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.

Approximate Best Proximity Points of Cyclic Self-maps in Metric Spaces and Cyclic Asymptotic Regularity

3rd International Conference on Mathematical Modeling in Physical Sciences (IC-MSQUARE) Madrid, AUG 28-31, 2014 / editado por Vagenas, EC; Vlachos, DS; Bastos, C; Hofer, T; Kominis, Y; Kosmas, O; LeLay, G; DePadova, P; Rode, B; Suraud, E; Varga, K

Approximate Solutions by Truncated Taylor Series Expansions of Nonlinear Differential Equations and Related Shadowing Property with Applications

This paper investigates the errors of the solutions as well as the shadowing property of a class of nonlinear differential equations which possess unique solutions on a certain interval for any admissible initial condition. The class of differential equations is assumed to be approximated by well-posed truncated Taylor series expansions up to a certain order obtained about certain, in general nonperiodic, sampling points t(i) is an element of [t(0), t(J)] for i = 0, 1, . . . , J of the solution. Two examples are provided.

A Behavioral Foundation for Models of Evolutionary Drift

Binmore and Samuelson (1999) have shown that perturbations (drift) are crucial to study the stability properties of Nash equilibria. We contribute to this literature by providing a behavioural foundation for models of evolutionary drift. In particular, this article introduces a microeconomic model of drift based on the similarity theory developed by Tversky (1977), Kahneman and Tversky (1979) and Rubinstein (1988),(1998). An innovation with respect to those works is that we deal with similarity relations that are derived from the perception that each agent has about how well he is playing the game. In addition, the similarity relations are adapted to a dynamic setting. We obtain different models of drift depending on how we model the agent´s assessment of his behaviour in the game. The examples of the ultimatum game and the chain-store game are used to show the conditions for each model to stabilize elements in the component of Nash equilibria that are not subgame- perfect. It is also shown how some models approximate the laboratory data about those games while others match the data.

Aproximación al pintor Epifanio Díaz de Arcaute (1845-1910)

[ES]Con este trabajo pretendemos aproximarnos a la figura de Epifanio Díaz de Arcaute (1845-1910), un pintor no demasiado conocido y con una producción artística, por el momento, escasa. Su formación fue tradicional y académica, vinculada a la Academia de Bellas Artes de Vitoria, de la que terminó siendo profesor.

Analysis of Spanish text-thesaurus as a complex network

[EN]Based on the theoretical tools of Complex Networks, this work provides a basic descriptive study of a synonyms dictionary, the Spanish Open Thesaurus represented as a graph. We study the main structural measures of the network compared with those of a random graph. Numerical results show that Open-Thesaurus is a graph whose topological properties approximate a scale-free network, but seems not to present the small-world property because of its sparse structure. We also found that the words of highest betweenness centrality are terms that suggest the vocabulary of psychoanalysis: placer (pleasure), ayudante (in the sense of assistant or worker), and regular (to regulate).

The Expanded mtDNA Phylogeny of the Franco-Cantabrian Region Upholds the Pre-Neolithic Genetic Substrate of Basques

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Language distance and non-native syntactic processing: Evidence from event-related potentials

[EN] In this study, we explore native and non-native syntactic processing, paying special attention to the language distance factor. To this end, we compared how native speakers of Basque and highly proficient non-native speakers of Basque who are native speakers of Spanish process certain core aspects of Basque syntax. Our results suggest that differences in native versus non-native language processing strongly correlate with language distance: native/non-native processing differences obtain if a syntactic parameter of the non-native grammar diverges from the native grammar. Otherwise, non-native processing will approximate native processing as levels of proficiency increase. We focus on three syntactic parameters: (i) the head parameter, (ii) argument alignment (ergative/accusative), and (iii) verb agreement. The first two diverge in Basque and Spanish, but the third is the same in both languages. Our results reveal that native and non-native processing differs for the diverging syntactic parameters, but not for the convergent one. These findings indicate that language distance has a significant impact in non-native language processing.