Sets in Excess Demand in Ascending Auctions with Unit-Demand Bidders

This paper analyzes the problem of selling a number of indivisible items to a set of unitdemand bidders. An ascending auction mechanism called the Excess Demand Ascending Auction (EDAA) is defined. The main results demonstrate that EDAA terminates in a finite number of iterations and that the exact auction mechanism in Demange, Gale and Sotomayor (J. Polit. Economy 94: 863–872, 1986) and its modification based on the Ford- Fulkerson method, proposed by Sankaran (Math. Soc. Sci. 28: 143–150, 1994), reduce to special cases of EDAA.Multi-item auction;Unit-demand bidders;Excess demand;Algorithms

Corporatism and Economic Performance

This paper models corporatism as affecting both the preferences of the parties involved as well as the rules of the game. The analysis is conducted in a union-government game on determining wages and unemployment benefits. The result indicates that international conditions might be important for the functions of the concept of corporatism. It may also serve as an explanation to the poor performance on production and employment in some of the former so successful European corporatist states in the 1990s. The implication of this is that corporatism might not be a successful social organisation in the globalised economy.Corporatism; Interest groups; Labour unions

Seismology of adolescent neutron stars: Accounting for thermal effects and crust elasticity

We study the oscillations of relativistic stars, incorporating key physics associated with internal composition, thermal gradients and crust elasticity. Our aim is to develop a formalism which is able to account for the state-of-the-art understanding of the complex physics associated with these systems. As a first step, we build models using a modern equation of state including composition gradients and density discontinuities associated with internal phase-transitions (like the crust-core transition and the point where muons first appear in the core). In order to understand the nature of the oscillation spectrum, we carry out cooling simulations to provide realistic snapshots of the temperature distribution in the interior as the star evolves through adolescence. The associated thermal pressure is incorporated in the perturbation analysis, and we discuss the presence of $g$-modes arising as a result of thermal effects. We also consider interface modes due to phase-transitions and the gradual formation of the star's crust and the emergence of a set of shear modes.Comment: 27 pages, 14 figure

Buoyancy and g-modes in young superfluid neutron stars

We consider the local dynamics of a realistic neutron star core, including composition gradients, superfluidity and thermal effects. The main focus is on the gravity g-modes, which are supported by composition stratification and thermal gradients. We derive the equations that govern this problem in full detail, paying particular attention to the input that needs to be provided through the equation of state and distinguishing between normal and superfluid regions. The analysis highlights a number of key issues that should be kept in mind whenever equation of state data is compiled from nuclear physics for use in neutron star calculations. We provide explicit results for a particular stellar model and a specific nucleonic equation of state, making use of cooling simulations to show how the local wave spectrum evolves as the star ages. Our results show that the composition gradient is effectively dominated by the muons whenever they are present. When the star cools below the superfluid transition, the support for g-modes at lower densities (where there are no muons) is entirely thermal. We confirm the recent suggestion that the g-modes in this region may be unstable, but our results indicate that this instability will be weak and would only be present for a brief period of the star's life. Our analysis accounts for the presence of thermal excitations encoded in entrainment between the entropy and the superfluid component. Finally, we discuss the complete spectrum, including the normal sound waves and, in superfluid regions, the second sound.Comment: 29 pages, 9 figures, submitted to MNRA

Robustness to Strategic Uncertainty (Revision of DP 2010-70)

We model a player’s uncertainty about other players’ strategy choices as smooth probability distributions over their strategy sets. We call a strategy profile (strictly) robust to strategic uncertainty if it is the limit, as uncertainty vanishes, of some sequence (all sequences) of strategy profiles, in each of which every player’s strategy is optimal under under his or her uncertainty about the others. We derive general properties of such robustness, and apply the definition to Bertrand competition games and the Nash demand game, games that admit infinitely many Nash equilibria. We show that our robustness criterion selects a unique Nash equilibrium in the Bertrand games, and that this agrees with recent experimental findings. For the Nash demand game, we show that the less uncertain party obtains the bigger share.Nash equilibrium;refinement;strategic uncertainty;price competition;Bertrand competition;bargaining;Nash demand game

Relativistic Two-stream Instability

We study the (local) propagation of plane waves in a relativistic, non-dissipative, two-fluid system, allowing for a relative velocity in the "background" configuration. The main aim is to analyze relativistic two-stream instability. This instability requires a relative flow -- either across an interface or when two or more fluids interpenetrate -- and can be triggered, for example, when one-dimensional plane-waves appear to be left-moving with respect to one fluid, but right-moving with respect to another. The dispersion relation of the two-fluid system is studied for different two-fluid equations of state: (i) the "free" (where there is no direct coupling between the fluid densities), (ii) coupled, and (iii) entrained (where the fluid momenta are linear combinations of the velocities) cases are considered in a frame-independent fashion (eg. no restriction to the rest-frame of either fluid). As a by-product of our analysis we determine the necessary conditions for a two-fluid system to be causal and absolutely stable and establish a new constraint on the entrainment.Comment: 15 pages, 2 eps-figure

