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.

Relatório apresentado a S. Ex. o Sr. Ministro da Industria, Viação e Obras Públicas =Rapport présenté a Son Ex. M. le Ministre de l'Industrie, de la Voirie et des Travaux Publics /por L. Cruls. --Relatório da Comissão Exploradora do Planalto Central do Brazil = Rapport de la Commission d'Exploration du Plateau Central du Brésil

Documento com duas páginas-de-rosto, em português e francês. Título em francês : Rapport présenté a Son Ex. M. le Ministre de l'Industrie, de la Voirie et des Travaux Publics

Studies of physical, chemical, and biological oceanography in the vicinity of the Revilla Gigedo Islands during the “Island Current Survey” of 1957

ENGLISH: The tendency of the tunas, especially the yellowfin (Neothunnus macropterus) to be more abundant in the near vicinity of islands and seamounts, or "banks", than in the surrounding oceanic areas, is well known to commercial fishermen. This has been confirmed by statistical analysis of fishing vessel logbook records, which demonstrates that the catch-per-day's-fishing is, indeed, higher in the near vicinity of these features. It is hypothesized that islands and seamounts cause changes in the physical circulation or the biochemical cycle resulting in greater supplies of food for tunas in their immediate environs. In order to examine this hypothesis, and in order to study possible mechanisms involved, the "Island Current Survey" was undertaken from 8 May to 12 June, 1957, under the joint auspices of the Inter-American Tropical Tuna Commission and the Scripps Institution of Oceanography. Surveys of varying nature and extent were made from M/V Spencer F. Baird near Alijos Rocks, Clarion Island, Shimada Bank and Socorro Island (Figure 1). These studies sought to provide knowledge of the action of islands and seamounts in arresting, stalling or deflecting the mean current past them, in establishing convergence and divergence in the surface flow, in producing vertical motion (mixing and upwelling), and in influencing the primary production and the standing crops of phytoplankton and zooplankton. Each survey is discussed below in detail. Observations made at a front on 10 June will be discussed in another paper. SPANISH: Los pescadores que realizan la pesca comercial conocen muy bien la tendencia de los atunes, en particular del atún aleta amarilla (Neothunnus macropterus), de presentarse en mayor abundancia en las cercanías inmediatas a las islas y cimas submarinas, o "bancos", que en las áreas oceánicas circundantes. Este hecho ha sido confirmado par el análisis estadístico de los registros de los cuadernos de bitácora de las embarcaciones pesqueras, demostrándose que la captura par dias de pesca es, en efecto, más abundante en la inmediata proximidad de tales formaciones. Hipotéticamente se admite que las islas y las cimas submarinas provocan cambios en la circulación física o en el ciclo bioquímico, lo cual se pone de manifiesto a través de un mejor abastecimiento de alimento para los atunes en sus cercanías inmediatas. Con la finalidad de verificar esta hipótesis y de estudiar los mecanismos que ella involucra, se realizó la “Island Current Survey” del 8 de mayo al 12 de junio de 1957, bajo los auspicios de la Comisión Interamericana del Atún Tropical y de la Institución Scripps de Oceanografia. Con el barco Spencer F. Baird se hicieron observaciones de distintas clases y alcances cerca de las Rocas Alijos, la Isla Clarion, el Banco Shimada y la Isla Socorro (Figura 1). Estos estudios tuvieron por objeto adquirir conocimientos sobre la acción que ejercen las islas y cimas submarinas sobre la corriente promedio, ya sea deteniéndola, reduciendo su velocidad o desviando su curso, así como estableciendo convergencia o divergencia en su flujo de superficie, o provocando un movimiento vertical (mezcla y afloramiento) e influyendo en la producción primaria y en las existencias de fitoplancton y zooplancton. Cada operación será tratada a continuación por separado. Las observaciones hechas el dia 10 de junio sobre un frente serán objeto de otra publicación.