# Publications

A pure Hotelling game is a spatial competition between a finite number of players who simultaneously select a location in order to attract as many consumers as possible. In this paper, we study the case of a general distribution of consumers on a network generated by a metric graph. Because players do not compete on price, the continuum of consumers shop at the closest player’s location. If the number of sellers is large enough, we prove the existence of an approximate equilibrium in pure strategies, and we construct it.

The purpose of this paper is twofold. First, we examine convergence properties of an inexact proximal point method with a quasi distance as a regularization term in order to find a critical point (in the sense of Toland) of a DC function (difference of two convex functions). Global convergence of the sequence and some convergence rates are obtained with additional assumptions. Second, as an application and its inspiration, we study in a dynamic setting, the very important and difficult problem of the limit of the firm and the time it takes to reach it (maturation time), when increasing returns matter in the short run. Both the formalization of the critical size of the firm in term of a recent variational rationality approach of human dynamics and the speed of convergence results are new in Behavioral Sciences.

We study optimal contracts in a regulator–agent setting with joint production, altruistic and selfish agents, limited liability, and uneasy outcome measurement. Such a setting represents sectors of activities such as education and healthcare provision. The agents and the regulator jointly produce an outcome for which they all care to some extent that is varying from agent to agent. Some agents, the altruistic ones, care more than the regulator does while others, the selfish agents, care less. Moral hazard is present due to both the agent's effort and the joint outcome that are not contractible. Adverse selection is present too since the regulator cannot a priori distinguish between altruistic and selfish agents. Contracts consist of a simple transfer from the regulator to the agents together with the regulator's input in the joint production. We show that, under the conditions of our setting and when we face both moral hazard and adverse selection, the regulator maximizes welfare with a menu of contracts, which specify higher transfers for the altruistic agents and higher regulator's inputs for the selfish agents.

Central properties of geometric quantiles have been well-established in the recent statistical literature. In this study, we try to get a grasp of how extreme geometric quantiles behave. Their asymp-totics are provided, both in direction and magnitude, under suitable moment conditions, when the norm of the associated index vector tends to one. Some intriguing properties are highlighted: in particular, it appears that if a random vector has a finite covariance matrix, then the magnitude of its extreme geometric quantiles grows at a fixed rate. We take profit of these results by defining a parametric estimator of extreme geometric quantiles of such a random vector. The consistency and asymptotic normality of the estimator are established, and contrasted with what can be obtained for univariate quantiles. Our results are illustrated on both simulated and real data sets. As a conclusion, we deduce from our observations some warnings which we believe should be known by practitioners who would like to use such a notion of multivariate quantile to detect outliers or analyze extremes of a random vector.

The promotion system for French academic economists provides an interesting environment to examine the promotion gap between men and women. Promotions occur through national competitions for which we have information both on candidates and on those eligible to be candidates. Thus, we can examine the two stages of the process: application and success. Women are less likely to seek promotion, and this accounts for up to 76 percent of the promotion gap. Being a woman also reduces the probability of promotion conditional on applying, although the gender difference is not statistically significant. Our results highlight the importance of the decision to apply.

This paper concerns applications of variational analysis to some local aspects of behavioral science modeling by developing an effective variational rationality approach to these and related issues. Our main attention is paid to local stationary traps, which reflect such local equilibrium and the like positions in behavioral science models that are not worthwhile to quit. We establish constructive linear optimistic evaluations of local stationary traps by using generalized differential tools of variational analysis that involve subgradients and normals for nonsmooth and nonconvex objects as well as variational and extremal principles.

In this paper, we propose a new variance reduction method for quantile regressions with endogeneity problems, for alpha-mixing or m-dependent covariates and error terms. First, we derive the asymptotic distribution of two-stage quantile estimators based on the fitted-value approach under very general conditions. Second, we exhibit an inconsistency transmission property derived from the asymptotic representation of our estimator. Third, using a reformulation of the dependent variable, we improve the efficiency of the two-stage quantile estimators by exploiting a tradeoff between an inconsistency confined to the intercept estimator and a reduction of the variance of the slope estimator. Monte Carlo simulation results show the fine performance of our approach. In particular, by combining quantile regressions with first-stage trimmed least-squares estimators, we obtain more accurate slope estimates than 2SLS, 2SLAD and other estimators for a broad set of distributions. Finally, we apply our method to food demand equations in Egypt.

After-tax income inequality has risen since the mid-1990's, as increases in market income inequality have not been offset by greater fiscal redistribution. This paper argues that the substantial increase in consumer goods diversity has mitigated mounting political pressures for redistribution. Within a probabilistic voting framework, we demonstrate that if the share of diversified goods in the consumption bundle increases sufficiently with income, then an increase in goods diversity can reduce the political equilibrium tax rate. Focusing on OECD countries, we find empirical support for both the model's micro-political foundations and the implied relation between goods diversity and fiscal policy outcomes. This article is protected by copyright. All rights reserved.

Bilateral bargaining between a multiple-worker firm and individual employees leads to overhiring. With a concave production function, the firm can reduce the marginal product by hiring an additional worker, thereby reducing the bargaining wage paid to all existing employees. We show that this externality is amplified when firms can adjust hours per worker as well as employment. Firms keep down workers’ wage demands by reducing the number of hours per worker and the resulting labor disutility. Our finding is particularly relevant for European economies where hours adjustment plays an important role.

We study the determination of public tuition fees through majority voting in a vertical differentiation model where agents' returns on educational investment differ and public and private universities coexist and compete in tuition fees. The private university offers higher educational quality than its competitor, incurring higher unit cost per trained student. The tuition fee for the state university is fixed by majority voting while that for the private follows from profit maximization. Then agents choose to train at the public university or the private one or to remain uneducated. The tax per head adjusts in order to balance the state budget. Because there is a private alternative, preferences for education are not single-peaked and no single-crossing condition holds. An equilibrium is shown to exist, which is one of three types: high tuition fee (the “ends” are a majority), low tuition fee (the “middle” is a majority), or mixed (votes tie). The cost structure determines which equilibrium obtains. The equilibrium tuition is either greater (majority at the ends) or smaller (majority at the middle) than the optimal one.