Learning to Play Bayesian Games

This paper discusses the implications of learning theory for the analysis of Bayesian games. One goal is to illuminate the issues that arise when modeling situations where players are learning about the distribution of Nature's move as well as learning about the opponents' strategies. A second goal is to argue that quite restrictive assumptions are necessary to justify the concept of Nash equilibrium without a common prior as a steady state of a learning process.

Two Conditions for Galaxy Quenching: Compact Centres and Massive Haloes

We investigate the roles of two classes of quenching mechanisms for central and satellite galaxies in the SDSS ($z<0.075$): those involving the halo and those involving the formation of a compact centre. For central galaxies with inner compactness $\Sigma_{\rm 1kpc} \sim 10^{9-9.4}M_{\odot} {\rm kpc}^{-2}$, the quenched fraction $f_{q}$ is strongly correlated with $\Sigma_{\rm 1kpc}$ with only weak halo mass $M_{\rm h}$ dependence. However, at higher and lower $\Sigma_{\rm 1kpc}$, sSFR is a strong function of $M_{\rm h}$ and mostly independent of $\Sigma_{\rm 1kpc}$. In other words, $\Sigma_{\rm 1kpc} \sim 10^{9-9.4} M_{\odot} {\rm kpc}^{-2}$ divides galaxies into those with high sSFR below and low sSFR above this range. In both the upper and lower regimes, increasing $M_{\rm h}$ shifts the entire sSFR distribtuion to lower sSFR without a qualitative change in shape. This is true even at fixed $M_{*}$, but varying $M_{*}$ at fixed $M_{\rm h}$ adds no quenching information. Most of the quenched centrals with $M_{\rm h} > 10^{11.8}M_{\odot}$ are dense ($\Sigma_{\rm 1kpc} > 10^{9}~ M_{\odot} {\rm kpc}^{-2}$), suggesting compaction-related quenching maintained by halo-related quenching. However, 21% are diffuse, indicating only halo quenching. For satellite galaxies in the outskirts of halos, quenching is a strong function of compactness and a weak function of host $M_{\rm h}$. In the inner halo, $M_{\rm h}$ dominates quenching, with $\sim 90\%$ of the satellites being quenched once $M_{\rm h} > 10^{13}M_{\odot}$. This regional effect is greatest for the least massive satellites. As demonstrated via semi-analytic modelling with simple prescriptions for quenching, the observed correlations can be explained if quenching due to central compactness is rapid while quenching due to halo mass is slow.Comment: 16 pages, 11 figures, MNRAS accepte

Cool gas accretion, thermal evaporation and quenching of star formation in elliptical galaxies

The most evident features of colour-magnitude diagrams of galaxies are the red sequence of quiescent galaxies, extending up to the brightest elliptical galaxies, and the blue cloud of star-forming galaxies, which is truncated at a luminosity L~L*. The truncation of the blue cloud indicates that in the most massive systems star formation must be quenched. For this to happen the virial-temperature galactic gas must be kept hot and any accreted cold gas must be heated. The elimination of accreted cold gas can be due to thermal evaporation by the hot interstellar medium, which in turn is prevented from cooling by feedback from active galactic nuclei.Comment: 2 pages, to appear in Astronomische Nachrichten (proceedings of Symposium 6 of the JENAM 2008, Vienna

Subjective Uncertainty Over Behavior Strategies: A Correction

In order to model the subjective uncertainty of a player over the behavior strategies of an opponent, one must consider the player's beliefs about the opponent's play at information sets that the player thinks have probability zero. This corregendum uses “trembles” to provide a definition of the convex hull of a set of behavior strategies. This corrects a definition we gave in [E. Dekel, D. Fudenberg, and D. K. Levine, 1999, J. Econ. Theory 89, 165–185], which led to two of the solution concepts we defined there not having the properties we intended.Economic

Learning to Play Bayesian Games

This paper discusses the implications of learning theory for the analysis of games with a move by Nature. One goal is to illuminate the issues that arise when modeling situations where players are learning about the distribution of Nature's move as well as learning about the opponents' strategies. A second goal is to argue that quite restrictive assumptions are necessary to justify the concept of Nash equilibrium without a common prior as a steady state of a learning process.Economic