352 research outputs found
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
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
Large-scale distributions of tropospheric nitric, formic, and acetic acids over the western Pacific basin during wintertime
We report here measurements of the acidic gases nitric (HNO3), formic (HCOOH), and acetic (CH3COOH) over the western Pacific basin during the February-March 1994 Pacific Exploratory Mission-West (PEM-West B). These data were obtained aboard the NASA DC-8 research aircraft as it flew missions in the altitude range of 0.3â12.5 km over equatorial regions near Guam and then further westward encompassing the entire Pacific Rim arc. Aged marine air over the equatorial Pacific generally exhibited mixing ratios of acidic gases \u3c100 parts per trillion by volume (pptv). Near the Asian continent, discrete plumes encountered below 6 km altitude contained up to 8 parts per billion by volume (ppbv) HNO3 and 10 ppbv HCOOH and CH3COOH. Overall there was a general correlation between mixing ratios of acidic gases with those of CO, C2H2, and C2Cl4, indicative of emissions from combustion and industrial sources. The latitudinal distributions of HNO3 and CO showed that the largest mixing ratios were centered around 15°N, while HCOOH, CH3COOH, and C2Cl4 peaked at 25°N. The mixing ratios of HCOOH and CH3COOH were highly correlated (r2 = 0.87) below 6 km altitude, with a slope (0.89) characteristic of the nongrowing season at midlatitudes in the northern hemisphere. Above 6 km altitude, HCOOH and CH3COOH were marginally correlated (r2 = 0.50), and plumes well defined by CO, C2H2, and C2Cl4 were depleted in acidic gases, most likely due to scavenging during vertical transport of air masses through convective cloud systems over the Asian continent. In stratospheric air masses, HNO3 mixing ratios were several parts per billion by volume (ppbv), yielding relationships with O3 and N2O consistent with those previously reported for NOy
Recommended from our members
Influence of biomass combustion emissions on the distribution of acidic trace gases over the southern Pacific basin during austral springtime
This paper describes the large-scale distributions of HNO3, HCOOH, and CH3COOH over the central and South Pacific basins during the Pacific Exploratory Mission-Tropics (PEM-Tropics) in austral springtime. Because of the remoteness of this region from continental areas, low part per trillion by volume (pptv) mixing ratios of acidic gases were anticipated to be pervasive over the South Pacific basin. However, at altitudes of 2â12 km over the South Pacific, air parcels were encountered frequently with significantly enhanced mixing ratios (up to 1200 pptv) of acidic gases. Most of these air parcels were centered in the 3â7 km altitude range and occurred within the 15°â65°S latitudinal band. The acidic gases exhibited an overall general correlation with CH3Cl, PAN, and O3, suggestive of photochemical and biomass burning sources. There was no correlation or trend of acidic gases with common industrial tracer compounds (e.g., C2Cl4 or CH3CCl3). The combustion emissions sampled over the South Pacific basin were relatively aged exhibiting C2H2/CO ratios in the range of 0.2â2.2 pptv/ppbv. The relationships between acidic gases and this ratio were similar to what was observed in aged air parcels (i.e., \u3e3â5 days since they were over a continental area) over the western North Pacific during the Pacific Exploratory Mission-West Phases A and B (PEM-West A and B). In the South Pacific marine boundary layer a median C2H2/CO ratio of 0.6 suggested that this region was generally not influenced by direct inputs of biomass combustion emissions. Here we observed the lowest mixing ratios of acidic gases, with median values of 14 pptv for HNO3, 19 pptv for HCOOH, and 18 pptv for CH3COOH. These values were coincident with low mixing ratios of NOx(\u3c10 pptv), CO (â50 parts per billion by volume (ppbv)), O3 (\u3c 20 ppbv), and long-lived hydrocarbons (e.g., C2H6 \u3c300 pptv). Overall, the PEM-Tropics data suggest an important influence of aged biomass combustion emissions on the distributions of acidic gases over the South Pacific basin in austral springtime
Recommended from our members
Reactive nitrogen in Asian continental outflow over the western Pacific: Results from the NASA Transport and Chemical Evolution over the Pacific (TRACE-P) airborne mission
We present here results for reactive nitrogen species measured aboard the NASA DC-8 aircraft during the Transport and Chemical Evolution over the Pacific (TRACE-P) mission. The large-scale distributions total reactive nitrogen (NOy,sum = NO + NO2 + HNO3 + PAN + C1âC5alkyl nitrates) and O3 and CO were better defined in the boundary layer with significant degradation of the relationships as altitude increased. Typically, NOy,sum was enhanced over background levels of âŒ260 pptv by 20-to-30-fold. The ratio C2H2/CO had values of 1â4 at altitudes up to 10 km and as far eastward as 150°E, implying significant vertical mixing of air parcels followed by rapid advection across the Pacific. Analysis air parcels originating from five principal Asian source regions showed that HNO3 and PAN dominated NOy,sum. Correlations of NOy,sum with C2Cl4 (urban tracer) were not well defined in any of the source regions, and they were only slightly better with CH3Cl (biomass tracer). Air parcels over the western Pacific contained a complex mixture of emission sources that are not easily resolvable as shown by analysis of the Shanghai mega-city plume. It contained an intricate mixture of pollution emissions and exhibited the highest mixing ratios of NOy,sum species observed during TRACE-P. Comparison of tropospheric chemistry between the earlier PEM-West B mission and the recent TRACE-P data showed that in the boundary layer significant increases in the mixing ratios of NOy,sum species have occurred, but the middle and upper troposphere seems to have been affected minimally by increasing emissions on the Asian continent over the last 7 years