Verifying black hole orbits with gravitational spectroscopy

Gravitational waves from test masses bound to geodesic orbits of rotating black holes are simulated, using Teukolsky's black hole perturbation formalism, for about ten thousand generic orbital configurations. Each binary radiates power exclusively in modes with frequencies that are integer-linear-combinations of the orbit's three fundamental frequencies. The following general spectral properties are found with a survey of orbits: (i) 99% of the radiated power is typically carried by a few hundred modes, and at most by about a thousand modes, (ii) the dominant frequencies can be grouped into a small number of families defined by fixing two of the three integer frequency multipliers, and (iii) the specifics of these trends can be qualitatively inferred from the geometry of the orbit under consideration. Detections using triperiodic analytic templates modeled on these general properties would constitute a verification of radiation from an adiabatic sequence of black hole orbits and would recover the evolution of the fundamental orbital frequencies. In an analogy with ordinary spectroscopy, this would compare to observing the Bohr model's atomic hydrogen spectrum without being able to rule out alternative atomic theories or nuclei. The suitability of such a detection technique is demonstrated using snapshots computed at 12-hour intervals throughout the last three years before merger of a kludged inspiral. Because of circularization, the number of excited modes decreases as the binary evolves. A hypothetical detection algorithm that tracks mode families dominating the first 12 hours of the inspiral would capture 98% of the total power over the remaining three years.Comment: 18 pages, expanded section on detection algorithms and made minor edits. Final published versio

Implications of an r-mode in XTE J1751-305: Mass, radius and spin evolution

Recently Strohmayer and Mahmoodifar presented evidence for a coherent oscillation in the X-ray light curve of the accreting millisecond pulsar XTE J1751-305, using data taken by RXTE during the 2002 outburst of this source. They noted that a possible explanation includes the excitation of a non-radial oscillation mode of the neutron star, either in the form of a g-mode or an r-mode. The r-mode interpretation has connections with proposed spin-evolution scenarios for systems such as XTE J1751-305. Here we examine in detail this interesting possible interpretation. Using the ratio of the observed oscillation frequency to the star's spin frequency, we derive an approximate neutron star mass-radius relation which yields reasonable values for the mass over the range of expected stellar radius (as constrained by observations of radius-expansion burst sources). However, we argue that the large mode amplitude suggested by the Strohmayer and Mahmoodifar analysis would inevitably lead to a large spin-down of the star, inconsistent with its observed spin evolution, regardless of whether the r-mode itself is in a stable or unstable regime. We therefore conclude that the r-mode interpretation of the observed oscillation is not consistent with our current understanding of neutron star dynamics and must be considered unlikely. Finally we note that, subject to the availability of a sufficiently accurate timing model, a direct gravitational-wave search may be able to confirm or reject an r-mode interpretation unambiguously, should such an event, with a similar inferred mode amplitude, recur during the Advanced detector era.Comment: 8 pages, 3 figures; submitted to MNRA

Pulsar spin-down: the glitch-dominated rotation of PSR J0537-6910

The young, fast-spinning, X-ray pulsar J0537-6910 displays an extreme glitch activity, with large spin-ups interrupting its decelerating rotation every ~100 days. We present nearly 13 years of timing data from this pulsar, obtained with the {\it Rossi X-ray Timing Explorer}. We discovered 22 new glitches and performed a consistent analysis of all 45 glitches detected in the complete data span. Our results corroborate the previously reported strong correlation between glitch spin-up size and the time to the next glitch, a relation that has not been observed so far in any other pulsar. The spin evolution is dominated by the glitches, which occur at a rate ~3.5 per year, and the post-glitch recoveries, which prevail the entire inter-glitch intervals. This distinctive behaviour provides invaluable insights into the physics of glitches. The observations can be explained with a multi-component model which accounts for the dynamics of the neutron superfluid present in the crust and core of neutron stars. We place limits on the moment of inertia of the component responsible for the spin-up and, ignoring differential rotation, the velocity difference it can sustain with the crust. Contrary to its rapid decrease between glitches, the spin-down rate increased over the 13 years, and we find the long-term braking index $n_{\rm l}=-1.22(4)$, the only negative braking index seen in a young pulsar. We briefly discuss the plausible interpretations of this result, which is in stark contrast to the predictions of standard models of pulsar spin-down.Comment: Minor changes to match the MNRAS accepted versio