Dynamic stackelberg game with risk-averse players: optimal risk-sharing under asymmetric information

The objective of this paper is to clarify the interactive nature of the leader-follower relationship when both players are endogenously risk-averse. The analysis is placed in the context of a dynamic closed-loop Stackelberg game with private information. The case of a risk-neutral leader, very often discussed in the literature, is only a borderline possibility in the present study. Each player in the game is characterized by a risk-averse type which is unknown to his opponent. The goal of the leader is to implement an optimal incentive compatible risk-sharing contract. The proposed approach provides a qualitative analysis of adaptive risk behavior profiles for asymmetrically informed players in the context of dynamic strategic interactions modelled as incentive Stackelberg games.

Spectral analysis of random sparse matrices

"Vegeu el resum a l'inici del document del fitxer adjunt."

Optimal coexistence of long-term and short-term contracts in labor Markets

We consider a market where firms hire workers to run their projects and such projects differ in profitability. At any period, each firm needs two workers to successfully run its project: a junior agent, with no specific skills, and a senior worker, whose effort is not verifiable. Senior workers differ in ability and their competence is revealed after they have worked as juniors in the market. We study the length of the contractual relationships between firms and workers in an environment where the matching between firms and workers is the result of market interaction. We show that, despite in a one-firm-one-worker set-up long-term contracts are the optimal choice for firms, market forces often induce firms to use short-term contracts. Unless the market only consists of firms with very profitable projects, firms operating highly profitable projects offer short-term contracts to ensure the service of high-ability workers and those with less lucrative projects also use short-term contracts to save on the junior workers' wage. Intermediate firms may (or may not) hire workers through long-term contracts.

The link between public support and private R&D effort: What is the optimal subsidy?

The effectiveness of R&D subsidies can vary substantially depending on their characteristics. Specifically, the amount and intensity of such subsidies are crucial issues in the design of public schemes supporting private R&D. Public agencies determine the intensities of R&D subsidies for firms in line with their eligibility criteria, although assessing the effects of R&D projects accurately is far from straightforward. The main aim of this paper is to examine whether there is an optimal intensity for R&D subsidies through an analysis of their impact on private R&D effort. We examine the decisions of a public agency to grant subsidies taking into account not only the characteristics of the firms but also, as few previous studies have done to date, those of the R&D projects. In determining the optimal subsidy we use both parametric and nonparametric techniques. The results show a non-linear relationship between the percentage of subsidy received and the firms’ R&D effort. These results have implications for technology policy, particularly for the design of R&D subsidies that ensure enhanced effectiveness.

On the stability of the optimal value and the optimal set in optimization problems

The paper develops a stability theory for the optimal value and the optimal set mapping of optimization problems posed in a Banach space. The problems considered in this paper have an arbitrary number of inequality constraints involving lower semicontinuous (not necessarily convex) functions and one closed abstract constraint set. The considered perturbations lead to problems of the same type as the nominal one (with the same space of variables and the same number of constraints), where the abstract constraint set can also be perturbed. The spaces of functions involved in the problems (objective and constraints) are equipped with the metric of the uniform convergence on the bounded sets, meanwhile in the space of closed sets we consider, coherently, the Attouch-Wets topology. The paper examines, in a unified way, the lower and upper semicontinuity of the optimal value function, and the closedness, lower and upper semicontinuity (in the sense of Berge) of the optimal set mapping. This paper can be seen as a second part of the stability theory presented in [17], where we studied the stability of the feasible set mapping (completed here with the analysis of the Lipschitz-like property).

On p-optimal proof systems and logics for PTIME

"Vegeu el resum a l'inici del document del fitxer adjunt"

On slicewise monotone parameterized problems and optimal proof systems for TAUT

"Vegeu el resum a l'inici del document del fitxer adjunt"

Optimal asymptotic bounds for spherical designs

"Vegeu el resum a l'inici del document del fitxer adjunt"

Approximation algorithms for two-state anti-ferromagnetic spin systems on bounded degree graphs

In a seminal paper [10], Weitz gave a deterministic fully polynomial approximation scheme for counting exponentially weighted independent sets (which is the same as approximating the partition function of the hard-core model from statistical physics) in graphs of degree at most d, up to the critical activity for the uniqueness of the Gibbs measure on the innite d-regular tree. ore recently Sly [8] (see also [1]) showed that this is optimal in the sense that if here is an FPRAS for the hard-core partition function on graphs of maximum egree d for activities larger than the critical activity on the innite d-regular ree then NP = RP. In this paper we extend Weitz's approach to derive a deterministic fully polynomial approximation scheme for the partition function of general two-state anti-ferromagnetic spin systems on graphs of maximum degree d, up to the corresponding critical point on the d-regular tree. The main ingredient of our result is a proof that for two-state anti-ferromagnetic spin systems on the d-regular tree, weak spatial mixing implies strong spatial mixing. his in turn uses a message-decay argument which extends a similar approach proposed recently for the hard-core model by Restrepo et al [7] to the case of general two-state anti-ferromagnetic spin systems.

Designing the Optimal Conservativeness of the Central Bank

In this paper we propose a new measure of the degree of conservativeness of an inde- pendent central bank and we derive the optimal value from the social welfare perspective. We show that the mere appointment of an independent central bank is not enough to achieve lower inflation, which may explain the mixed results found between central bank independence and inflation in the empirical literature. Further, the optimal central bank should not be too conservative. For instance, we will show that in some circumstances it will be optimal that the central bank is less conservative than society in the Rogoff sense. JEL classification: E58, E63. Keywords: Central bank; Conservativeness; Independence.

On spectral properties of the modified convolution operator

Vegeu el resum a l'inici del document del fitxer adjunt.

Krein's strings whose spectral functions are of polynomial growth

In case Krein's strings with spectral functions of polynomial growth a necessary and su fficient condition for the Krein's correspondence to be continuous is given.

Weighted Logratio Biplots, Correspondence Analysis and Spectral Maps

Starting with logratio biplots for compositional data, which are based on the principle of subcompositional coherence, and then adding weights, as in correspondence analysis, we rediscover Lewi's spectral map and many connections to analyses of two-way tables of non-negative data. Thanks to the weighting, the method also achieves the property of distributional equivalence