Calendrier du 01 février 2018
TOM (Théorie, Organisation et Marchés) Lunch Seminar
Du 01/02/2018 de 12:30 à 13:30
salle R2-20, campus Jourdan - 48 bd Jourdan 75014 Paris
LARAKI Rida (CNRS et Lamsade)
Acyclic Gambling Games
écrit avec J. Renault
We consider two-player zero-sum stochastic games where each player controls his own state variable living in a compact metric space. The terminology of the title comes from gambling problems where the state of a player represents its wealth in a casino. Under natural assumptions (such as continuous running payoff and non expansive transitions), we consider for each discount factor the value $v_lambda$ of the $lambda$-discounted stochastic game and investigate its limit when $lambda$ goes to 0 (players are more and more patient). We show that under a strong acyclicity condition, the limit exists and is characterized as the unique solution of a system of functional equations: the limit is the unique continuous excessive and depressive function such that each player, if his opponent does not move, can reach the zone when the current payoff is at least as good than the limit value, without degrading the limit value. The approach generalizes and provides a new viewpoint on the Mertens-Zamir system coming from the study of zero-sum repeated games with lack of information on both sides. A counterexample shows that under a slightly weaker notion of acyclicity, convergence of $(v_lambda)$ may fail.
Travail et économie publique externe
Du 01/02/2018 de 12:30 à 13:45
MELLY Blaise (University of Bern)
Generic Inference on Quantile and Quantile Effect Functions for Discrete Outcomes
écrit avec Co-authors: V. Chernozhukov, I. Fernandez-Val, and K. Wuethrich
Quantile and quantile effect functions are important tools for descriptive and
inferential analysis due to their natural and intuitive interpretation. Existing inference
methods for these functions do not apply to discrete and mixed continuous-discrete random
variables. This paper offers a simple, practical construction of the simultaneous
confidence bands for quantile and quantile effect functions. It is based on a natural transformation
of simultaneous confidence bands for distribution functions, which are readily
available for many problems. The construction is generic and does not depend on the
nature of the underlying problem. It works in conjunction with parametric, semiparametric,
and nonparametric modeling strategies and does not depend on the sampling scheme.
We apply our method to characterize the distributional impact of insurance coverage on
health care utilization and obtain the distributional decomposition of the racial test score
gap. Our analysis generates new, interesting empirical findings, and complements previous
analyses that focused on mean effects only. In both applications, the outcomes of
interest are discrete rendering existing inference methods invalid for obtaining uniform
confidence bands for quantile and quantile effects functions.
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