Implementation, elimination of weakly dominated strategies and evolutionary dynamics

This paper is concerned with the realism of mechanisms that implementsocial choice functions in the traditional sense. Will agents actually playthe equilibrium assumed by the analysis? As an example, we study theconvergence and stability properties of Sj\"ostr\"om's (1994) mechanism, onthe assumption that boundedly rational players find their way to equilibriumusing monotonic learning dynamics and also with fictitious play. Thismechanism implements most social choice functions in economic environmentsusing as a solution concept the iterated elimination of weakly dominatedstrategies (only one round of deletion of weakly dominated strategies isneeded). There are, however, many sets of Nash equilibria whose payoffs maybe very different from those desired by the social choice function. Withmonotonic dynamics we show that many equilibria in all the sets ofequilibria we describe are the limit points of trajectories that havecompletely mixed initial conditions. The initial conditions that lead tothese equilibria need not be very close to the limiting point. Furthermore,even if the dynamics converge to the ``right'' set of equilibria, it stillcan converge to quite a poor outcome in welfare terms. With fictitious play,if the agents have completely mixed prior beliefs, beliefs and play convergeto the outcome the planner wants to implement.

Shaping mechanisms of metal specificity in a family of metazoan Metallothioneins: evolutionary differentiation of Mollusc MTs.

Background: The degree of metal binding specificity in metalloproteins such as metallothioneins (MTs) can be crucial for their functional accuracy. Unlike most other animal species, pulmonate molluscs possess homometallic MT isoforms loaded with Cu+ or Cd2+. They have, so far, been obtained as native metal-MT complexes from snail tissues, where they are involved in the metabolism of the metal ion species bound to the respective isoform. However, it has not as yet been discerned if their specific metal occupation is the result of a rigid control of metal availability, or isoform expression programming in the hosting tissues or of structural differences of the respective peptides determining the coordinative options for the different metal ions. In this study, the Roman snail (Helix pomatia) Cu-loaded and Cd-loaded isoforms (HpCuMT and HpCdMT) were used as model molecules in order t o elucidate the biochemical and evolutionary mechanisms permitting pulmonate MTs to achieve specificity for their cognate metal ion. Results: HpCuMT and HpCdMT were recombinantly synthesized in the presence of Cd2+, Zn2+ or Cu2+ and corresponding metal complexes analysed by electrospray mass spectrometry and circular dichroism (CD) and ultra violet-visible (UV-Vis) spectrophotometry. Both MT isoforms were only able to form unique, homometallic and stable complexes (Cd6-HpCdMT and Cu12-HpCuMT) with their cognate metal ions. Yeast complementation assays demonstrated that the two isoforms assumed metal-specific functions, in agreement with their binding preferences, in heterologous eukaryotic environments. In the snail organism, the functional metal specificity of HpCdMT and HpCuMT was contributed by metal-specific transcription programming and cell-specific expression. Sequence elucidation and phylogenetic analysis of MT isoforms from a number of snail species revealed that they possess an unspecific and two metal-specific MT isoforms, whose metal specificity was achieved exclusively by evolutionary modulation of non-cysteine amino acid positions. Conclusion: The Roman snail HpCdMT and HpCuMT isoforms can thus be regarded as prototypes of isoform families that evolved genuine metal-specificity within pulmonate molluscs. Diversification into these isoforms may have been initiated by gene duplication, followed by speciation and selection towards opposite needs for protecting copper-dominated metabolic pathways from nonessential cadmium. The mechanisms enabling these proteins to be metal-specific could also be relevant for other metalloproteins.

A system-level, molecular evolutionary analysis of mammalian phototransduction

Visual perception is initiated in the photoreceptor cells of the retina via the phototransduction system.This system has shown marked evolution during mammalian divergence in such complex attributes as activation time and recovery time. We have performed a molecular evolutionary analysis of proteins involved in mammalianphototransduction in order to unravel how the action of natural selection has been distributed throughout thesystem to evolve such traits. We found selective pressures to be non-randomly distributed according to both a simple protein classification scheme and a protein-interaction network representation of the signaling pathway. Proteins which are topologically central in the signaling pathway, such as the G proteins, as well as retinoid cycle chaperones and proteins involved in photoreceptor cell-type determination, were found to be more constrained in their evolution. Proteins peripheral to the pathway, such as ion channels and exchangers, as well as the retinoid cycle enzymes, have experienced a relaxation of selective pressures. Furthermore, signals of positive selection were detected in two genes: the short-wave (blue) opsin (OPN1SW) in hominids and the rod-specific Na+/Ca2+,K+ ion exchanger (SLC24A1) in rodents. The functions of the proteins involved in phototransduction and the topology of the interactions between them have imposed non-random constraints on their evolution. Thus, in shaping or conserving system-level phototransduction traits, natural selection has targeted the underlying proteins in a concerted manner.

