On optimality in intergenerational risk sharing

This paper defines and studies optimality in a dynamic stochastic economy with finitely lived agents, and investigates the optimality properties of an equilibrium with or without sequentially complete markets. Various Pareto optimality concepts are considered, including interim and ex ante optimality. We show that, at an equilibrium with a productive asset (land) and sequentially complete markets, the intervention of a government may be justified, but only to improve risk sharing between generations. If markets are incomplete, constrained interim optimality is investigated in two-period lived OLG economies. We extend the optimality properties of an equilibrium with land and examine conditions under which introducing a pay-as-you-go system would not lead to any Pareto improvement upon an equilibrium.Overlapping generations; Incomplete markets; Optimality

Sharing aggregate risks under moral hazard

This paper analyzes the efficient design of insurance schemes in the presence of aggregate shocks and moral hazard. The population is divided into groups, the labour force in different sectors for instance. In each group, individuals are ex ante identical but are subject to idiosyncratic shocks. Without moral hazard, optimality requires (1) full insurance against idiosyncratic shocks, which gives rise to a representative agent for each group and (2) optimal sharing of macro-economic risks between these representative agents. The paper investigates what remains of this analysis when the presence of moral hazard conflicts with the full insurance of idiosyncratic shocks. In particular, how is the sharing of macro-economic risks across groups affected by the partial insurance against idiosyncratic risks? The design of unemployment insurance schemes in different economic sectors, and the design of pension annuities in an unfunded social security system are two potential applications.moral hazard ; insurance ; mutuality principle ; macro-economic risk

On group stability in hierarchies and networks

A hierarchical structure is a widespread organizational form in many areas. My aim in this paper is to provide a rationale for this fact based on two premises. First, a group organizes itself so as to achieve efficient coordination. Second, efficient coordination is achieved only if subgroups as well as individuals agree to cooperate. Even in situations in which there are gains to coordination, the agreement of each possible subgroup may be impossible to reach, resulting in instabilities. I argue that a hierarchical organization avoids such instabilities by distributing in an optimal way autonomy and blocking power to a restricted set of subgroups. Comparisons with nondirected networks are drawn.Efficient Coordination; Instabilities; Hierarchical structure

Information revelation in a security market: The impact of uncertain participation

The paper analyzes how uncertainty on traders' participation affects a competitive security market in which there are some informed traders. We show that discontinuities, or "crashes", can arise at equilibrium, even when no investor posts a priori an increasing demand. Because of uncertain participation, the precision of the information brought by a price is endogenous, affected by the size of the trades. As a result, two prices with different volumes and information revelation may clear the market for the same values of the fundamentals. At one price, insurance motives drive the exchanges, noise is large and little information is revealed. At another price, uninformed trades are small, which makes the clearing price much more informative. This multiplicity of prices with different precision of information generates discontinuities.rational expectations equilibrium ; asymmetric information ; crashes

Investigations on a Pedagogical Calculus of Constructions

In the last few years appeared pedagogical propositional natural deduction systems. In these systems, one must satisfy the pedagogical constraint: the user must give an example of any introduced notion. First we expose the reasons of such a constraint and properties of these "pedagogical" calculi: the absence of negation at logical side, and the "usefulness" feature of terms at computational side (through the Curry-Howard correspondence). Then we construct a simple pedagogical restriction of the calculus of constructions (CC) called CCr. We establish logical limitations of this system, and compare its computational expressiveness to Godel system T. Finally, guided by the logical limitations of CCr, we propose a formal and general definition of what a pedagogical calculus of constructions should be.Comment: 18 page

Signatures of three coalescing eigenfunctions

Parameter dependent non-Hermitian quantum systems typically not only possess eigenvalue degeneracies, but also degeneracies of the corresponding eigenfunctions at exceptional points. While the effect of two coalescing eigenfunctions on cyclic parameter variation is well investigated, little attention has hitherto been paid to the effect of more than two coalescing eigenfunctions. Here a characterisation of behaviours of symmetric Hamiltonians with three coalescing eigenfunctions is presented, using perturbation theory for non-Hermitian operators. Two main types of parameter perturbations need to be distinguished, which lead to characteristic eigenvalue and eigenvector patterns under cyclic variation. A physical system is introduced for which both behaviours might be experimentally accessible.Comment: 14 pages, 4 figures. Typos corrected, slightly extended, to appear in J. Phys.

The 0-1 inverse maximum stable set problem

Given an instance of a weighted combinatorial optimization problem and its feasible solution, the usual inverse problem is to modify as little as possible (with respect to a fixed norm) the given weight system to make the giiven feasible solution optimal. We focus on its 0-1 version, which is to modify as little as possible the structure of the given instance so that the fixed solution becomes optimal in the new instance. In this paper, we consider the 0-1 inverse maximum stable set problem against a specific (optimal or not) algorithm, which is to delete as few vertices as possible so that the fixed stable set S* can be returned as a solution by the given algorithm in the new instance. Firstly, we study the hardness and approximation results of the 0-1 inverse maximum stable set problem against the algorithms. Greedy and 2-opt. Secondly, we identify classes of graphs for which the 0-1 inverse maximum stable set problem can be polynomially solvable. We prove the tractability of the problem for several classes of perfect graphs such as comparability graphs and chordal graphs.Combinatorial inverse optimization, maximum stable set problem, NP-hardness, performance ratio, perfect graphs.

Competition in the quality of higher education: the impact of students' mobility

This paper analyzes in a two-country model the impact of students' mobility on the country-specific level of higher educational quality. Individuals decide whether and where to study based on their individual ability and the implemented quality of education. We show that the mobility of students affects educational quality in countries and welfare in a very different way depending on the degree of return migration. With a low return probability, countries choose suboptimally differentiated levels of educational quality, or even no differentiation at all.higher education ; migration ; tuition fees ; education quality ; vertical differentiation

On the influence of rankings

Ranking systems are becoming increasingly important in many areas, in the Web environment and academic life for instance. In a world with a tremendous amount of choices, rankings play the crucial role of influencing which objects are 'tasted' or selected. This selection generates a feedback when the ranking is based on citations, as is the case for the widely used invariant method. The selection affects new stated opinions (citations), which will, in turn, affect next ranking. The purpose of this paper is to investigate this feedback in the context of journals by studying some simple but reasonable dynamics. Our main interest is on the long run behavior of the process and how it depends on the preferences, in particular on their diversity. We show that multiple long run behavior may arise due to strong self enforcing mechanisms at work with the invariant method. These effects are not present in a simple search model in which individuals are influenced by the cites of the papers they first read.ranking, scoring, invariant method, search

The strategy structure of some coalition formation games

In coalitional games with side payments, the core predicts which coalitions form and how benefits are shared. The predictions however run into difficulties if the core is empty or if some coalitions benefit from not blocking truthfully. These difficulties are analyzed in games in which an a priori given collection of coalitions can form, as the collection of pairs of buyer-seller in an assignment game. The incentive properties of the core and of its selections are investigated in function of the collection. Furthermore the relationships with Vickrey-Clarke-Groves mechanisms are drawn.coalition formation ; assignment ; manipulability ; substitutes ; incremental value ; Vickrey-Clarke-Groves mechanism