Belief-free Equilibria in Games with Incomplete Information: Characterization and Existence

We characterize belief-free equilibria in infinitely repeated games with incomplete information with N \ge 2 players and arbitrary information structures. This characterization involves a new type of individual rational constraint linking the lowest equilibrium payoffs across players. The characterization is tight: we define a set of payoffs that contains all the belief-free equilibrium payoffs; conversely, any point in the interior of this set is a belief-free equilibrium payoff vector when players are sufficiently patient. Further, we provide necessary conditions and sufficient conditions on the information structure for this set to be non-empty, both for the case of known-own payoffs, and for arbitrary payoffs.Repeated games with incomplete information, Harsanyi doctrine, Belief-free equilibria

Barium-isotopic fractionation in seawater mediated by barite cycling and oceanic circulation

Author Posting. © The Author(s), 2015. This is the author's version of the work. It is posted here by permission of Elsevier for personal use, not for redistribution. The definitive version was published in Earth and Planetary Science Letters, 430 (2015): 511-522, doi:10.1016/j.epsl.2015.07.027.The marine biogeochemical cycle of Ba is thought to be controlled by particulate BaSO4 (barite) precipitation associated with the microbial oxidation of organic carbon and its subsequent dissolution in the BaSO4-undersaturated water column. Despite many of these processes being largely unique to Ba cycling, concentrations of Ba and Si in seawater exhibit a strong linear correlation. The reasons for this correlation are ambiguous, as are the depth ranges corresponding to the most active BaSO4 cycling and the intermediate sources of Ba to particulate BaSO4. Stable isotopic analyses of dissolved Ba in seawater should help address these issues, as Ba-isotopic compositions are predicted to be sensitive to the physical and biogeochemical process that cycle Ba. We report a new methodology for the determination of dissolved Ba-isotopic compositions in seawater and results from a 4, 500 m depth profile in the South Atlantic at 39.99 S, 0.92 E that exhibit oceanographically-consistent variation with depth. These data reveal that water masses obtain their [Ba] and Ba-isotopic signatures when at or near the surface, which relates to the cycling of marine BaSO4. The shallow origin of these signatures requires that the substantial Ba-isotopic variations in the bathypelagic zone were inherited from when those deep waters were last ventilated. Indeed, the water column below 600 m is well explained by conservative mixing of water masses with distinct [Ba] and Ba-isotopic compositions. This leads us to conclude that large scale oceanic circulation is important for sustaining the similar oceanographic distributions of Ba and Si in the South Atlantic, and possibly elsewhere. These data demonstrate that the processes of organic carbon oxidation, BaSO4 cycling, and Ba-isotopic fractionation in seawater are closely coupled, such that Ba-isotopic analyses harbor great potential as a tracer of the carbon cycle in the modern and paleo-oceans.T.J.H. acknowledges support from Makoto A. Saito (Gordon and Betty Moore Foundation; Project # 3782) and the Postdoctoral Scholar Program at the Woods Hole Oceanographic Institution, with funding provided by the Doherty Foundation. Development of Ba-isotopic protocols at NIRVANA was made possible with funding from The Andrew W. Mellon Foundation Endowed Fund for Innovative Research (T.J.H. and S.G.N.)

Analysis of high-precision vanadium isotope ratios by medium resolution MC-ICP-MS

Author Posting. © The Author(s), 2015. This is the author's version of the work. It is posted here by permission of Royal Society of Chemistry for personal use, not for redistribution. The definitive version was published in Journal of Analytical Atomic Spectrometry 31 (2016): 531-536 , doi:10.1039/C5JA00397K.We present and verify a new method to measure vanadium isotope ratios using a Thermo Scientific Neptune multi-collector inductively-coupled plasma mass spectrometer (MCICP- MS) operated in medium mass resolution mode. We collect masses 48 through 53 simultaneously using the L2, L1, Center, H1, H2 and H3 collectors. The Center cup is equipped with a 1012 ; resistor, H1 is equipped with a 1010 ; resistor, while the rest of the collectors have standard 1011 ; resistors. Unlike previous low-resolution methods, the use of medium mass resolution (=M/M ~ 4,000) permits separation of V, Ti and Cr isotopes from all interfering molecular species representing combinations of C, N, O, S, Cl, and Ar. We show that the external reproducibility follows a power law function with respect to the number of V+ ions collected and achieve an external reproducibility of ± 0.15 ‰ with total V+ ion beam intensities of ~ 1 nA. The separation of interfering molecular species from the V mass spectrum reduces the V requirement for precise isotope data to as little as 200-300 ng V per analysis — a reduction of ~90% compared with previous methods — making several low-V matrices amenable to V isotope analysis.This study was funded by a WHOI IR&D grant to SGN and NSF OCE grant 1434785 to JDO and SGN and Agouron Geobiology Fellowships to JDO and TJH.2016-11-1