Affinity distribution functions in multicomponent heterogeneous adsorption. Analytical inversion of isotherms to obtain affinity spectra

An analytical approach for the interpretation of multicomponent heterogeneous adsorption or complexation isotherms in terms of multidimensional affinity spectra is presented. Fourier transform, applied to analyze the corresponding integral equation, leads to an inversion formula which allows the computation of the multicomponent affinity spectrum underlying a given competitive isotherm. Although a different mathematical methodology is used, this procedure can be seen as the extension to multicomponent systems of the classical Sips’s work devoted to monocomponent systems. Furthermore, a methodology which yields analytical expressions for the main statistical properties (mean free energies of binding and covariance matrix) of multidimensional affinity spectra is reported. Thus, the level of binding correlation between the different components can be quantified. It has to be highlighted that the reported methodology does not require the knowledge of the affinity spectrum to calculate the means, variances, and covariance of the binding energies of the different components. Nonideal competitive consistent adsorption isotherm, widely used in metal/proton competitive complexation to environmental macromolecules, and Frumkin competitive isotherms are selected to illustrate the application of the reported results. Explicit analytical expressions for the affinity spectrum as well as for the matrix correlation are obtained for the NICCA case. © 2004 American Institute of Physics.

Urban population density functions : the case of the Barcelona region

L'anàlisi de la densitat urbana és utilitzada per examinar la distribució espacial de la població dins de les àrees urbanes, i és força útil per planificar els serveis públics. En aquest article, s'estudien setze formes funcionals clàssiques de la relació existent entre la densitat i la distancia en la regió metropolitana de Barcelona i els seus onze subcentres.

Embedding theorems of funcitional classes, III

In this paper we obtain the necessary and sufficient conditions for embedding results of different function classes. The main result is a criterion for embedding theorems for the so-called generalized Weyl-Nikol'skii class and the generalized Lipschitz class. To define the Weyl-Nikol'skii class, we use the concept of a (λ,β)-derivative, which is a generalization of the derivative in the sense of Weyl. As corollaries, we give estimates of norms and moduli of smoothness of transformed Fourier series.

Some remarks on the class of continuous (Semi-) strictcly quasiconvex functions

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Clarke critical values of subanalytic Lipschitz continuous functions

We prove that any subanalytic locally Lipschitz function has the Sard property. Such functions are typically nonsmooth and their lack of regularity necessitates the choice of some generalized notion of gradient and of critical point. In our framework these notions are defined in terms of the Clarke and of the convex-stable subdifferentials. The main result of this note asserts that for any subanalytic locally Lipschitz function the set of its Clarke critical values is locally finite. The proof relies on Pawlucki's extension of the Puiseuxlemma. In the last section we give an example of a continuous subanalytic function which is not constant on a segment of "broadly critical" points, that is, points for which we can find arbitrarily short convex combinations of gradients at nearby points.

Embedding theorems of function classes, IV

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Embedding theorems of function classes, II

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Embedding theorems of function classes, I

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Elicited bid functions in (a)symmetric first-price auctions

We report on a series of experiments that examine bidding behavior in first-price sealed bid auctions with symmetric and asymmetric bidders. To study the extent of strategic behavior, we use an experimental design that elicits bidders' complete bid functions in each round (auction) of the experiment. In the aggregate, behavior is consistent with the basic equilibrium predictions for risk neutral or homogenous risk averse bidders (extent of bid shading, average seller's revenues and deviations from equilibrium). However, when we look at the extent of best reply behavior and the shape of bid functions, we find that individual behavior is not in line with the received equilibrium models, although it exhibits strategic sophistication.

Increasing quasiconcave production and utility functions with diminishing returns to scale

In microeconomic analysis functions with diminishing returns to scale (DRS) have frequently been employed. Various properties of increasing quasiconcave aggregator functions with DRS are derived. Furthermore duality in the classical sense as well as of a new type is studied for such aggregator functions in production and consumer theory. In particular representation theorems for direct and indirect aggregator functions are obtained. These involve only small sets of generator functions. The study is carried out in the contemporary framework of abstract convexity and abstract concavity.

Can genetic algorithms explain experimental anomalies? An application to common property resources

It is common to find in experimental data persistent oscillations in the aggregate outcomes and high levels of heterogeneity in individual behavior. Furthermore, it is not unusual to find significant deviations from aggregate Nash equilibrium predictions. In this paper, we employ an evolutionary model with boundedly rational agents to explain these findings. We use data from common property resource experiments (Casari and Plott, 2003). Instead of positing individual-specific utility functions, we model decision makers as selfish and identical. Agent interaction is simulated using an individual learning genetic algorithm, where agents have constraints in their working memory, a limited ability to maximize, and experiment with new strategies. We show that the model replicates most of the patterns that can be found in common property resource experiments.