Type space on a purely measurable parameter space

Several game theoretical topics require the analysis of hierarchical beliefs, particularly in incomplete information situations. For the problem of incomplete information, Hars´anyi suggested the concept of the type space. Later Mertens & Zamir gave a construction of such a type space under topological assumptions imposed on the parameter space. The topological assumptions were weakened by Heifetz, and by Brandenburger & Dekel. In this paper we show that at very natural assumptions upon the structure of the beliefs, the universal type space does exist. We construct a universal type space, which employs purely a measurable parameter space structure

Algebraic duality theorems for infinite LP problems

In this paper we consider a primal-dual infinite linear programming problem-pair, i.e. LPs on infinite dimensional spaces with infinitely many constraints. We present two duality theorems for the problem-pair: a weak and a strong duality theorem. We do not assume any topology on the vector spaces, therefore our results are algebraic duality theorems. As an application, we consider transferable utility cooperative games with arbitrarily many players

On the completeness of the universal knowledge-belief space

Meier (2008) shows that the universal knowledge-belief space exists. However, besides the universality there is an other important property might be imposed on knowledge-belief spaces, inherited also from type spaces, the completeness. In this paper we introduce the notion of complete knowledge-belief space, and demonstrate that the universal knowledge-belief space is not complete, that is, some subjective beliefs (probability measures) on the universal knowledge-belief space are not knowledge-belief types

Birth, life and death of the Pannonian Lake

The Miocene-Pliocene Pannonian Lake formed in an extensional basin system behind the compressional arc of the Carpathians. Its size and depth were comparable to those of the Caspian Sea. Subsidence began in Middle Miocene times, forming deep, pelagic basins, separated by reef-bearing ridges. Clastic influx filled the marginal basins during Middle Miocene time. Prograding deltas dissected the lake and completed the infilling of the basin system by the end of the Pliocene. Basin plain, prodelta, delta front, delta plain, beach, fluviatile, and marsh environments can be recognized. Terminal Miocene uplift of the Carpathians isolated the Pannonian region from the rest of Paratethys. The subsequent decrease of salinity resulted in the evolution of an endemic, freshwater mollusc fauna. Rich nutrient influx from rivers supported high organic productivity (dinoflagellates, diatoms, nannoplankton, foraminifers, ostracods, etc.), yielding organic-rich sediments. Preservation of organic matter was helped by a stratified water column and oxygen deficient bottom conditions. Deep burial, continuing subsidence, and high geothermal flux due to an extremely thin crust, led to the formation of commercially exploitable oil and gas accumulations. Shallow lacustrine zones of basin margins provided suitable environments for a rich Congeria-Melanopsis mollusc fauna. Wave action on beaches produced commercially exploitable pure quartz sand deposits. Taxodium and Alnus forests flourished around the lake producing enormous lignite deposits. Besides a rich land snail and mammal fauna, prehominids lived in the forests. There was a warm, temperate climate, with probably frostfree winters. Basaltic volcanoes overlooked the landscape, and maars hosted minor lakes with rich algal flora forming oil shale. The catchment area included most of the Carpathians and parts of the Alps and Dinarides. The positive water balance resulted in a supposed overflow in the southern margin, supplying exotic fauna to the South Carpathian and Dacian basins of the Eastern Paratethys. The Pannonian Lake was completely filled by the end of Pliocene. Recent lakes in the Carpathian Basin are not descendants of it