Dynamic equilibrium in games with randomly arriving players

This note follows our previous works on games with randomly arriving players [3] and [5]. Contrary to these two articles, here we seek a dynamic equilibrium, using the tools of piecewise deterministic control systems The resulting discrete Isaacs equation obtained is rather involved. As usual, it yields an explicit algorithm in the finite horizon, linear-quadratic case via a kind of discrete Riccati equation. The infinite horizon problem is briefly considered. It seems to be manageable only if one limits the number of players present in the game. In that case, the linear quadratic problem seems solvable via essentially the same algorithm, although we have no convergence proof, but only very convincing numerical evidence. We extend the solution to more general entry processes, and more importantly , to cases where the players may leave the game, investigating several stochastic exit mechanisms. We then consider the continuous time case, with a Poisson arrival process. While the general Isaacs equation is as involved as in the discrete time case, the linear quadratic case is simpler, and, provided again that we bound the maximum number of players allowed in the game, it yields an explicit algorithm with a convergence proof to the solution of the infinite horizon case, subject to a condition reminiscent of that found in [20]. As in the discrete time case, we examine the case where players may leave the game, investigating several possible stochastic exit mechanisms. MSC: 91A25, 91A06, 91A20, 91A23, 91A50, 91A60, 49N10, 93E03. Foreword This report is a version of the article [2] where players minimize instead of maximizing, and the linear-quadratic examples are somewhat different.On détermine les stratégies d'équilibre dans un jeu dynamique où des joueurs identiques arrivent de façon aléatoire, comme, par exemple, des congénères arrivant sur une même ressource. On considère aussi divers mécanismes de sortie aléatoire. On obtient des théorèmes d'existence et des algorithmes de calcul, plus explicites dans le cas particulier linéaire quadratique. Toute l'étude est conduite en horizon fini et en horizon infini, et en temps discret et en temps continu.Ce rapport est une version du working paper CRESE des mêmes auteurs (en économie mathématique), référence [2], mais où les joueurs minimisent au lieu de maximiser, et les exemples linéaires quadratiques sont un peu différents

Labor Mobility and Racial Discrimination

This paper assesses the impact of labor mobility on racial discrimination. We present an equilibrium search model that reveals an inverted U-shaped relationship between labor mobility and race-based wage differentials. We explore this relationship empirically with an exogenous mobility shock on the European soccer labor market. The Bosman ruling by the European Court of Justice in 1995 lifted restrictions on soccer player mobility. Using a panel of all clubs in the English first division from 1981 to 2008, we compare the pre- and post-Bosman ruling market to identify the causal effect of intensified mobility on race-based wage differentials. Consistent with a taste-based explanation, we find evidence that increasing labor market mobility decreases racial discrimination

Inversion Schemes to Retrieve Atmospheric and Oceanic Parameters from SeaWiFS Data

Firstly, we have analyzed atmospheric transmittance and sky radiance data connected at the Scripps Institution of Oceanography pier, La Jolla during the winters of 1993 and 1994. Aerosol optical thickness at 870 nm was generally low in La Jolla, with most values below 0.1 after correction for stratospheric aerosols. For such low optical thickness, variability in aerosol scattering properties cannot be determined, and a mean background model, specified regionally under stable stratospheric component, may be sufficient for ocean color remote sensing, from space. For optical thicknesses above 0. 1, two modes of variability characterized by Angstrom exponents of 1.2 and 0.5 and corresponding, to Tropospheric and Maritime models, respectively, were identified in the measurements. The aerosol models selected for ocean color remote sensing, allowed one to fit, within measurement inaccuracies, the derived values of Angstrom exponent and 'pseudo' phase function (the product of single scattering albedo and phase function), key atmospheric correction parameters. Importantly, the 'pseudo' phase function can be derived from measurements of the Angstrom exponent. Shipborne sun photometer measurements at the time of satellite overpass are usually sufficient to verify atmospheric correction for ocean color

Comments on the "Spatial variability of coastal surface water temperature during upwelling"

International audienceComments on the article "Spatial variability of coastal surface water temperature during upwelling

Influence of intensive agriculture and geological heterogeneity on the recharge of an arid aquifer system (Saq–Ram, Arabian Peninsula) inferred from GRACE data

This study assesses the detailed water budget of the Saq–Ram Aquifer System (520 000 km2) over the 2002–2019 period using satellite gravity data from the Gravity Recovery And Climate Experiment (GRACE). The three existing GRACE solutions were tested for their local compatibility to compute groundwater storage (GWS) variations in combination with the three soil moisture datasets available from the land surface models (LSMs) of the Global Land Data Assimilation System (GLDAS). Accounting for groundwater pumping, artificial recharge, and natural discharge uniformly distributed over the Saq–Ram domain, the GRACE-derived mass balance calculation for water yields a long-term estimate of the domain-averaged natural recharge of (2.4±1.4) mm yr−1, corresponding to (4.4±2.6) % of the annual average rainfall (AAR). Beyond the regional-scale approach proposed here, spatial heterogeneities regarding the groundwater recharge were identified. The first source of heterogeneity is of anthropogenic origin: chiefly induced by irrigation excess over irrigated surfaces (about 1 % of the domain), artificial recharge corresponds to half of the total recharge of the aquifer. The second source of recharge heterogeneity identified here is natural: volcanic lava deposits (called harrats on the Arabian Peninsula) which cover 8 % of the Saq–Ram aquifer domain but contribute to more than 50 % of the natural recharge. Hence, in addition to this application on the Arabian Peninsula, this study strongly indicates a major control of geological context on arid aquifer recharge, which has been poorly discussed hitherto. Due to large lag times of the diffuse recharge mechanism, the annual analysis using this GRACE–GLDAS approach in arid domains should be limited to areas where focused recharge is the main mechanism, while long-term analysis is valid regardless of the recharge mechanism. Moreover, it appears that about 15 years of GRACE records are required to obtain a relevant long-term recharge estimate.</p