Juan Carlos Cesco

Perfection of Nash equilibria in continuous games

Abstract In this paper we introduce a generalization of Seltens perfect equilibrium for continuous n -person games in normal form. We also study some properties of our new concept as well as its relationship with other equilibria. Some facts that we show contrast significantly with the finite theory.

Hedonic games related to many-to-one matching problems

We consider the existence problem of stable matchings in many-to-one matching problems. Unlike other approaches which use algorithmic techniques to give necessary and sufficient conditions, we adopt a game theoretic point of view. We first associate, with each many-to-one matching problem, a hedonic game to take advantage of recent results guaranteeing the existence of core-partitions for that class of games, to build up our conditions. The main result states that a many-to-one matching problem, with no restrictions on individual preferences, has stable* matchings if and only if a related hedonic game is pivotally balanced. In the case that the preferences in the matching problem are substitutable, the notions of stability and stability* coincide.

Numerical evaluation of three‐ and four‐center bielectronic integrals using exponential‐type atomic orbitals

Three‐ and four‐center Slater orbital bielectronic integrals are evaluated by means of a complete function set. The method provides a series to approximate the bielectronic integrals. Their corresponding partial sums are analyzed in detail for 1s orbitals. The comparison with the Fourier transform–based method brings forth encouraging perspectives for the present approach.

Fundamental cycles of pre-imputations in non-balanced TU-games

In this paper we prove a characterization for the subclass of non-balanced TU-games. The result is stated in terms of certain class of cycles of pre-imputations. A cycle is a finite sequence of pre-imputations, where each pair of neighbouring elements are interrelated to each other through a transfer of some amount of utility from members of a certain coalition to the members of the complementary coalition, with the understanding that individual gains or losses within any coalition are proportional to the number of members of the coalition. These cycles are strongly connected with a transfer scheme designed to reach a point in the core of a TU-game provided this set is non-empty.The main result of this paper provides an alternative characterization of balanced TU-games to Shapley-Bondareva’s theorem.

U-CYCLES IN n-PERSON TU-GAMES WITH ONLY 1, n - 1 AND n-PERSON PERMISSIBLE COALITIONS

It has been recently proved that the non-existence of certain type of cycles of pre-imputation, fundamental cycles, is equivalent to the balancedness of a TU-games (Cesco (2003)). In some cases, the class of fundamental cycles can be narrowed and still obtain a characterization theorem. In this paper we prove that existence of maximal U-cycles, which are related to a transfer scheme designed for computing a point in the core of a game, is condition necessary and sufficient for a TU-game be non-balanced, provided n - 1 and n-person are the only coalitions with non-zero value. These games are strongly related to games with only 1, n - 1 and n-person permissible coalitions (Maschler (1963)).

Implementation of atomic basis set composed of 1s Gaussian and 1s Slater‐type orbitals to carry out quantum mechanics molecular calculations

A mixed atomic basis set formed with ls Slater‐type orbitals and 1s floating spherical Gaussian orbitals is implemented. Evaluation of multicenter integrals is carried out using a method based on expansion of binary products of atomic basis functions in terms of a complete basis set, and a systematic analysis is performed. The proposed algorithm is very stable and furnishes fairly good results for total energy and geometry. An LCAO‐SCF test calculation is carried out on LiH. The trends observed show that there are some combinations of mixed orbitals that are appropriate to describe the system. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 604–609, 1999

A simple graphical method for estimating the components of the fault-slip vector

Abstract A simple calculation of the components of the total slip vector ( D ) on a fault plane allows the relationships between the magnitudes of the three slip components of D , the lateral horizontal displacement ( L ), the transversal horizontal displacement ( T ) and the vertical offset ( V ), to be determined. The contribution of each slip component to the total slip can be plotted jointly in a ternary diagram, assuming a unit length of the vector modulus and a suitable normalization for D . Each component equals the magnitude of D at the vertices of the diagram, hence it is possible to estimate the percentage contribution of each slip component to the total movement of a fault or a set of faults. The dip of the fault surface and the rake of the slickenlines are the input data required for displaying L , T and V relationships in these diagrams. This information may be useful in the analysis of movement geometry for different fault populations and in the determination of D by measuring just one of the fault-slip components, such as vertical slip associated with a fault scarp.

On the geometric dimension of the core of a TU-game

Fil: Cesco, Juan Carlos. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Centro Cientifico Tecnologico San Luis. Instituto de Matematica Aplicada de San Luis; Argentina

An extension of Peleg's inequality

In this note, we prove an extension of a remarkable result due to B. Peleg. Pelegs result concerns the simultaneous validity of a set of inequalities for families of functions defined on a finite product of standard simplices in finite-dimensional spaces. The main result we prove here provides an extension of that result to the case of functions defined on a rather general product of simplices. Some topological requirements lead us to deal with this problem from a functional point of view.

A NECESSARY AND SUFFICIENT CONDITION FOR THE NON-EMPTINESS OF THE SOCIALLY STABLE CORE IN STRUCTURED TU-GAMES

In this note we provide a neccesary and sufficient condition for the non-emptiness of the socially stable core of a general structured TU-game which resembles closely the classical condition of balancedness given by Bondareva (1963) and Shapley (1967) to guarantee the non-emptiness of the classical core. Structured games have been introduced in Herings et al. (2007a) and more recently, in Herings et al. (2007b), studied in the framework of games with transferable utility. In the latter paper, the authors provide suffcient conditions for the non-emptiness of the socially stable core, but up to now, no necessary and sufficient condition is known.