maximize prots using numerical methods. However, this is not required to identify productivity and will not be pursued here. In the empirical work that follows, , and x are allowed to change from period to period
in response to changing market and mine conditions. 8 The contract the mine paid its workers is not the optimal contract that solves the classic **principal** **agent** model. Such a contract would depend on all observable characteristics which are related to productivity such as tenure and oc- cupation. One possible explanation for the simplicity of the observed scheme is that more complicated contracts have prohibitively high trans- action costs associated with them. Ferrall and Shearer (1994) investigate empirically the role of transaction costs in determining the rm's choice of the bonus system at Britannia.

En savoir plus
This paper considers the information systems induced by auditing policies in a **principal**-**agent** model with moral hazard. We point out that two such information systems A and B are seldom comparable using the customary mean-preserving spread relation between their respective likelihood ratio distributions. We offer a general extension of this criterion, however, and we use it to show that, provided the sign of the third derivative of the agent's inverse utility function is constant, it is yet often possible to rank A against B because one of the corresponding likelihood ratio distributions dominates the other in the third order. The upshot is that the design of optimal auditing policies involves not only the well-known tradeoff between risk- sharing and incentives, but also an examination of the location of risk.

En savoir plus
importante. Dans le modèle, l’effort mis en œuvre pour observer l’agent est une variable de contrôle. Nous montrons qu’une implication du modèle **principal**-**agent** est que le **principal** devrait faire d’autant plus d’effort pour observer l’agent quand ses intérêts divergent de ceux de l’agent. Nous testons ensuite ces prédictions en utilisant les données de performance des projets d’aide de la Banque mondiale. Nous mesurons le degré de divergence entre les intérêts du donneur et du receveur, telle que perçue par le donneur, par la classification des receveurs comme ‘partenariats difficiles’. Comme prédit par le modèle, nous trouvons que la supervision des projets d’aide par le donneur permet d’autant plus d’assurer le succès des projets que les intérêts du donneur et du receveur diffèrent. Toutefois, le donneur ne semble pas faire plus d’effort de supervision dans les partenariats difficiles.

En savoir plus
importante. Dans le modèle, l’effort mis en œuvre pour observer l’agent est une variable de contrôle. Nous montrons qu’une implication du modèle **principal**-**agent** est que le **principal** devrait faire d’autant plus d’effort pour observer l’agent quand ses intérêts divergent de ceux de l’agent. Nous testons ensuite ces prédictions en utilisant les données de performance des projets d’aide de la Banque mondiale. Nous mesurons le degré de divergence entre les intérêts du donneur et du receveur, telle que perçue par le donneur, par la classification des receveurs comme ‘partenariats difficiles’. Comme prédit par le modèle, nous trouvons que la supervision des projets d’aide par le donneur permet d’autant plus d’assurer le succès des projets que les intérêts du donneur et du receveur diffèrent. Toutefois, le donneur ne semble pas faire plus d’effort de supervision dans les partenariats difficiles.

En savoir plus
efficiency of informational rents may be reduced if appropriate performance measures on which to base the contract between the MoF and the LM are unreliable or even
unavailable.
• The model may also help sequencing reforms, although we do not develop this aspect in the paper. As causes for the poor performance of the PEM system are identified, it is possible to decide on what measures should take priority. For instance, if the MoF is not in a position to deter cheating by introducing internal controls, nor to grant informational rents, it is trapped in the so-called cheating-inducing regime. A first step could be to announce that private audit firms will be hired. In our model, this would relate to implementing a mixed-strategy equilibrium, which tends to be an easily implementable and cheaper solution (as it incurs no fixed cost) to reduce the extent of cheating. If the country lacks reliable fiscal data, ex post audits are not very effective and the priority should be to reinforce the accounting system, before reinvigorating the court of audit. Finally, although the **principal**-**agent** theory provides very interesting insights for the design of PEM systems, we have only considered a few aspects and many more are worth exploring. For instance, a **principal**-**agent** analysis could be applied to the allocation of resources for control purposes between different LMs (for example because they have different

