Approximate knowledge of rationality and correlated equilibria

We extend Aumann's [3] theorem deriving correlated equilibria as a consequence of common priors and common knowledge of rationality by explicitly allowing for non-rational behavior. We replace the assumption of common knowledge of rationality with a substantially weaker notion, joint p-belief of rationality, where agents believe the other agents are rational with probabilities p = (pi)i2I or more. We show that behavior in this case constitutes a constrained correlated equilibrium of a doubled game satisfying certain p-belief constraints and characterize the topological structure of the resulting set of p-rational outcomes. We establish continuity in the parameters p and show that, for p su ciently close to one, the p-rational outcomes are close to the correlated equilibria and, with high probability, supported on strategies that survive the iterated elimination of strictly dominated strategies. Finally, we extend Aumann and Dreze's [4] theorem on rational expectations of interim types to the broader p-rational belief systems, and also discuss the case of non-common priors.

On Bounded Strictly Positive Operators of Closed Range and Some Applications to Asymptotic Hyperstability of Dynamic Systems

The problem discussed is the stability of two input-output feedforward and feedback relations, under an integral-type constraint defining an admissible class of feedback controllers. Sufficiency-type conditions are given for the positive, bounded and of closed range feed-forward operator to be strictly positive and then boundedly invertible, with its existing inverse being also a strictly positive operator. The general formalism is first established and the linked to properties of some typical contractive and pseudocontractive mappings while some real-world applications and links of the above formalism to asymptotic hyperstability of dynamic systems are discussed later on.

Efficient learning of decomposable models with a bounded clique size

The learning of probability distributions from data is a ubiquitous problem in the fields of Statistics and Artificial Intelligence. During the last decades several learning algorithms have been proposed to learn probability distributions based on decomposable models due to their advantageous theoretical properties. Some of these algorithms can be used to search for a maximum likelihood decomposable model with a given maximum clique size, k, which controls the complexity of the model. Unfortunately, the problem of learning a maximum likelihood decomposable model given a maximum clique size is NP-hard for k > 2. In this work, we propose a family of algorithms which approximates this problem with a computational complexity of O(k · n^2 log n) in the worst case, where n is the number of implied random variables. The structures of the decomposable models that solve the maximum likelihood problem are called maximal k-order decomposable graphs. Our proposals, called fractal trees, construct a sequence of maximal i-order decomposable graphs, for i = 2, ..., k, in k − 1 steps. At each step, the algorithms follow a divide-and-conquer strategy based on the particular features of this type of structures. Additionally, we propose a prune-and-graft procedure which transforms a maximal k-order decomposable graph into another one, increasing its likelihood. We have implemented two particular fractal tree algorithms called parallel fractal tree and sequential fractal tree. These algorithms can be considered a natural extension of Chow and Liu’s algorithm, from k = 2 to arbitrary values of k. Both algorithms have been compared against other efficient approaches in artificial and real domains, and they have shown a competitive behavior to deal with the maximum likelihood problem. Due to their low computational complexity they are especially recommended to deal with high dimensional domains.

The role of personal involvement and responsibility in dictatorial allocations: A classroom experiment

Paper was revised on 2009-11-11.-- Published as article in: Rationality and Society (2009), 21(2), 1-24.

Stability of Switched Feedback Time-Varying Dynamic Systems Based on the Properties of the Gap Metric for Operators

The stabilization of dynamic switched control systems is focused on and based on an operator-based formulation. It is assumed that the controlled object and the controller are described by sequences of closed operator pairs (L, C) on a Hilbert space H of the input and output spaces and it is related to the existence of the inverse of the resulting input-output operator being admissible and bounded. The technical mechanism addressed to get the results is the appropriate use of the fact that closed operators being sufficiently close to bounded operators, in terms of the gap metric, are also bounded. That philosophy is followed for the operators describing the input-output relations in switched feedback control systems so as to guarantee the closed-loop stabilization.

Fixed Points of Closed and Compact Composite Sequences of Operators and Projectors in a Class of Banach Spaces

Some results on fixed points related to the contractive compositions of bounded operators in a class of complete metric spaces which can be also considered as Banach's spaces are discussed through the paper. The class of composite operators under study can include, in particular, sequences of projection operators under, in general, oblique projective operators. In this paper we are concerned with composite operators which include sequences of pairs of contractive operators involving, in general, oblique projection operators. The results are generalized to sequences of, in general, nonconstant bounded closed operators which can have bounded, closed, and compact limit operators, such that the relevant composite sequences are also compact operators. It is proven that in both cases, Banach contraction principle guarantees the existence of unique fixed points under contractive conditions.