Constraints on the vital effect in coccolithophore and dinoflagellate calcite by oxygen isotopic modification of seawater

Author Posting. © The Author(s), 2014. This is the author's version of the work. It is posted here by permission of Elsevier for personal use, not for redistribution. The definitive version was published in Geochimica et Cosmochimica Acta 141 (2014): 612-627, doi:10.1016/j.gca.2014.05.002.In this study, we show that there are independent controls of 18O/16O and 13C/12C fractionation in coccolithophore and dinoflagellate calcite due to the contrasting kinetics of each isotope system. We demonstrate that the direction and magnitude of the oxygen isotope fractionation with respect to equilibrium is related to the balance between calcification rate and the replenishment of the internal pool of dissolved inorganic carbon (DIC). As such, in fast growing cells, such as those of Emiliania huxleyi and Gephyrocapsa oceanica (forming the so-called “heavy group”), calcification of the internal carbon pool occurs faster than complete isotopic re-adjustment of the internal DIC pool with H2O molecules. Hence, coccoliths reflect the heavy oxygen isotope signature of the CO2 overprinting the whole DIC pool. Conversely, in large and slow growing cells, such as Coccolithus pelagicus ssp. braarudii, complete re-equilibration is achieved due to limited influx of CO2 leading to coccoliths that are precipitated in conditions close to isotopic equilibrium (“equilibrium group”). Species exhibiting the most negative oxygen isotope composition, such as Calcidiscus leptoporus (“light group”), precipitate coccolith under increased pH in the coccolith vesicle, as previously documented by the “carbonate ion effect”. We suggest that, for the carbon isotope system, any observed deviation from isotopic equilibrium is only “apparent”, as the carbon isotopic composition in coccolith calcite is controlled by a Rayleigh fractionation originating from preferential incorporation of 12C into organic matter. Therefore, species with low PIC/POC ratios as E. huxleyi and G. oceanica are shifted towards positive carbon isotope values as a result of predominant carbon fixation into the organic matter. By contrast, cells with higher PIC/POC as C. braarudii and C. leptoporus maintain, to some extent, the original negative isotopic composition of the CO2. The calcareous dinoflagellate Thoracosphaera heimii exhibits different behaviour for both isotopic systems, in particular with respect to its very negative carbon isotope composition, owing to coeval intra and extracellular biomineralisation in this group. In this study, we also investigate the sensitivity of 18O/16O fractionation to varying ambient oxygen isotope composition of the medium for inorganic, coccolithophore, and dinoflagellate calcite precipitated under controlled laboratory conditions. The varying responses of different taxa to increased oxygen isotope composition of the growth medium may point to a potential bias in sea surface temperature reconstructions that are based on the oxygen isotopic compositions of sedimentary calcite, especially during times of changing seawater oxygen isotopic composition. Overall, this study represent an important step towards establishing a mechanistic understanding of the “vital effect” in coccolith and dinoflagellate calcite, and provides valuable information for interpreting the geochemistry of the calcareous nannofossils in the sedimentary record, at both monospecific and interspecies levels.MH is grateful to the Natural Environment Research Council (NERC) for funding through Postdoctoral Fellowship (NE/H015523/1). TJH is supported by the Postdoctoral Scholar Program at the Woods Hole Oceanographic Institution, with funding provided by the Doherty Foundation. REMR was supported through European Research Council (ERC) grant SP2-GA-2008-200915

Thallium-isotopic compositions of euxinic sediments as a proxy for global manganese-oxide burial