En savoir plus
[Jac75] J. Jacod. Multivariate Point Processes: Predictable Projection, Radon-Nikodym Derivatives, Representation of Martingales. Z. Wahrscheinlichkeitstheorie verw, 31(3):235–253, 1975.
[Lac15] D. Lacker. Mean field games via controlled martingale problems: existence of Marko- vian equilibria. Stochastic Processes and their Applications, 125(7):2856–2894, 2015. [LL07] J.-M. Lasry and P.-L. Lions. Mean field games. Jpn. J. Math., 2(1):229–260, 2007. [MR18] Thibaut Mastrolia and Zhenjie Ren. **Principal**-**Agent** problem with common agency

Les schémas **principal**-**agent** se concentrent principalement sur le comportement de l’agent et les incitations nécessaires pour les motiver à adapter le comportement souhaité par le **principal**. Dans la première partie, il a été discuté de la relation entre la DDC et les ONG, de la dépendance financière d’une dizaine des plus grandes ONG suisses des fonds publics, de la durée et de la continuité de cette relation, de l’augmentation du contrôle de la DDC par rapport à leurs résultats et de la précision des procédures d’attribution de fonds. Le modèle **principal**-**agent** décrit bien ce type de relation qui est caractérisée par la délégation des tâches et par l’impossibilité partielle de vérifier les résultats, en raison du caractère des services, dont les résultats ne sont pas toujours mesurables et pas immédiatement visibles. La DDC connaît ses agents depuis longtemps ; ce sont les même ONG qui bénéficient année après année du financement public de l’APD. De plus, une procédure d’accréditation des ONG auprès de la DDC est en cours. C’est ainsi qu’elle résout le problème de la sélection adverse. Enfin, comme cela a déjà été mis en exergue, le fait de coopérer pendant des années mène à une convergence des méthodes de travail, ce qui atténue le problème de la sélection adverse.

En savoir plus
238 En savoir plus

2. Interpretation of PEM under the **principal**-**agent** theory 2.1. The contract
We base our analysis on standard **principal**-**agent** models involving supervision (Kofman and Lawarrée, 1993, 1996; Khalil and Lawarrée, 2006). We essentially focus on the control of line ministries or assimilated bodies by the MoF, which is supposed to represent the public interest. Line ministries can be seen as agents of the MoF (the **principal**) because they are required to produce a certain level of public output – including the quality of this output – in exchange for their budget appropriation. The pair “expenditure programme – budget appropriation” can be interpreted as the two components of the contract between the MoF and the line ministries. 9 The objective of the MoF is to induce the line ministries into implementing their expenditure programmes, while the line ministries pursue their own objectives. That relationship entails both hidden actions (e.g. the productive “effort” of the civil servants, possible perquisite consumption, or corruption) and hidden information (e.g. the exogenous productivity of that particular sector of the economy), with the agents having the informational advantage over the **principal**. Hidden information could also refer to poor programme design, which would lead to inefficiency and would be difficult to dissociate from the inefficiency originating from a weak PEM system. 10

En savoir plus
(iii) Notice that the controlled drift σλ is assumed to lie in the range of the diffusion matrix. When the diffusion matrix is allowed to degenerate, this represents a restriction of the model, which translates to the so-called structure condition in the theory of backward SDEs. The structure condition is crucial for our methodology of characterizing Agent’s path-dependent control problem by means of backward SDEs. (iv) The weak formulation of the problem is standard in the current continuous-time **Principal**-**Agent** litera- ture. First, as Agent’s effort is impacting the problem only through the induced distribution, the weak formulation naturally allows for a larger class of controls. Second, Principal’s contract is crucially re- stricted to be measurable with respect to the output process, thus capturing the differential information between **Agent** and **Principal**. In the present weak formulation, no additional measurability restriction is needed in order to account for this key-feature of the problem.

