Stable Sets and Public Projects

We introduce von Neumann-Morgenstern solution concepts in market models involving the choice of a public project. We show that vN-M stable sets, suitably defined in connection to public goods provision, are consistent with results from bargaining via cartels. We find as necessary the assumption that stability is defined with respect to blocking procedures in which coalitions do not necessarily pay for the whole realization of the project, but only for a fraction of it and that costs are distributed uniformly in each corner of the market. Under this assumption, we obtain large games solutions by the finite ones via embedding procedures. Going further in the investigation of stable solutions, we define stable sets following the “sophisticated” approach suggested by Harsanyi (see [15] and [17]), proving that a sigma-sophisticated stable set corresponds to the solution in the associated payoff space.Public project, sigma-core, von Neumann-Morgenstern sigma-stable set, sigma-sophisticated stable sets

A Limit Theorem for Equilibria under Ambiguous Beliefs Correspondences

Previous literature shows that, in many different models, limits of equilibria of perturbed games are equilibria of the unperturbed game when the sequence of perturbed games converges to the unperturbed one in an appropriate sense. The question whether such limit property extends to the equilibrium notions in ambiguous games is not yet clear as it seems; in fact, previous literature shows that the extension fails in simple examples. The contribution in this paper is to show that the limit property holds for equilibria under ambiguous beliefs correspondences (presented by the authors in a previous paper). Key for our result is the sequential convergence assumption imposed on the sequence of beliefs correspondences. Counterexamples show why this assumption cannot be removed.Ambiguous games, beliefs correspondences, limit equilibria

RASS-SDSS Galaxy Cluster Survey. VII. On the Cluster Mass to Light ratio and the Halo Occupation Distribution

We explore the mass-to-light ratio in galaxy clusters and its relation to the cluster mass. We study the relations among the optical luminosity ($L_{op}$), the cluster mass ($M_{200}$) and the number of cluster galaxies within $r_{200}$ ($N_{gal}$) in a sample of 217 galaxy clusters with confirmed 3D overdensity. We correct for projection effects, by determining the galaxy surface number density profile in our cluster sample. This is best fitted by a cored King profile in low and intermediate mass systems. The core radius decreases with cluster mass, and, for the highest mass clusters, the profile is better represented by a generalized King profile or a cuspy Navarro, Frenk & White profile. We find a very tight proportionality between $L_{op}$ and $N_{gal}$, which, in turn, links the cluster mass-to-light ratio to the Halo Occupation Distribution $N_{gal}$ vs. $M_{200}$. After correcting for projection effects, the slope of the $L_{op}-M_{200}$ and $N_{gal}-M_{200}$ relations is found to be $0.92\pm0.03$, close, but still significantly less than unity. We show that the non-linearity of these relations cannot be explained by variations of the galaxy luminosity distributions and of the galaxy M/L with the cluster mass. We suggest that the nonlinear relation between number of galaxies and cluster mass reflects an underlying nonlinear relation between number of subhaloes and halo mass.Comment: 15 pages, 15 figures, accepted for publication in A&

Predicted HST FOC and broad band colours for young and intermediate Simple Stellar Populations

This paper presents theoretical HST and broad band colours from population synthesis models based on an homogeneous set of stellar evolutionary tracks as computed under canonical (no overshooting) assumptions, covering the range of cluster ages from t=8 Myr to t=5 Gyr for three different metallicities (Z=0.02, 0.006, and 0.001). Statistical fluctuations in the cluster population have been investigated, assessing the predicted fluctuations of the various colours as a function of the cluster integrated absolute magnitude. We show that the red leak in HST UV filters deeply affects the predicted fluxes and colours. However, we find that for F152M-F307M < 0.5 and for F170M-F278M < 0.5 (which means ages lower than 1 Gyr) the HST UV colours can still be used to infer reliable indications on the age of distant clusters. Moreover, one finds that the age calibration of these colours is scarcely affected by the amount of original helium or by the assumed IMF. On this basis, we present a calibration of the HST UV two-colours (F152M-F307M vs F170M-F278M) in terms of cluster ages for the three above quoted metallicities. We suggest the combined use of HST UV colours and IR colours (V-K in particular) to disentangle the metallicity-age effect in integrated colours of young stellar populations (t< 1 Gyr).Comment: Latex 18 pages, 16 encapsulated figures, 6 tables, A&ASS accepte

Oil price and shale oil rig nexus: an evaluation of oil price resilience

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