© The Author(s), 2017. This is the author's version of the work. It is posted here under a nonexclusive, irrevocable, paid-up, worldwide license granted to WHOI. It is made available for personal use, not for redistribution. The definitive version was published in Geochimica et Cosmochimica Acta 213 (2017): 291-307, doi:10.1016/j.gca.2017.06.041.Thallium (Tl) isotopes are a new and potentially powerful paleoredox proxy that may track bottom water oxygen conditions based on the global burial flux of manganese oxides. Thallium has a residence time of ~20 thousand years, which is longer than the ocean mixing time, and it has been inferred that modern oxic seawater is conservative with respect to both concentration and isotopes. Marine sources of Tl have nearly identical isotopic values. Therefore, the Tl sinks, adsorption onto manganese oxides and low temperature oceanic crust alteration (the dominant seawater output), are the primary controls of the seawater isotopic composition. For relatively short-term, ~million years, redox events it is reasonable to assume that the dominant mechanism that alters the Tl isotopic composition of seawater is associated with manganese oxide burial because large variability in low temperature ocean crust alteration is controlled by long-term, multi-million years, average ocean crust production rates. This study presents new Tl isotope data for an open ocean transect in the South Atlantic, and depth transects for two euxinic basins (anoxic and free sulfide in the water column), the Cariaco Basin and Black Sea. The Tl isotopic signature of open ocean seawater in the South Atlantic was found to be homogeneous with ε205Tl = -6.0 ± 0.3 (± 2 SD, n = 41) while oxic waters from Cariaco and the Black Sea are -5.6 and -2.2, respectively. Combined with existing data from the Pacific and Arctic Oceans, our Atlantic data establish the conservatism of Tl isotopes in the global ocean. In contrast, partially- and predominantly-restricted basins reveal Tl isotope differences that vary between open-ocean (-6) and continental material (-2) ε205Tl, scaling with the degree of restriction. Regardless of the differences between basins, Tl is quantitatively removed from their euxinic waters below the chemocline. The burial of Tl in euxinic sediments is estimated to be an order of magnitude less than each of the modern ocean outputs and imparts no isotopic fractionation. Thallium removal into pyrite appears to be associated with a small negative fractionation between -1 and -3 ε205Tl, which renders Tl-depleted waters below the chemocline enriched in isotopically-heavy Tl. Due to the quantitative removal of Tl from euxinic seawater, Tl isotope analyses of the authigenic fraction of underlying euxinic sediments from both the Black Sea and Cariaco Basin capture the Tl isotope value of the oxic portion of their respective water column with no net isotope fractionation. Since the Tl isotope composition of seawater is largely dictated by the relative fraction of Mn-oxide burial versus oceanic crust alteration, we contend that the Tl isotope composition of authigenic Tl in black shales, deposited under euxinic conditions but well-connected to the open ocean, can be utilized to reconstruct the Tl isotope composition of seawater, and thus to reconstruct the global history of Mn-oxide burial.JDO and SGN would like to thank NSF and NASA for funding; JDO and TJH gratefully acknowledges support from the Agouron Institute Postdoctoral Fellowship Program

Reply to Morel : cadmium as a micronutrient and macrotoxin in the oceans

Author Posting. © The Author(s), 2013. This is the author's version of the work. It is posted here by permission of National Academy of Sciences for personal use, not for redistribution. The definitive version was published in Proceedings of the National Academy of Sciences of the United States of America 110 (2013): E1878, doi:10.1073/pnas.1305068110.We thank François Morel for his interest in our study. Morel states that our conclusions are based on the approximate match between the Cd-isotope composition of cultured bacteria and the fractionation of Cd isotopes seen in seawater (1). This match is only a minor component of our argument, and we welcome the opportunity to reiterate our case

