A note on the convergence to competitive equilibria in economies with moral hazard

We examine the conditions under which competitive equilibria can beobtained as the limit, when the number of strategic traders getslarge, of Nash equilibria in economies with asymmetric informationon agents' effort and possibly imperfect observability of agents'trades. Convergence always occur when either effort is publiclyobserved (no matter what is the information available tointermediaries on agents' trades); or effort is private informationbut agents' trades are perfectly observed; or no information at allis available on agents' trades. On the other hand, when eachintermediary can observe its trades with an agent, but not theagent's trades with other intermediaries, the (Nash) equilibriawith strategic intermediaries do not converge to any of thecompetitive equilibria, for an open set of economies. The source ofthe difficulties for convergence is the combination of asymmetricinformation and the restrictions on the observability of tradeswhich prevent the formation of exclusive contractual relationshipsand generate barriers to entry in the markets for contracts.

A note on the dual scaling of dominance data and its relationship to correspondence analysis

Dual scaling of a subjects-by-objects table of dominance data (preferences,paired comparisons and successive categories data) has been contrasted with correspondence analysis, as if the two techniques were somehow different. In this note we show that dual scaling of dominance data is equivalent to the correspondence analysis of a table which is doubled with respect to subjects. We also show that the results of both methods can be recovered from a principal components analysis of the undoubled dominance table which is centred with respect to subject means.

A note on the Malliavin differentiability of the Heston volatility

We show that the Heston volatility or equivalently the Cox-Ingersoll-Ross process is Malliavin differentiable and give an explicit expression for the derivative. This result assures the applicability of Malliavin calculus in the framework of the Heston stochastic volatility model and the Cox-Ingersoll-Ross model for interest rates.

Note on the blocking flow shop problem

We present some results attained with different algorithms for the Fm|block|Cmax problem using as experimental data the well-known Taillard instances.

A note on quadrics through an algebraic curve

In this note we describe the intersection of all quadric hypersur- faces containing a given linearly normal smooth projective curve of genus n and degree 2n + 1

A note on the coincidence between Stackelberg and Nash equilibria in a differential game between government and firms

[cat] A Navas i Marín Solano es va demostrar la coincidència entre els equilibris de Nash i de Stackelberg per a una versi´o modificada del joc diferencial proposat por Lancaster (1973). Amb l’objectiu d’obtenir una solució interior, es van imposar restriccions importants sobre el valors dels paràmetres del model. En aquest treball estenem aquest resultat, en el límit en que la taxa de descompte és igual a zero, eliminant les restriccions i considerant totes les solucions possibles.

A Note on Shapley's convex measure games

L. S. Shapley, in his paper 'Cores of Convex Games', introduces Convex Measure Games, those that are induced by a convex function on R, acting over a measure on the coalitions. But in a note he states that if this function is a function of several variables, then convexity for the function does not imply convexity of the game or even superadditivity. We prove that if the function is directionally convex, the game is convex, and conversely, any convex game can be induced by a directionally convex function acting over measures on the coalitions, with as many measures as players

A Note on Shapley's convex measure games

L. S. Shapley, in his paper 'Cores of Convex Games', introduces Convex Measure Games, those that are induced by a convex function on R, acting over a measure on the coalitions. But in a note he states that if this function is a function of several variables, then convexity for the function does not imply convexity of the game or even superadditivity. We prove that if the function is directionally convex, the game is convex, and conversely, any convex game can be induced by a directionally convex function acting over measures on the coalitions, with as many measures as players

A note on the coincidence between Stackelberg and Nash equilibria in a differential game between government and firms

[cat] A Navas i Marín Solano es va demostrar la coincidència entre els equilibris de Nash i de Stackelberg per a una versi´o modificada del joc diferencial proposat por Lancaster (1973). Amb l’objectiu d’obtenir una solució interior, es van imposar restriccions importants sobre el valors dels paràmetres del model. En aquest treball estenem aquest resultat, en el límit en que la taxa de descompte és igual a zero, eliminant les restriccions i considerant totes les solucions possibles.

A note on the Lorenz-maximal allocations in the imputation set

In this note we introduce the Lorenz stable set and provide an axiomatic characterization in terms of constrained egalitarianism and projection consistency. On the domain of all coalitional games, we find that this solution connects the weak constrained egalitarian solution (Dutta and Ray, 1989) with their strong counterpart (Dutta and Ray, 1991)

A note on the degree sequences of graphs with restrictions

Degree sequences of some types of graphs will be studied and characterizedin this paper.

Compromise solutions for bankruptcy situations: a note

Although classic bankruptcy problems take into account a single claims vector, Pulido et al. (2008) show that there are real bankruptcy situations where agents face more than one reference vector. In particular, they consider the claims and an additional reference vector. To analyze these situations, they propose the extreme and the diagonal approaches. Nonetheless, the former approach depends on the order of the vectors: if we interchange the claims and the reference vectors, the result changes. Moreover their study is limited to the case in which the reference vector is lower than the claims vector. In the present note, we propose an extension that solves these short- comings by introducing the idea of impartiality. Keywords: bankruptcy problems; reference point; compromise solution; impartiality.

When cholesterol is not cholesterol: a note on the enzymatic determination of its concentration in model systems containing vegetable extracts

Background: Experimental evidences demonstrate that vegetable derived extracts inhibit cholesterol absorption in the gastrointestinal tract. To further explore the mechanisms behind, we modeled duodenal contents with several vegetable extracts. Results: By employing a widely used cholesterol quantification method based on a cholesterol oxidase-peroxidase coupled reaction we analyzed the effects on cholesterol partition. Evidenced interferences were analyzed by studying specific and unspecific inhibitors of cholesterol oxidase-peroxidase coupled reaction. Cholesterol was also quantified by LC/MS. We found a significant interference of diverse (cocoa and tea-derived) extracts over this method. The interference was strongly dependent on model matrix: while as in phosphate buffered saline, the development of unspecific fluorescence was inhibitable by catalase (but not by heat denaturation), suggesting vegetable extract derived H2O2 production, in bile-containing model systems, this interference also comprised cholesterol-oxidase inhibition. Several strategies, such as cholesterol standard addition and use of suitable blanks containing vegetable extracts were tested. When those failed, the use of a mass-spectrometry based chromatographic assay allowed quantification of cholesterol in models of duodenal contents in the presence of vegetable extracts. Conclusions: We propose that the use of cholesterol-oxidase and/or peroxidase based systems for cholesterol analyses in foodstuffs should be accurately monitored, as important interferences in all the components of the enzymatic chain were evident. The use of adequate controls, standard addition and finally, chromatographic analyses solve these issues.

A note on the periodic orbits and topological entropy of graph maps

This paper deals with the relationship between the periodic orbits of continuous maps on graphs and the topological entropy of the map. We show that the topological entropy of a graph map can be approximated by the entropy of its periodic orbits.