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In monotone simple games, larger coalitions typically wield more power, but do all players align their efforts effectively? Consider a voting scenario where a coalition forms, but needs more voters to pass a bill. The cohesion of the new group of voters hinges on whether all the new members can proficiently collaborate with the existing players to ensure the bill's passage or if subgroups form that pursue an independent alternative, thus generating antagonism among the new voters. This research introduces the coopetition index, ranging from -1 to 1, to measure agents' preferences for cooperation (near 1) or competition (near -1) with the remaining players. We also introduce the Banzhaf and Shapley-Owen coopetition indices, addressing limitations of previous indices. By applying our index to the apex game and symmetric majority games, we observe that cooperation and competition frequently balance each other out, leading to null values for the Shapley-Owen and Banzhaf coopetition indices. To distinguish balanced scenarios from those involving powerless coalitions, we define a decisiveness index that measures the extent of coalition involvement in negotiations., Comment: 24 pages, 4 tables

We define a notion of the criticality of a player for simple monotone games based on cooperation with other players, either to form a winning coalition or to break a winning one, with an essential role for all the players involved. We compare it with the notion of differential criticality given by Beisbart that measures power as the opportunity left by other players. We prove that our proposal satisfies an extension of the strong monotonicity introduced by Young, assigns no power to null players and does not reward free riders, and can easily be computed from the minimal winning and blocking coalitions. An application to the Italian elections is presented. Our analysis shows that the measures of group criticality defined so far cannot weigh essential players while only remaining an opportunity measure. We propose a group opportunity test to reconcile the two views., Comment: 28 pages, 5 tables, 5 figures. First presented at the 12th Conference on Economic Design, Padova, June 9, 2022 and at EURO 2022, Espoo, July 6, 2022

Inheritances, divorces or liquidations of companies require common assets to be divided among the entitled parties. Legal methods usually consider the market value of goods, while fair division theory takes into account the parties' preferences expressed as utilities. I combine the two practices to define a procedure that optimally allocates divisible goods with market values to people with easily elicited preferences. Imposing exact equality in the bundles' monetary values may produce unacceptable solutions. I drop the tight requirement and suggest a procedure in which the differences in the monetary values are explained in terms of satisfaction per monetary share as perceived by the agents. A robustness study shows the consequences of misspecification in the model parameters., Comment: 49 pages, 9 figures, 14 tables

In Briata, Dall'Aglio and Fragnelli (2012), the authors introduce a cooperative game with transferable utility for allocating the gain of a collusion among completely risk-averse agents involved in the fair division procedure introduced by Knaster (1946). In this paper we analyze the Shapley value (Shapley, 1953) of the game and propose its use as a measure of the players' attitude towards collusion. Furthermore, we relate the sign of the Shapley value with the ranking order of the players' evaluation, and show that some players in a given ranking will always deter collusion. Finally, we characterize the coalitions that maximize the gain from collusion, and suggest an ad-hoc coalition formation mechanism., Comment: 20 pages, 1 table. This new version corrects some mistakes and improves the layout

We consider the division of a finite number of homogeneous divisible items among three players. Under the assumption that each player assigns a positive value to every item, we characterize the optimal allocations and we develop two exact algorithms for its search. Both the characterization and the algorithm are based on the tight relationship two geometric objects of fair division: the Individual Pieces Set (IPS) and the Radon-Nykodim Set (RNS)., Comment: 28 pages, 10 figures

In this paper we deal with parabolic problems whose simplest model is $$ \begin{cases} u'- \Delta_{p} u + B\frac{|\nabla u|^p}{u} = 0 & \text{in} (0,T) \times \Omega,\newline u(0,x)= u_0 (x) &\text{in}\ \Omega, \newline u(t,x)=0 &\text{on}\ (0,T) \times \partial\Omega, \end{cases} $$ where $T>0$, $N\geq 2$, $p>1$, $B > 0$, and $u_{0}$ is a positive function in $L^{\infty}(\Omega)$ bounded away from zero.

