# Publications

We formulate a hydro-economic model of the North-Western Sahara Aquifer System (NWSAS) to assess the effects of intensive pumping on the groundwater stock and examine the subsequent consequences of aquifer depletion. This large system comprises multi-layer reservoirs with vertical exchanges, all exploited under open access properties. We first develop a theoretical model to account for relevant features of the NWSAS by introducing, in the standard Gisser-Sanchez model, a non-stationary demand and quadratic stock-dependent cost functions. In the second step, we calibrate parameters values using data from the NWSAS over 1955–2000. We finally simulate the time evolution of the aquifer system with exploitation under an open-access regime. We specifically examine time trajectories of the piezometric levels in the two reservoirs, the natural outlets, and the modification of water balances. We find that natural outlets of the two reservoirs might be totally dried before 2050.

We establish general versions of the Ekeland variational principle (EVP), where we include two perturbation bifunctions to discuss and obtain better perturbations for obtaining three improved versions of the principle. Here, unlike the usual studies and applications of the EVP, which aim at exact minimizers via a limiting process, our versions provide good-enough approximate minimizers aiming at applications in particular situations. For the presentation of applications chosen in this paper, the underlying space is a partial quasi-metric one. To prove the aforementioned versions, we need a new proof technique. The novelties of the results are in both theoretical and application aspects. In particular, for applications, using our versions of the EVP together with new concepts of Ekeland points and stop and go dynamics, we study in detail human dynamics in terms of a psychological traveler problem, a typical model in behavioral sciences.

We first give a pre-order principle whose form is very general. Combining the pre-order principle and generalized Gerstewitz functions, we establish a general equilibrium version of set-valued Ekeland variational principle (denoted by EVP), where the objective function is a set-valued bimap defined on the product of quasi-metric spaces and taking values in a quasi-ordered linear space, and the perturbation consists of a subset of the ordering cone multiplied by the quasi-metric. From this, we obtain a number of new results which essentially improve the related results. Particularly, the earlier lower boundedness condition has been weakened. Finally, we apply the new EVPs to Psychology.

We investigate whether and how an individual giving decision is affected in risky environments in which the recipient’s wealth is random. We demonstrate that, under risk neutrality, the donation of dictators with a purely ex post view of fairness should, in general, be affected by the riskiness of the recipient’s payoff, while dictators with a purely ex ante view should not be. Furthermore, we observe that some influential inequality aversion preferences functions yield opposite predictions when we consider ex post view of fairness. Hence, we report on dictator games laboratory experiments in which the recipient’s wealth is exposed to an actuarially neutral and additive background risk. Our experimental data show no statistically significant impact of the recipient’s risk exposure on dictators’ giving decisions. This result appears robust to both the experimental design (within subjects or between subjects) and the origin of the recipient’s risk exposure (chosen by the recipient or imposed on the recipient). Although we cannot sharply validate or invalidate alternative fairness theories, the whole pattern of our experimental data can be simply explained by assuming ex ante view of fairness and risk neutrality.

In recent years there has been a surge of interest in the subject of inequality, fuelled by new facts and new thinking. The literature on inequality has expanded rapidly as official data on income, wealth, and other personal information have become richer and more easily accessible. Ideas about the meaning of inequality have expanded to encompass new concepts and different dimensions of economic inequality. The purpose of this chapter is to give a concise overview of the issues that are involved in translating ideas about inequality into practice using various types of data.

Carl Menger is remembered less for his analysis of entrepreneurship (which in the following analysis refers to his fundamental notions related to the nature of business practice) than for his views on matters like money, individualism or the nature of institutions (there are exceptions to this subdued interest, such as Kirzner 1978). However, these issues are related and a long-debated notion among Austrians, namely time, relates investment, entrepreneurship, uncertainty and Menger’s tentative quasi-anthropology (kept in his notes). This paper conscientiously investigates those issues through Menger’s views on the notion of time.

This paper proposes a new empirical conceptualization of financial integration of sovereign bond markets in the euro area. We introduce a methodology based on the joint testing of the assumptions of efficient market and convergence/divergence of the yield spreads. We test these assumptions by proposing parametric and non-parametric techniques. We find that markets have been more fragmented than usually advocated in the literature. We also show that the information contained in the fundamentals are not always fully reflected in the spreads, which suggests that either they have insignificant effects, or that their coefficients in the spread equations appear with the wrong sign.

This paper investigates duopoly competition when horizontally differentiated firms are able to make personalized product-price offers to returning customers, within a behavior-based discrimination model. In the second period, firms can profile old customers according to their preferences, selling them targeted products at personalized prices. Product-price personalization (PP) allows firms to retain all old customers, eliminating second-period customer poaching. The overall profit effects of PP are shown to be ambiguous. In the second period, PP improves the matching between customers’ preferences and firms’ offers, but firms do not make any revenues in the rival’s turf. In the Bertrand outcome, second-period profits only increase for both firms if the size of their old turfs are not too different or initial products are not too differentiated. However, the additional second-period profits may be offset by lower first-period profits. PP is likely to increase firms’ overall discounted profits when consumers’ (firms’) discount factor is low (high) and firms’ initial products are exogenous and sufficiently different. When the location of initial products is endogenous, profits are hurt because of an additional location (strategic) effect aggravating head-to-head competition in the first period. Likewise, when a fraction of active consumers conceals their identity, PP increases second-period profits at the cost of aggressive first-period price competition. Finally, we show that the room for profitable PP enlarges considerably if firms rely on PP as an effective device to sustain tacit collusive outcomes, with firms credibly threatening to respond to first-period price deviations with second-period aggressive relocations of their standard products.

This paper was accepted by Matthew Shum, marketing.

We study price personalization in a two period duopoly with horizontally differentiated products. In the second period, a firm has collected detailed information on its old customers, using it to engage in price personalization. Customers, when returning to buy, may choose to incur a cost in order to access the standard offer of their previous provider in addition to its personalized offer and the standard offer of its rival. The analysis confirms that firms’ second period profits are boosted when consumers are active in this sense (being equal to perfect price discrimination ones when initial market hares do not differ too much) but it reveals that this advantage is dissipated and possibly over-dissipated by the resulting fierce first-period competition for the market. Two-period aggregate profits are smaller with active customers provided the consumers are naive and/or the firms patient enough. Consumers’ access to both personalized and standard firms’ offers which benefit the oligopolists in mature markets may plausibly hurt them in emergent ones. The equilibrium is shown not to depend on the level of the cost as long as it is below some critical value.

We present an inexact proximal point algorithm using quasi distances to solve a minimization problem in the Euclidean space. This algorithm is motivated by the proximal methods introduced by Attouch et al., section 4, (Math Program Ser A, 137: 91–129, 2013) and Solodov and Svaiter (Set Valued Anal 7:323–345, 1999). In contrast, in this paper we consider quasi distances, arbitrary (non necessary smooth) objective functions, scalar errors in each objective regularized approximation and vectorial errors on the residual of the regularized critical point, that is, we have an error on the optimality condition of the proximal subproblem at the new point. We obtain, under a coercivity assumption of the objective function, that all accumulation points of the sequence generated by the algorithm are critical points (minimizer points in the convex case) of the minimization problem. As an application we consider a human location problem: How to travel around the world and prepare the trip of a lifetime.