton biomass, distribution and size composition in the KwaZulu-Natal Bight, South Africa

Zooplankton biomass and distribution in the KwaZulu-Natal Bight were investigated in relation to environmental parameters during summer (January–February 2010) and winter (July–August 2010). Mean zooplankton biomass was significantly higher in winter (17.1 mg dry weight [DW] m–3) than in summer (9.5 mg DW m−3). In summer, total biomass was evenly distributed within the central bight, low off the Thukela River mouth and peaked near Durban. In winter, highest biomass was found offshore between Richards Bay and Cape St Lucia. Zooplankton biomass in each size class was significantly, negatively related to sea surface temperature and integrated nitrate, but positively related to surface chlorophyll a and dissolved oxygen. Zooplankton biomass was significantly related to bottom depth, with greatest total biomass located inshore (<50 m). Distribution across the shelf varied with zooplankton size. Seasonal differences in copepod size composition suggest that a smaller, younger community occupied the cool, chlorophyll-rich waters offshore from the St Lucia upwelling cell in winter, and a larger, older community occurred within the relatively warm and chlorophyll-poor central bight in summer. Nutrient enrichment from quasi-permanent upwelling off Durban and Richards Bay appears to have a greater influence on zooplankton biomass and distribution in the bight than the strongly seasonal nutrient input from the Thukela River.DHE

Rapid Assessment of Octocoral Diversity and Habitat on Saba Bank, Netherlands Antilles

Saba Bank is a large submerged platform (∼2200 km2), average depth 30 m, located 4 km southwest of Saba Island in Netherlands Antilles, Caribbean Sea. Ships traveling to and from oil terminals on nearby St. Eustatius routinely anchor on the Bank, damaging benthic megafauna. Gorgonian octocorals are vulnerable to anchor damage, and they are common and conspicuous in shallow water (15–50 m) around the banks. This prompted a rapid assessment of octocoral habitat and diversity. The primary objectives were to estimate total species richness and to characterize habitats vis a vis gorgonians. Landsat imagery and multibeam bathymetry were employed to identify random sites for quantitative transects. A Seabotix LBV200L remotely operated vehicle (ROV) and SCUBA were used to collect and survey to 130 m. A total of 14 scuba dives and 3 ROV dives were completed in 10 days. During that time, 48 octocoral species were collected, including two likely undescribed species in the genera Pterogorgia and Lytreia. Gorgonian richness was exceptional, but not all species were collected, because the species accumulation curve remained steeply inclined after all surveys. Two shallow-water gorgonian habitat types were identified using multidimensional scaling and hierarchical cluster analyses: 1) a high diversity, high density fore-reef environment characterized by Eunicea spp., Gorgonia spp., and Pseudopterogorgia spp. and 2) a low diversity, low density plateau environment characterized by Pseudopterogorgia acerosa, Pterogorgia guadalupensis, and Gorgonia mariae. The analyses support hypotheses of broad (∼15 km) habitat homogeneity (ANOSIM, P>0.05), but a significant difference between fore-reef and plateau environments (ANOSIM, P<0.05). However, there was some indication of habitat heterogeneity along the 15 km study section of the 50 km platform edge along the southeast rim. Our results highlight the complexity and biodiversity of the Saba Bank, and emphasize the need for more scientific exploration

Giving risk management culture a role in strategic planning

WOS: 000413939000023Strategically planned and implemented risk management paves the way for competitive advantage and a decisive edge for global financial institutions. The importance of risk management becomes more evident in financial instability periods. The failure of global financial institutions in the recent financial crisis revealed that firms with strong risk management and culture were more prepared and economically less damaged. As financial institutions have been criticized severely about risk management practices, it also becomes clear that most financial institutions have difficulties in developing a risk management culture. To have a clear understanding of risk management culture, the chapter aims to highlight a need to extend our understanding of risk management culture and how it can find a voice in the strategic planning of global financial institutions