A productivity collapse to end earth's great oxidation

Author Posting. © National Academy of Sciences, 2019. This article is posted here by permission of National Academy of Sciences for personal use, not for redistribution. The definitive version was published in Proceedings of the National Academy of Sciences 116 (35), (2019): 17207-17212, doi:10.1073/pnas.1900325116.It has been hypothesized that the overall size of—or efficiency of carbon export from—the biosphere decreased at the end of the Great Oxidation Event (GOE) (ca. 2,400 to 2,050 Ma). However, the timing, tempo, and trigger for this decrease remain poorly constrained. Here we test this hypothesis by studying the isotope geochemistry of sulfate minerals from the Belcher Group, in subarctic Canada. Using insights from sulfur and barium isotope measurements, combined with radiometric ages from bracketing strata, we infer that the sulfate minerals studied here record ambient sulfate in the immediate aftermath of the GOE (ca. 2,018 Ma). These sulfate minerals captured negative triple-oxygen isotope anomalies as low as ∼ −0.8‰. Such negative values occurring shortly after the GOE require a rapid reduction in primary productivity of >80%, although even larger reductions are plausible. Given that these data imply a collapse in primary productivity rather than export efficiency, the trigger for this shift in the Earth system must reflect a change in the availability of nutrients, such as phosphorus. Cumulatively, these data highlight that Earth’s GOE is a tale of feast and famine: A geologically unprecedented reduction in the size of the biosphere occurred across the end-GOE transition.Olivia M. J. Dagnaud assisted during fieldwork. S. V. Lalonde and E. A. Sperling provided helpful comments on an early version of the manuscript. We thank N. J. Planavsky and an anonymous reviewer for their constructive feedback. M.S.W.H. was supported by an NSERC PGS-D and student research grants from National Geographic, the APS Lewis and Clark Fund, Northern Science Training Program, McGill University Graduate Research Enhancement and Travel Awards, Geological Society of America, Mineralogical Association of Canada, and Stanford University. P.W.C. acknowledges support from the University of Colorado Boulder, the Agouron Institute Geobiology postdoctoral Fellowship program, a Natural Sciences and Engineering Council of Canada Postgraduate Scholarship–Doctoral Program scholarship, and the NSTP. Y.P. was supported by the Strategic Priority Research Program of CAS (XDB26000000). T.J.H. thanks Maureen E. Auro for laboratory assistance and the NSF for supporting isotope research in the NIRVANA Labs.2020-02-1

Particulate multi-element geochemical concentrations, dissolved barium concentrations and barium-isotopic data collected during the R/V Blue Heron cruise BH15-11 in Lake Superior during August 2015

Dataset: Particulate and dissolved Lake Superior geochemistryParticles are important vectors of nutrients, carbon, and several trace metals within large bodies of water. Broadly speaking, particle distributions can be classified into three major groups on the basis of their multi-element geochemistry: biogenic (organic matter-associated phases and tests); lithogenic (highly refractory rock-derived materials); and authigenic (formed in situ below the euphotic zone). We collected particulate samples spanning the full water column of Lake Superior at Stations FWM (46.998528, -91.246250) and WM (47.331611, -89.821389) during the height of 2015 summer thermal stratification (cruise BH15-11). We analyzed particle leachates for their multi-element geochemistry using ICP-MS (inductively-coupled plasma mass spectrometry) at the Woods Hole Oceanographic Institution Plasma Facility. We report elemental concentrations in Lake Superior particulate matter in (nano or pico) moles per liter, defined by a 0.44 um filter cutoff. Lithogenic cycles are resolved by Al, Fe, Ti, V, and Y; biogenic phases by Ca, Cd, P, and Sr; and authigenic processes by Ba, Cd, and Mn. Several elements exhibit hybrid-type distributions depending on the depth range under investigation. Also reported are stable barium-isotopic distributions for particulate and total dissolvable Ba, measured using multiple-collector ICP-MS and reported relative to NIST SRM 3104a in permill. For a complete list of measurements, refer to the supplemental document 'Field_names.pdf', and a full dataset description is included in the supplemental file 'Dataset_description.pdf'. The most current version of this dataset is available at: http://www.bco-dmo.org/dataset/680091NSF Division of Ocean Sciences (NSF OCE) OCE-1430015, NSF Division of Ocean Sciences (NSF OCE) OCE-144357