We provide a two-sided inequality for the alpha-optimal partition value of a measurable space according to n nonatomic finite measures. The result extends and often improves Legut (1988) since the bounds are obtained considering several partitions that maximize the weighted sum of the partition values with varying weights, instead of a single one., Comment: 14 pages, 1 figure. This version contains a corrected proof of part (i) of Theorem 2

Interval bankruptcy problems arise in situations where an estate has to be liquidated among a fixed number of creditors and uncertainty about the amounts of the claims is modeled by intervals. We extend in the interval setting the classical results by Curiel, Maschler and Tijs (1987) that characterize division rules which correspond to solutions of the cooperative bankruptcy game. Finally, we analyze the difficulties with incorporating the uncertainty about the estate., Comment: 14 pages, no figures. Updated version of the CentER Discussion Paper Series (No. 2008-97) Tilburg University

We present the first search for galaxy counterparts of intervening high-z (2

In this paper, we study the regularity of weak solutions and subsolutions of second-order elliptic equations having a gradient term with superquadratic growth. We show that, under appropriate integrability conditions on the data, all weak subsolutions in a bounded and regular open set $\Om$ are H\"older-continuous up to the boundary of $\Om$. Some local and global summability results are also presented. The main feature of this kind of problems is that the gradient term, not the principal part of the operator, is responsible for the regularity., Comment: 26 pages

The classical Bayesian posterior arises naturally as the unique solution of several different optimization problems, without the necessity of interpreting data as conditional probabilities and then using Bayes' Theorem. For example, the classical Bayesian posterior is the unique posterior that minimizes the loss of Shannon information in combining the prior and the likelihood distributions. These results, direct corollaries of recent results about conflations of probability distributions, reinforce the use of Bayesian posteriors, and may help partially reconcile some of the differences between classical and Bayesian statistics., Comment: 6 pages, no figures

We consider upper and lower bounds for maxmin allocations of a completely divisible good in both competitive and cooperative strategic contexts. We then derive a subgradient algorithm to compute the exact value up to any fixed degree of precision., Comment: 20 pages, 3 figures. This third version improves the overll presentation; Optimization and Control (math.OC), Computer Science and Game Theory (cs.GT), Probability (math.PR)

The paper search for the minimum of the entropy of a two- dimensional distribution in the Fr\'echet class, the class of distributions with given marginals. The main result for discrete distributions is an algorithm for building the minimizing distribution, which is given by the maximum distribution function of the Fr\'echet class after a suitable rearrangement of the rows and of the columns. For absolutely continuous distributions a minimum does not exists, and the infimum is equal to -\infty.

We report on the detection of strongly varying intergalactic HeII absorption in HST/COS spectra of two z~3 quasars. From our homogeneous analysis of the HeII absorption in these and three archival sightlines, we find a marked increase in the mean HeII effective optical depth from tau~1 at z~2.3 to tau>5 at z~3.2, but with a large scatter of 2< tau <5 at 2.7< z <3 on scales of ~10 proper Mpc. This scatter is primarily due to fluctuations in the HeII fraction and the HeII-ionizing background, rather than density variations that are probed by the co-eval HI forest. Semianalytic models of HeII absorption require a strong decrease in the HeII-ionizing background to explain the strong increase of the absorption at z>2.7, probably indicating HeII reionization was incomplete at z>2.7. Likewise, recent three-dimensional numerical simulations of HeII reionization qualitatively agree with the observed trend only if HeII reionization completes at z=2.7 or even below, as suggested by a large tau>3 in two of our five sightlines at z<2.8. By doubling the sample size at 2.7< z <3, our newly discovered HeII sightlines for the first time probe the diversity of the second epoch of reionization when helium became fully ionized., Comment: 6 pages, 4 color figures; ApJL in press; One clarification, typo corrections

We study the proximity effect in the Ly-a forest around high redshift quasars as a function of redshift and environment employing a set of 3D radiative transfer simulations. The analysis is based on dark matter only simulations at redshifts 3, 4, and 4.9 and, adopting an effective equation of state for the baryonic matter, we infer the HI densities and temperatures in the cosmological box. The UV background (UVB) and additional QSO radiation with Lyman limit flux of L_{\nu LL} = 1e31 and 1e32 erg / Hz s are implemented with a radiative transfer code until an equilibrium configuration is reached. We analyse mock spectra originating at the QSO in the most massive halo, in a random filament and in a void. The proximity effect is studied using flux transmission statistics, in particular with the normalised optical depth. Beyond a radius of r > 1 Mpc / h from the quasar, we measure a transmission profile consistent with geometric dilution of the QSO ionising radiation. A departure from geometric dilution is only seen, when strong absorbers intervene the line-of-sight. The cosmic density distribution around the QSO causes a large scatter in the normalised optical depth. The scatter decreases with increasing redshift and increasing QSO luminosity. The mean proximity effect provides an average signal that is biased by random large scale density enhancements on scales up to r \approx 15 Mpc / h. The distribution of the proximity effect strength provides a measure of the proximity effect along individual lines of sight. It shows a clear maximum almost without an environmental bias. Therefore it can be used for an unbiased estimate of the UVB. Differing spectral energy distributions between the QSO and the UVB modify the profile which can be reasonably well corrected analytically. A few Lyman limit systems have been identified that prevent the detection of the proximity effect due to shadowing., Comment: 18 pages, 16 figures, submitted to A&A, including corrections due to the referees report