Asian Influence Over the Western North Pacific during the Fall Season: Inferences from Lead 210, Soluble Ionic Species and Ozone
Aerosol samples collected over the western Pacific during the NASA/Global Tropospheric Experiment Pacific Exploratory Mission (PEM-West A) expedition (September - October 1991) revealed mean Pb-210 concentrations in the free troposphere in the 5-10 fCi m(exp -3) STP range. Most soluble ionic aerosol-associated species were near detection limits [much less than 40 parts per trillion by volume (pptv)] in these same samples. The altitude distribution of O3 near Asia closely resembled that of Pb-210, while no relationship was found between the concentrations of O3 and Be-7. Free tropospheric air over the western Pacific was depleted in soluble aerosol-associated species but enriched in Pb-210 and O3, indicative of deep wet convection over the Asian continent. The influence of Asian air on the composition of the free troposphere over the western Pacific was evident on most of the PEM-West A flights. However, evidence of continental influence was largely restricted to those species that are relatively insoluble (or have insoluble precursors), hence escape scavenging during vertical transport from the boundary layer into the free troposphere by wet convective activity
Fixation, transient landscape and diffusion's dilemma in stochastic evolutionary game dynamics
Agent-based stochastic models for finite populations have recently received
much attention in the game theory of evolutionary dynamics. Both the ultimate
fixation and the pre-fixation transient behavior are important to a full
understanding of the dynamics. In this paper, we study the transient dynamics
of the well-mixed Moran process through constructing a landscape function. It
is shown that the landscape playing a central theoretical "device" that
integrates several lines of inquiries: the stable behavior of the replicator
dynamics, the long-time fixation, and continuous diffusion approximation
associated with asymptotically large population. Several issues relating to the
transient dynamics are discussed: (i) multiple time scales phenomenon
associated with intra- and inter-attractoral dynamics; (ii) discontinuous
transition in stochastically stationary process akin to Maxwell construction in
equilibrium statistical physics; and (iii) the dilemma diffusion approximation
facing as a continuous approximation of the discrete evolutionary dynamics. It
is found that rare events with exponentially small probabilities, corresponding
to the uphill movements and barrier crossing in the landscape with multiple
wells that are made possible by strong nonlinear dynamics, plays an important
role in understanding the origin of the complexity in evolutionary, nonlinear
biological systems.Comment: 34 pages, 4 figure
Computing optimal coalition structures in polynomial time
The optimal coalition structure determination problem is in general computationally hard. In this article, we identify some problem instances for which the
space of possible coalition structures has a certain form and constructively prove that the problem is polynomial time solvable. Specifically, we consider games with an ordering over the players and introduce a distance metric for measuring the distance between any two structures. In terms of this metric, we define the property of monotonicity, meaning that coalition structures closer to the optimal, as measured by
the metric, have higher value than those further away. Similarly, quasi-monotonicity means that part of the space of coalition structures is monotonic, while part of it is non-monotonic. (Quasi)-monotonicity is a property that can be satisfied by coalition
games in characteristic function form and also those in partition function form. For a setting with a monotonic value function and a known player ordering, we prove that the optimal coalition structure determination problem is polynomial time solvable
and devise such an algorithm using a greedy approach. We extend this algorithm to quasi-monotonic value functions and demonstrate how its time complexity improves from exponential to polynomial as the degree of monotonicity of the value function increases. We go further and consider a setting in which the value function is monotonic and an ordering over the players is known to exist but ordering itself is unknown. For this setting too, we prove that the coalition structure determination problem is polynomial time solvable and devise such an algorithm
Chemical characteristics of air from differing source regions during the Pacific Exploratory MissionâTropics A (PEMâTropics A)
