A Compromise Stable Extension of Bankruptcy Games: Multipurpose Resource Allocation

This paper considers situations characterized by a common-pool resource, which needs to be divided among agents. Each of the agents has some claim on this pool and an individual reward function for assigned resources. This paper analyzes not only the problem of max- imizing the total joint reward, but also the allocation of these rewards among the agents. Analyzing these situations a new class of transferable utility games is introduced, called multipurpose resource games. These games are based on the bankruptcy model, as intro- duced by O'Neill (1982). It is shown that every multipurpose resource game is compromise stable. Moreover, an explicit expression for the nucleolus of these games is provided.bankruptcy games;compromise stability;nucleolus

Multiple Fund Investment Situations and Related Games

This paper deals with interactive multiple fund investment situations, in which investors can invest their capital in a number of funds.The investors, however, face some restrictions.In particular, the investment opportunities of an investor depend on the behaviour of the other investors.Moreover, the individual investment returns may differ.We consider this situation from a cooperative game theory point of view.Based on different assumptions modelling the gains of joint investment, we consider corresponding types of games and analyse their properties.We propose an explicit allocation process for the maximal total investment revenues.investment trusts;cooperative games

Extensions of the t-value to NTU-games

Game Theory;econometrics

Current and fluctuation in a two-state stochastic system under non-adiabatic periodic perturbation

We calculate a current and its fluctuation in a two-state stochastic system under a periodic perturbation. The system could be interpreted as a channel on a cell surface or a single Michaelis-Menten catalyzing enzyme. It has been shown that the periodic perturbation induces so-called pump current, and the pump current and its fluctuation are calculated with the aid of the geometrical phase interpretation. We give a simple calculation recipe for the statistics of the current, especially in a non-adiabatic case. The calculation scheme is based on the non-adiabatic geometrical phase interpretation. Using the Floquet theory, the total current and its fluctuation are calculated, and it is revealed that the average of the current shows a stochastic-resonance-like behavior. In contrast, the fluctuation of the current does not show such behavior.Comment: 7 pages, 1 figur

Effects of turbulence and rotation on protostar formation as a precursor to seed black holes

Context. The seeds of the first supermassive black holes may have resulted from the direct collapse of hot primordial gas in $\gtrsim 10^4$ K haloes, forming a supermassive or quasistar as an intermediate stage. Aims. We explore the formation of a protostar resulting from the collapse of primordial gas in the presence of a strong Lyman-Werner radiation background. Particularly, we investigate the impact of turbulence and rotation on the fragmentation behaviour of the gas cloud. We accomplish this goal by varying the initial turbulent and rotational velocities. Methods. We performed 3D adaptive mesh refinement simulations with a resolution of 64 cells per Jeans length using the ENZO code, simulating the formation of a protostar up to unprecedentedly high central densities of $10^{21}$ cm$^{-3}$, and spatial scales of a few solar radii. To achieve this goal, we employed the KROME package to improve modelling of the chemical and thermal processes. Results. We find that the physical properties of the simulated gas clouds become similar on small scales, irrespective of the initial amount of turbulence and rotation. After the highest level of refinement was reached, the simulations have been evolved for an additional ~5 freefall times. A single bound clump with a radius of $2 \times 10^{-2}$ AU and a mass of ~$7 \times 10^{-2}$ M$_{\odot}$ is formed at the end of each simulation, marking the onset of protostar formation. No strong fragmentation is observed by the end of the simulations, regardless of the initial amount of turbulence or rotation, and high accretion rates of a few solar masses per year are found. Conclusions. Given such high accretion rates, a quasistar of $10^5$ M$_{\odot}$ is expected to form within $10^5$ years.Comment: 18 pages, 7 figures, fixed typos, added references and clarified some details; accepted for publication in A&

Contracts and Insurance Group Formation by Myopic Players

This paper employs a cooperative approach to insurance group formation problems.The insurance group formation is analyzed in terms of stability with respect to one-person deviations.Depending on the exact contractual setting, three stability concepts are proposed: individual, contractual and compensation stability.When we apply our general framework to the standard insurance setting of Rothschild and Stiglitz (1976), we find that, in each type of contractual setting, there are stable individually rational pooling outcomes while, on the contrary, individually rational separating outcomes are not stable.

A UV flux constraint on the formation of direct collapse black holes

The ability of metal free gas to cool by molecular hydrogen in primordial halos is strongly associated with the strength of ultraviolet (UV) flux produced by the stellar populations in the first galaxies. Depending on the stellar spectrum, these UV photons can either dissociate $\rm H_{2}$ molecules directly or indirectly by photo-detachment of $\rm H^{-}$ as the latter provides the main pathway for $\rm H_{2}$ formation in the early universe. In this study, we aim to determine the critical strength of the UV flux above which the formation of molecular hydrogen remains suppressed for a sample of five distinct halos at $z>10$ by employing a higher order chemical solver and a Jeans resolution of 32 cells. We presume that such flux is emitted by PopII stars implying atmospheric temperatures of $\rm 10^{4}$~K. We performed three-dimensional cosmological simulations and varied the strength of the UV flux below the Lyman limit in units of $\rm J_{21}$. Our findings show that the value of $\rm J_{21}^{crit}$ varies from halo to halo and is sensitive to the local thermal conditions of the gas. For the simulated halos it varies from 400-700 with the exception of one halo where $\rm J_{21}^{crit} \geq 1500$. This has important implications for the formation of direct collapse black holes and their estimated population at z > 6. It reduces the number density of direct collapse black holes by almost three orders of magnitude compared to the previous estimates.Comment: 10 pages, 6 figures, matches the accepted version to ber published in MNRAS, higher resolution version is available at http://www.astro.physik.uni-goettingen.de/~mlatif/Jcrit.pd