The amplitude of fluctuations in the Ly-a forest on small spatial scales is sensitive to the temperature of the IGM and its spatial fluctuations. The temperature of the IGM and its spatial variations contain important information about hydrogen and helium reionization. We present a new measurement of the small-scale structure in the Ly-a forest from 40 high resolution, high signal-to-noise, VLT spectra at z=2.2-4.2. We convolve each Ly-a forest spectrum with a suitably chosen wavelet filter, which allows us to extract the amount of small-scale structure in the forest as a function of position across each spectrum. We compare these measurements with high resolution hydrodynamic simulations of the Ly-a forest which track more than 2 billion particles. This comparison suggests that the IGM temperature close to the cosmic mean density (T_0) peaks near z=3.4, at which point it is greater than 20,000 K at 2-sigma confidence. The temperature at lower redshift is consistent with the fall-off expected from adiabatic cooling ($T_0 \propto (1+z)^2$), after the peak temperature is reached near z=3.4. At z=4.2 our results favor a temperature of T_0 = 15-20,000 K. However, owing mostly to uncertainties in the mean transmitted flux at this redshift, a cooler IGM model with T_0 = 10,000 K is only disfavored at the 2-sigma level here, although such cool IGM models are strongly discrepant with the z ~ 3-3.4 measurement. We do not detect large spatial fluctuations in the IGM temperature at any redshift covered by our data set. The simplest interpretation of our measurements is that HeII reionization completes sometime near z ~ 3.4, although statistical uncertainties are still large [Abridged]., Comment: Submitted to ApJ. Best printed in color

(Abridged) We present the results from the largest investigation to date of the proximity effect in the HI Lyalpha forest, using the fifth SDSS data release. The sample consists of 1733 QSOs at redshifts z>2.3 and S/N>10. We adopted the flux statistic to infer the evolution of the HI effective optical depth in the Lyalpha forest between 23., Comment: 14 pages, 14 figures, submitted to the Astrophysical Journal

Using numerical simulations of structure formation, we investigate multiple methods of determining the strength of the proximity effect in the HI Lyalpha forest. We analyze three high resolution (~10kpc) redshift snapshots (z=4,3,2.25) of a Hydro-Particle-Mesh simulation to obtain realistic absorption spectra of the HI Lyalpha forest. We begin our analysis investigating the intrinsic biases thought to arise in the widely adopted standard technique of combining multiple lines of sight when searching for the proximity effect. We confirm the existence of this biases. We then concentrate on the analysis of the proximity effect along individual lines of sight. We construct the proximity effect strength distribution (PESD) and confirm that the PESD inferred from a simple averaging technique accurately recovers the input strength of the proximity effect at all redshifts. Moreover, the PESD closely follows the behaviors found in observed samples of quasar spectra. However, the PESD obtained from our new simulated sight lines presents some differences to that of simple Monte Carlo simulations. After developing three new theoretical methods of recovering the strength of the proximity effect on individual lines of sight, we compare their accuracy to the PESD from the simple averaging technique. All our new approaches are based on the maximization of the likelihood function, albeit invoking some modifications. The new techniques presented here fail to recover the input proximity effect in an un-biased way. Thus, employing complex 3D simulations, we provide strong evidence in favor of the proximity effect strength distribution obtained from the simple averaging technique, as method of estimating the UV background intensity, free of any biases., Comment: 12 pages, 14 figures, accepted by the Astrophysical journal