En savoir plus
With unlimited liability, the technique for minimizing the expected payment to the agent is well known Hölmstrom 1979: the principal charges the agent a fixed participation fee equal to [r]

Abstract
In this paper, we consider a problem of contract theory in which sev- eral Principals hire a common **Agent** and we study the model in the con- tinuous time setting. We show that optimal contracts should satisfy some equilibrium conditions and we reduce the optimisation problem of the Prin- cipals to a system of coupled Hamilton-Jacobi-Bellman (HJB) equations. We provide conditions ensuring that for risk-neutral Principals, the system of coupled HJB equations admits a solution. Further, we apply our study in a more specific linear-quadratic model where two interacting Principals hire one common **Agent**. In this continuous time model, we extend the result of [BW86] in which the authors compare the optimal effort of the **Agent** in a non-cooperative Principals model and that in the aggregate model, by showing that these two optimisations coincide only in the first best case (see Proposition 5.2). We also study the sensibility of the optimal effort and the optimal remunerations with respect to appetence parameters and the corre- lation between the projects (see Proposition 5.3).

En savoir plus
Abstract
In this paper, we consider a problem of contract theory in which sev- eral Principals hire a common **Agent** and we study the model in the con- tinuous time setting. We show that optimal contracts should satisfy some equilibrium conditions and we reduce the optimisation problem of the Prin- cipals to a system of coupled Hamilton-Jacobi-Bellman (HJB) equations. We provide conditions ensuring that for risk-neutral Principals, the system of coupled HJB equations admits a solution. Further, we apply our study in a more specific linear-quadratic model where two interacting Principals hire one common **Agent**. In this continuous time model, we extend the result of [BW86] in which the authors compare the optimal effort of the **Agent** in a non-cooperative Principals model and that in the aggregate model, by showing that these two optimisations coincide only in the first best case (see Proposition 5.2). We also study the sensibility of the optimal effort and the optimal remunerations with respect to appetence parameters and the corre- lation between the projects (see Proposition 5.3).

En savoir plus
These experimental results have been obtained in designing **principal** – **agent** games as a one-to-one relationship in which one **principal** faces one **agent**. However, in real life, most people are working within teams. Do these results hold when considering a **principal** – multi-**agent** relationship? As pointed out by Holmström in his seminal paper on moral hazard in teams (1982), a multi-**agent** setting is characterized both by an incentive for agents to free-ride in the context of joint production and by competition in controlling incentives, as agents play a non-cooperative game. An optimal allocation cannot be achieved as a Nash equilibrium with a binding budget balancing constraint (where the outcome is fully allocated to team members). A budget breaking rule, realized by introducing a **principal** as a residual claimant, can be efficiency-enhancing. The rule stipulates that the joint outcome will accrue to the **principal** in the event that the actual outcome has not reached the expected target level. Introducing a budget breaker would be more efficient than an active monitoring.

En savoir plus
June 24, 2019
Abstract
The first order behavior of multivariate heavy-tailed random vectors above large radial thresholds is ruled by a limit measure in a regular variation framework. For a high dimensional vector, a reasonable assumption is that the support of this mea- sure is concentrated on a lower dimensional subspace, meaning that certain linear combinations of the components are much likelier to be large than others. Identify- ing this subspace and thus reducing the dimension will facilitate a refined statistical analysis. In this work we apply **Principal** Component Analysis (PCA) to a re-scaled version of radially thresholded observations.

En savoir plus
activity of which is switched on and off by regulatory mechanisms. Model reduction is one possible approach to deal with model complexity and help deciphering the design principle of these networks. However, the reduced models can be still too complex to study and this does not answer the question on the role of each individual process in the network behaviour. Ideally, one would like to identify the major processes, quantify and then under- stand their contribution to the system dynamics. **Principal** Process Analysis was developed with this objective in mind, and with the final goal of simplifying the original model in one or several sub-models around core active processes that are responsible for the dynamics of the original system. The dynamics of the core processes is much more tractable in the sub-models than in the origi- nal one. Questions remained open though concerning the scalability and robustness of this approach.

