Cognition and framing in sequential bargaining for gains and losses

Noncooperative game-theoretic models of sequential bargaining give an underpinning to cooperative solution concepts derived from axioms, and have proved useful in applications (see Osborne and Rubinstein 1990). But experimental studies of sequential bargaining with discounting have generally found systematic deviations between the offers people make and perfect equilibrium offers derived from backward induction (e.g., Ochs and Roth 1989). We have extended this experimental literature in two ways. First, we used a novel software system to record the information subjects looked at while they bargained. Measuring patterns of information search helped us draw inferences about how people think, testing as directly as possible whether people use backward induction to compute offers. Second, we compared bargaining over gains that shrink over time (because of discounting) to equivalent bargaining over losses that expand over time. In the games we studied, two players bargain by making a finite number of alternating offers. A unique subgame-perfect equilibrium can be computed by backward induction. The induction begins in the last period and works forward. Our experiments use a three-round game with a pie of $5.00 and a 50-percent discount factor (so the pie shrinks to$2.50 and $1.25 in the second and third rounds). In the perfect equilibrium the first player offers the second player$1.25 and keeps $3.75

The process-performance paradox in expert judgment - How can experts know so much and predict so badly?

A mysterious fatal disease strikes a large minority of the population. The disease is incurable, but an expensive drug can keep victims alive. Congress decides that the drug should be given to those whose lives can be extended longest, which only a few specialists can predict. The experts work around the clock searching for a cure; allocating the drug is a new chore they would rather avoid

A note on reducing spurious pressure oscillations in fully conservative discontinuous Galerkin simulations of multicomponent flows

A well-known issue associated with the use of fully conservative schemes in multicomponent-flow simulations is the generation of spurious pressure oscillations at contact interfaces. These oscillations can rapidly lead to solver divergence even in the presence of smooth interfaces that are not fully resolved. In this note, we compare various strategies for reducing such oscillations that do not (a) introduce conservation error, (b) rely on artificial viscosity or limiting, or (c) degrade order of accuracy in smooth regions of the flow. The considered test case is one-dimensional advection of a high-pressure nitrogen/n-dodecane thermal bubble using the thermally perfect gas model. Several results are presented that contradict those corresponding to the more conventional hydrogen/oxygen thermal-bubble case

Detecting Failures of Backward Induction: Monitoring Information Search in Sequential Bargaining

We ran three-round sequential bargaining experiments in which the perfect equilibrium offer was $1.25 and an equal split was$2.50. Subjects offered $2.11 to other subjects,$1.84 to “robot” players (who are known to play subgame perfectly), and $1.22 to robots after instruction in backward induction. Measures of information search showed that subjects did not look at the amounts being divided in different rounds in the correct order, and for the length of time, necessary for backward induction, unless they were specifically instructed. The results suggest that most of the departure from perfect equilibrium is due to limited computation and some is due to fairness

The Panchromatic Hubble Andromeda Treasury. VI. The reliability of far-ultraviolet flux as a star formation tracer on sub-kpc scales

We have used optical observations of resolved stars from the Panchromatic Hubble Andromeda Treasury (PHAT) to measure the recent (< 500 Myr) star formation histories (SFHs) of 33 FUV-bright regions in M31. The region areas ranged from ~$10^4$ to $10^6$ pc$^2$, which allowed us to test the reliability of FUV flux as a tracer of recent star formation on sub-kpc scales. The star formation rates (SFRs) derived from the extinction-corrected observed FUV fluxes were, on average, consistent with the 100-Myr mean SFRs of the SFHs to within the 1$\sigma$ scatter. Overall, the scatter was larger than the uncertainties in the SFRs and particularly evident among the smallest regions. The scatter was consistent with an even combination of discrete sampling of the initial mass function and high variability in the SFHs. This result demonstrates the importance of satisfying both the full-IMF and the constant-SFR assumptions for obtaining precise SFR estimates from FUV flux. Assuming a robust FUV extinction correction, we estimate that a factor of 2.5 uncertainty can be expected in FUV-based SFRs for regions smaller than $10^5$ pc$^2$, or a few hundred pc. We also examined ages and masses derived from UV flux under the common assumption that the regions are simple stellar populations (SSPs). The SFHs showed that most of the regions are not SSPs, and the age and mass estimates were correspondingly discrepant from the SFHs. For those regions with SSP-like SFHs, we found mean discrepancies of 10 Myr in age and a factor of 3 to 4 in mass. It was not possible to distinguish the SSP-like regions from the others based on integrated FUV flux.Comment: Accepted for publication in The Astrophysical Journa