We present a study of 15 long-duration gamma-ray burst (GRB) host galaxies at z>2. The GRBs are selected with available early-time afterglow spectra in order to compare interstellar medium (ISM) absorption-line properties with stellar properties of the host galaxies. In addition to five previously studied hosts, we consider new detections for the host galaxies of GRB050820 and GRB060206 and place 2-sigma upper limits to the luminosities of the remaining unidentified hosts. We examine the nature of the host galaxy population and find that (1) the UV luminosity distribution of GRB host galaxies is consistent with expectations from a UV luminosity weighted random galaxy population with a median luminosity of =0.1 L*; (2) there exists a moderate correlation between UV luminosity and SiII 1526 absorption width, which together with the observed large line widths of W(1526)>1.5 Ang for a large fraction of the objects suggests a galactic outflow driven velocity field in the host galaxies; (3) there is tentative evidence for a trend of declining ISM metallicity with decreasing galaxy luminosity in the star-forming galaxy population at z=2-4; (4) the interstellar UV radiation field is found ~ 35-350 times higher in GRB hosts than the Galactic mean value; and (5) additional galaxies are found at < 2" from the GRB host in all fields with known presence of strong MgII absorbers, but no additional faint galaxies are found at < 2" in fields without strong MgII absorbers. Our study confirms that the GRB host galaxies (with known optical afterglows) are representative of unobscured star-forming galaxies at z>2, and demonstrates that high spatial resolution images are necessary for an accurate identification of GRB host galaxies in the presence of strong intervening absorbers., Comment: 24 emulateapj pages, 24 figures, ApJ in press; full-resolution version available at http://lambda.uchicago.edu/public/tmp/ghost.pdf

We used 40 high resolution, high S/N QSO spectra at 2.1

We exploit a set of high signal-to-noise (~70), low-resolution (R~800) quasar spectra to search for the signature of the so-called proximity effect in the HI Ly alpha forest. Our sample consists of 17 bright quasars in the redshift range 2.7

We report the discovery of 14 quasars in the vicinity of HE2347-4342, one of the two quasars whose intergalactic HeII forest has been resolved with FUSE. By analysing the HI and the HeII opacity variations separately, no transverse proximity effect is detected near three foreground quasars of HE2347-4342: QSOJ23503-4328 (z=2.282, $\vartheta=3.59$ arcmin), QSOJ23500-4319 (z=2.302, $\vartheta=8.77$ arcmin) and QSOJ23495-4338 (z=2.690, $\vartheta=16.28$ arcmin). This is primarily due to line contamination and overdensities probably created by large-scale structure. By comparing the HI absorption and the corresponding HeII absorption, we estimated the fluctuating spectral shape of the extragalactic UV radiation field along this line of sight. We find that the UV spectral shape near HE2347-4342 and in the projected vicinity of the three foreground quasars is statistically harder than expected from UV background models dominated by quasars. In addition, we find three highly ionised metal line systems near the quasars. However, they do not yield further constraints on the shape of the ionising field. We conclude that the foreground quasars show a transverse proximity effect that is detectable as a local hardening of the UV radiation field, although the evidence is strongest for QSOJ23495-4338. Thus, the relative spectral hardness traces the proximity effect also in overdense regions prohibiting the traditional detection in the HI forest. Furthermore, we emphasise that softening of quasar radiation by radiative transfer in the intergalactic medium is important to understand the observed spectral shape variations. From the transverse proximity effect of QSOJ23495-4338 we obtain a lower limit on the quasar lifetime of ~25 Myr., Comment: 15 pages, 11 figures, accepted by A&A, major revision of Section 5 following the referee's comments

Tentative analysis of alternative peer review and journal models. Open Access and Impact factor issues are not covered. The bibliography, in alphabetical order, lists articles and web sites (with brief description)., Comment: 18 pages

In this paper we study the continuous dependence with respect to obstacles for obstacle problems with measure data. This is deeply investigated introducing a suitable type of convergence, which gives stability under very general hypotheses. Moreover stability with respect to H^1 and uniform convergent obstacles is proved., Comment: 25 pages

The behaviour of solutions to fourth order problems is studied through the decomposition into a system of second order ones, which leads to relaxed formulations with the introduction of measure terms. This allows to solve a shape optimization problem for a simply supported thin plate., Comment: 18 pages

We give a definition for Obstacle Problems with measure data and general obstacles. For such problems we prove existence and uniqueness of solutions and consistency with the classical theory of Variational Inequalities. Continuous dependence with respect to data is discussed., Comment: 24 pages

We study some properties of the obstacle reactions associated with the solutions of unilateral obstacle problems with measure data. These results allow us to prove that, under very weak assumptions on the obstacles, the solutions do not depend on the components of the negative parts of the data which are concentrated on sets of capacity zero. The proof is based on a careful analysis of the behaviour of the potentials of two mutually singular measures near the points where both potentials tend to infinity., Comment: 18 pages