En savoir plus
Catherine Schnedecker : Are premier, **principal**, primordial falling out of line adjectives?
The three adjectival expressions premier, **principal**, primordial are generally considered as being synonymous. Yet, primordial is close to the so called "qualifiers" whereas premier & **principal** are not. On the other hand premier & **principal** present original properties such as bi-valency, "parallel" graduability, partitivity and even performativity, a fact that general studies do not account for preferring giving credence to the idea of an adjectival category. Besides, premier & **principal** are complementary. Actually, premier comes from a "hierarchy" in the strict sense, unlike **principal**. It does not only account for the constraints weighing on adjacent nouns but also for the way the relations between a whole and its parts are conceptualized. Premier involving seemingly countables entities connected by a successivity relation whereas **principal** is operating in a "massiver way on blurred outlined entities".

En savoir plus
1.5. Contents. In Section 2 we introduce the categories of completed Harish- Chandra bimodules we will work with, and prove that restriction to a Kostant section is fully faithful on an appropriate subcategory. In Section 3 we develop our localization theory for Harish-Chandra bimodules. In Section 4 we prove (for later use) some technical results using the relation between U g and differential operators on the flag variety. In Section 5 we recall Abe’s results, and use them to construct our monoidal functor from the Hecke category to the appropriate category of rep- resentations of the universal centralizer. Finally, in Section 6 we prove the main result of the paper, i.e. we construct the Hecke action on the **principal** block and prove that objects associated with simple reflections act via wall-crossing functors. 1.6. Acknowledgements. We are given to understand that J. Ciappara has re- cently proved a result similar to our main theorem via a completely different method. His proof relies on the Smith–Treumann theory of [ RW2 ], and is still in preparation. We thank G. Williamson for keeping us informed of this work, and for useful comments.

En savoir plus
Fig. 6 Clustering results for the 200 first images of the MNIST database for digits 6 and 7.
encoded as a vector in lexicographic order where pixels with null variance (i.e., pixels mainly located in the image corners) have been removed, leading to observa- tion vectors of dimension D = 572. The objective of this experiment is to evaluate the need and impact for dimension reduction for this binary classification task. The results provided by the proposed method are compared with those obtained by using an expectation-maximization (EM) algorithm 2 as well as an MCMC al- gorithm, both inferring the parameters associated with the conventional Gaussian mixture model ( 41 ) described above. Both algorithms, denoted respectively by GMM-EM and GMM-MCMC, are preceded by a supervised dimension reduction preprocessing which consists in computing the first K **principal** components, for a wide set of dimensions K. We emphasize that the proposed BNP-PCA approach combined to an MCMC algorithm for inference addresses jointly the dimension re- duction and classification tasks as well as it identifies the dimension of the relevant latent subspace and estimates the noise level.

En savoir plus
2.1 The conditional Karhunen-Lo` eve expansion
The Karhunen-Lo`eve expansion (Lo`eve, 1978, Castro et al. 1986), also called empirical orthogonal functions in climatology (Preisendorfer and Mobley, 1988), is a direct extension of the **principal** components analysis when the observations are realizations of a random function. It can be seen as an optimal linear decomposition, according to a variance criterion, of the ran- dom function Y in a finite dimension functional space. This finite dimension space is spanned by the eigenfunctions associated to the largest values of the covariance operator of Y.

En savoir plus
visualize the natural force flow of an applied load through a structural system, 28 which approximately indicates the de- sirable material continuity for a given design domain. 29
The study of stress lines is related to Michell’s classical studies on structural optimization. 30 Michell’s theory states that a framework S within a region of space R resisting a loading Q will be of minimal volume if (1) any of its members are stressed up to their maximal allowable compression or tension stress; and (2) members of S are subjected to the same strain e in absolute value, with e defined as the maximum allowable strain within R. As denoted by Chen, 8 Hemp, 31 or Strang and Kohn, 32 such conditions imply that the members of S will lie along the lines of **principal** strains within R. Since stress and strain have the same **principal** directions, as Hooke’s law in linear elasticity for isotropic material indi- cates, the structures derived from principle stress line meth- ods are related to the optimal structures theorized by Michell, providing an explanation to the design convergence that is typically evident between the results of classical optimization methods (Fig. 5.2, 5.3) and both the **principal** stress lines (Fig. 5.4) and the Michell structures (Fig. 5.1) of the corre- sponding design domain. 33

En savoir plus