Development of Dual-Gain SiPM Boards for Extending the Energy Dynamic Range

Astronomical observations with gamma rays in the range of several hundred keV to hundreds of MeV currently represent the least explored energy range. To address this so-called MeV gap, we designed and built a prototype CsI:Tl calorimeter instrument using a commercial off-the-shelf (COTS) SiPMs and front-ends which may serve as a subsystem for a larger gamma-ray mission concept. During development, we observed significant non-linearity in the energy response. Additionally, using the COTS readout, the calorimeter could not cover the four orders of magnitude in energy range required for the telescope. We, therefore, developed dual-gain silicon photomultiplier (SiPM) boards that make use of two SiPM species that are read out separately to increase the dynamic energy range of the readout. In this work, we investigate the SiPM's response with regards to active area ($3\times3 \ \mathrm{mm}^2$ and $1 \times 1 \ \mathrm{mm}^2$) and various microcell sizes ($10$, $20$, and $35 \ \mu \mathrm{m}$). We read out $3\times3\times6 \ \mathrm{cm}^3$ CsI:Tl chunks using dual-gain SiPMs that utilize $35 \ \mu \mathrm{m}$ microcells for both SiPM species and demonstrate the concept when tested with high-energy gamma-ray and proton beams. We also studied the response of $17 \times 17 \times 100 \ \mathrm{mm}^3$CsI bars to high-energy protons. With the COTS readout, we estimate (with several assumptions) that the dual-gain prototype has an energy range of$0.25-400 \ \mathrm{MeV}$with the two SiPM species overlapping at a range of around$2.5-30 \ \mathrm{MeV}$. This development aims to demonstrate the concept for future scintillator-based high-energy calorimeters with applications in gamma-ray astrophysics

Positivity-preserving and entropy-bounded discontinuous Galerkin method for the chemically reacting, compressible Navier-Stokes equations

This article concerns the development of a fully conservative, positivity-preserving, and entropy-bounded discontinuous Galerkin scheme for simulating the multicomponent, chemically reacting, compressible Navier-Stokes equations with complex thermodynamics. In particular, we extend to viscous flows the fully conservative, positivity-preserving, and entropy-bounded discontinuous Galerkin method for the chemically reacting Euler equations that we previously introduced. An important component of the formulation is the positivity-preserving Lax-Friedrichs-type viscous flux function devised by Zhang [J. Comput. Phys., 328 (2017), pp. 301-343], which was adapted to multicomponent flows by Du and Yang [J. Comput. Phys., 469 (2022), pp. 111548] in a manner that treats the inviscid and viscous fluxes as a single flux. Here, we similarly extend the aforementioned flux function to multicomponent flows but separate the inviscid and viscous fluxes. This separation of the fluxes allows for use of other inviscid flux functions, as well as enforcement of entropy boundedness on only the convective contribution to the evolved state, as motivated by physical and mathematical principles. We also discuss in detail how to account for boundary conditions and incorporate previously developed pressure-equilibrium-preserving techniques into the positivity-preserving framework. Comparisons between the Lax-Friedrichs-type viscous flux function and more conventional flux functions are provided, the results of which motivate an adaptive solution procedure that employs the former only when the element-local solution average has negative species concentrations, nonpositive density, or nonpositive pressure. A variety of multicomponent, viscous flows is computed, ranging from a one-dimensional shock tube problem to multidimensional detonation waves and shock/mixing-layer interaction