Tenâday backward trajectories are used to determine the origins of air parcels arriving at airborne DCâ8 chemical measurement sites during NASA\u27s Pacific Exploratory MissionâTropics A (PEMâT) that was conducted during AugustâOctober 1996. Those sites at which the air had a common geographical origin and transport history are grouped together, and statistical measures of chemical characteristics are computed. Temporal changes in potential temperature are used to determine whether trajectories experience a significant convective influence during the 10âday period. Those trajectories that do not experience a significant convective influence are divided into four geographical categories depending on their origins and paths. Air parcels originating over Africa and South America are characterized by enhanced mixing ratios of O3, CO, HNO3, and PAN. The backward trajectories travel at high altitudes (âŒ10â11 km), covering long distances due to strong upperâtropospheric westerly winds. The observed enhancement of combustionârelated species is attributed to biomass burning from distant sources to the west, extending even to South America. The relatively large value of Beâ7 probably is due either to less efficient removal of aerosols from upper tropospheric air or to small stratospheric contributions. Aged marine parcels are found to have relatively small concentrations of burningârelated species. Although these trajectories arrive at a wide range of aircraft altitudes, they do not pass over a land mass during the preceding 10âday period. Air passing over Australia but no other land mass exhibits a combustion signature; however, photochemical product species such as O3 and PAN are less enhanced than in the longârange transport category. These trajectories travel shorter distances and are at lower altitudes (âŒ5â8 km) than those reaching Africa and/or South America. The combustion influence on these parcels is attributed to biomass burning emissions injected over Australia. That burning is less widespread than in Africa and South America. Finally, trajectories originating over Southeast Asia appear to receive a weak combustion influence. However, compared to Africa and South America, Southeast Asia has a relatively small incidence of biomass burning. There is little combustion input from Australia due to the high transport altitudes compared to the lower heights of the convection. The Southeast Asian parcels exhibit the greatest NOx to âNOi ratio of any category, perhaps due to lightning. Parcels experiencing a significant convective influence also are examined. Most of these parcels pass through widespread, persistent convection along either the South Pacific Convergence Zone or Intertropical Convergence Zone approximately 5 days prior to arriving at the aircraft locations. Thus the category mostly represents marine convection. Mixing ratios of peroxides and acids in the convective category are found to be smaller than in parcels not experiencing convection. Small mixing ratios of Beâ7 and Pbâ210 suggest particle removal by precipitation
Recommended from our members
Atmospheric sampling of Supertyphoon Mireille with NASA DC-8 aircraft on September 27,1991, during PEM-West A
The DC-8 mission of September 27, 1991, was designed to sample air flowing into Typhoon Mireille in the boundary layer, air in the upper tropospheric eye region, and air emerging from the typhoon and ahead of the system, also in the upper troposphere. The objective was to find how a typhoon redistributes trace constituents in the West Pacific region and whether any such redistribution is important on the global scale. The boundary layer air (300 m), in a region to the SE of the eye, contained low mixing ratios of the tracer species O3, CO, C2H6, C2H2, C3H8, C6H6and CS2 but high values of dimethylsulfide (DMS). The eye region relative to the boundary layer, showed somewhat elevated levels of CO, substantially increased levels of O3, CS2 and all nonmethane hydrocarbons (NMHCs), and somewhat reduced levels of DMS. Ahead of the eye, CO and the NMHCs remained unchanged, O3 and CS2 showed a modest decrease, and DMS showed a substantial decrease. There was no evidence from lidar cross sections of ozone for the downward entrainment of stratospheric air into the eye region; these sections show that low ozone values were measured in the troposphere. The DMS data suggest substantial entrainment of boundary layer air into the system, particularly into the eye wall region. Estimates of the DMS sulphur flux between the boundary layer and the free troposphere, based on computations of velocity potential and divergent winds, gave values of about 69 ÎŒg S mâ2 dâ1 averaged over a 17.5° grid square encompassing the typhoon. A few hours after sampling with the DC-8, Mireille passed over Oki Island, just to the north of Japan, producing surface values of ozone of 5.5 ppbv. These O3 levels are consistent with the low tropospheric values found by lidar and are more typical of equatorial regions. We suggest that the central eye region may act like a Taylor column which has moved poleward from low latitudes. The high-altitude photochemical environment within Typhoon Mireille was found to be quite active as evidenced by significant levels of measured gas phase H2O2 and CH3OOH and model-computed levels of OH
- âŠ