Reproducibility of Ba/Ca variations recorded by northeast Pacific bamboo corals

Author Posting. © American Geophysical Union, 2017. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Paleoceanography 32 (2017): 966–979, doi:10.1002/2017PA003178.Trace elemental ratios preserved in the calcitic skeleton of bamboo corals have been shown to serve as archives of past ocean conditions. The concentration of dissolved barium (BaSW), a bioactive nutrientlike element, is linked to biogeochemical processes such as the cycling and export of nutrients. Recent work has calibrated bamboo coral Ba/Ca, a new BaSW proxy, using corals spanning the oxygen minimum zone beneath the California Current System. However, it was previously unclear whether Ba/Cacoral records were internally reproducible. Here we investigate the accuracy of using laser ablation inductively coupled plasma mass spectrometry for Ba/Cacoral analyses and test the internal reproducibility of Ba/Ca among replicate radial transects in the calcite of nine bamboo corals collected from the Gulf of Alaska (643–720 m) and the California margin (870–2054 m). Data from replicate Ba/Ca transects were aligned using visible growth bands to account for nonconcentric growth; smoothed data were reproducible within ~4% for eight corals (n = 3 radii/coral). This intracoral reproducibility further validates using bamboo coral Ba/Ca for BaSW reconstructions. Sections of the Ba/Ca records that were potentially influenced by noncarbonate bound Ba phases occurred in regions where elevated Mg/Ca or Pb/Ca and coincided with anomalous regions on photomicrographs. After removing these regions of the records, increased Ba/Cacoral variability was evident in corals between ~800 and 1500 m. These findings support additional proxy validation to understand BaSW variability on interannual timescales, which could lead to new insights into deep sea biogeochemistry over the past several centuries.NSF Grant Number: OCE-1420984; NOAA/OE Grant Number: NA16RP2637; MIT-WHOI Joint Program; American Geophysical Union Travel Grant; UC Davis President's Undergraduate Fellowship; Bowdoin College Gibbons Summer Research Fellowship2018-03-1

Concentrations, ratios, and sinking fluxes of major bioelements at Ocean Station Papa

© The Author(s), 2021. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Roca-Marti, M., Benitez-Nelson, C. R., Umhau, B. P., Wyatt, A. M., Clevenger, S. J., Pike, S., Horner, T. J., Estapa, M. L., Resplandy, L., & Buesseler, K. O. Concentrations, ratios, and sinking fluxes of major bioelements at Ocean Station Papa. Elementa: Science of the Anthropocene, 9(1), (2021): 00166, https://doi.org/10.1525/elementa.2020.00166.Fluxes of major bioelements associated with sinking particles were quantified in late summer 2018 as part of the EXport Processes in the Ocean from RemoTe Sensing (EXPORTS) field campaign near Ocean Station Papa in the subarctic northeast Pacific. The thorium-234 method was used in conjunction with size-fractionated (1–5, 5–51, and >51 μm) concentrations of particulate nitrogen (PN), total particulate phosphorus (TPP), biogenic silica (bSi), and particulate inorganic carbon (PIC) collected using large volume filtration via in situ pumps. We build upon recent work quantifying POC fluxes during EXPORTS. Similar remineralization length scales were observed for both POC and PN across all particle size classes from depths of 50–500 m. Unlike bSi and PIC, the soft tissue–associated POC, PN, and TPP fluxes strongly attenuated from 50 m to the base of the euphotic zone (approximately 120 m). Cruise-average thorium-234-derived fluxes (mmol m–2 d–1) at 120 m were 1.7 ± 0.6 for POC, 0.22 ± 0.07 for PN, 0.019 ± 0.007 for TPP, 0.69 ± 0.26 for bSi, and 0.055 ± 0.022 for PIC. These bioelement fluxes were similar to previous observations at this site, with the exception of PIC, which was 1 to 2 orders of magnitude lower. Transfer efficiencies within the upper twilight zone (flux 220 m/flux 120 m) were highest for PIC (84%) and bSi (79%), followed by POC (61%), PN (58%), and TPP (49%). These differences indicate preferential remineralization of TPP relative to POC or PN and larger losses of soft tissue relative to biominerals in sinking particles below the euphotic zone. Comprehensive characterization of the particulate bioelement fluxes obtained here will support future efforts linking phytoplankton community composition and food-web dynamics to the composition, magnitude, and attenuation of material that sinks to deeper waters.The authors would like to acknowledge support from the National Aeronautics and Space Administration as part of the EXport Processes in the Ocean from RemoTe Sensing program awards 80NSSC17K0555 and 80NSSC17K0662. They also acknowledge the funding from the Woods Hole Oceanographic Institution’s Ocean Twilight Zone study for MRM and KOB, the National Science Foundation Graduate Research Fellowship Program for AMW, and the Ocean Frontier Institute for MRM