Some Results on Fixed and Best Proximity Points of Multivalued

This paper is devoted to investigate the fixed points and best proximity points of multivalued cyclic self-mappings on a set of subsets of complete metric spaces endowed with a partial order under a generalized contractive condition involving a Hausdorff distance. The existence and uniqueness of fixed points of both the cyclic self-mapping and its associate composite self-mappings on each of the subsets are investigated, if the subsets in the cyclic disposal are nonempty, bounded and of nonempty convex intersection. The obtained results are extended to the existence of unique best proximity points in uniformly convex Banach spaces.

Viability Conditions for a Compartmentalized Protometabolic System: A Semi-Empirical Approach

In this work we attempt to find out the extent to which realistic prebiotic compartments, such as fatty acid vesicles, would constrain the chemical network dynamics that could have sustained a minimal form of metabolism. We combine experimental and simulation results to establish the conditions under which a reaction network with a catalytically closed organization (more specifically, an (M, R)-system) would overcome the potential problem of self-suffocation that arises from the limited accessibility of nutrients to its internal reaction domain. The relationship between the permeability of the membrane, the lifetime of the key catalysts and their efficiency (reaction rate enhancement) turns out to be critical. In particular, we show how permeability values constrain the characteristic time scale of the bounded protometabolic processes. From this concrete and illustrative example we finally extend the discussion to a wider evolutionary context.

Uncertain Information Structures and Backward Induction

In everyday economic interactions, it is not clear whether sequential choices are visible or not to other participants: agents might be deluded about opponents'capacity to acquire,interpret or keep track of data, or might simply unexpectedly forget what they previously observed (but not chose). Following this idea, this paper drops the assumption that the information structure of extensive-form games is commonly known; that is, it introduces uncertainty into players' capacity to observe each others' past choices. Using this approach, our main result provides the following epistemic characterisation: if players (i) are rational,(ii) have strong belief in both opponents' rationality and opponents' capacity to observe others' choices, and (iii) have common belief in both opponents' future rationality and op-ponents' future capacity to observe others' choices, then the backward induction outcome obtains. Consequently, we do not require perfect information, and players observing each others' choices is often irrelevant from a strategic point of view. The analysis extends {from generic games with perfect information to games with not necessarily perfect information{the work by Battigalli and Siniscalchi (2002) and Perea (2014), who provide different sufficient epistemic conditions for the backward induction outcome.

Gestión de recursos humanos en empresas cooperativas

ESPAÑOL Desde 2008, a causa de la crisis internacional, Mondragón Corporación Cooperativa se ve obligado a emplear ciertas políticas de gestión de los recursos humanos para sobrevivir a esa situación. La finalidad de este trabajo es identificar dichas políticas y valorar si realmente ofrecen los resultados esperados, analizando minuciosamente la relación entre el absentismo laboral y el compromiso y la motivación de los trabajadores. Este estudio propone que en situaciones de recesión económica, las políticas de formación y empleo y las prestaciones cubiertas por Lagun-Aro EPSV aumentan la motivación de los empleados y en consecuencia reducen la tasa de absentismo. La investigación se fundamenta en la lectura de artículos académicos, memorias de Lagun-Aro y una detallada entrevista realizada al que fue jefe de contabilidad en Eroski durante 9 años y director administrativo y responsable de las participadas de Lagun-Aro EPSV durante 30 años. Los resultados obtenidos muestran la existencia de una relación inversa entre el compromiso y la motivación y el absentismo laboral. Además se comprueba la eficiencia de las políticas llevadas a cabo por las cooperativas de Mondragón y se destaca el principio de intercooperatividad para la efectividad de esas políticas.

Contributions on agreement in dynamic distributed systems

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El mapa de Hecateo

[EN] The work of Hecataeus has not been sufficiently recogniced in its scientifical and symbolical importance. The elaboration of the map is in the origin of the theory of proportions, which is essential to the Greek mathematics, origin this that has not been never in mind of the investigators of the Greek mathematics. Its «Genealogies» break the cyclical experience of time of that archaic society. And the scientifical prose, of which he is one of the beginners, opens to new experiences of time, too, introduces a new type of privacy and exploits the potential rationality of the ordinary language, that the sacred poetry obstructed to manifest.

El «Ión»,fundador de la hermenéutica occidental

[ES] En el «Ión» Platón funda la hermenéutica occidental, no la práctica de la exégesis. Para ello debe rechazar el liderazgo de la poesía. Y en un triple frente. Como saber, la poesía no distingue entre significante y significado, y considera la interpretación como un mero descifrado, no como un análisis de la verdad y falsedad del significado. Como discurso legitimador, es una liturgia, no una funcionalización técnica, además de que oculta el conflicto en que toda sociedad consiste. Como competencia interactiva, el poeta no es autónomo, sino alienado, y pone en juego la emotividad, no la racionalidad. Desde este breve diálogo, la filosofía y la literatura se han disociado dramáticamente en la cultura occidental.