INVESTIGADORES
VIGLIZZO Ignacio Dario
artículos
Título:
Harsanyi Type Spaces and Final Coalgebras Constructed from Satisfied Theories
Autor/es:
LAWRENCE S. MOSS; IGNACIO VIGLIZZO
Revista:
ELECTRONIC NOTES IN THEORETICAL COMPUTER SCIENCE
Editorial:
Elsevier
Referencias:
Año: 2004 vol. 106 p. 279 - 295
ISSN:
1571-0661
Resumen:
This
paper connects coalgebra with a long discussion in the foundations of
game theory on the modeling of type spaces. We argue that type spaces
are coalgebras, that universal type spaces are final coalgebras, and
that the modal logics already proposed in the economic theory
literature are closely related to those in recent work in coalgebraic
modal logic. In the other direction, the categories of interest in
this work are usually measurable spaces or compact (Hausdorff)
topological spaces. A coalgebraic version of the construction of the
universal type space due to Heifetz and Samet [5]
is generalized for some functors in those categories. Since the
concrete categories of interest have not been explored so deeply in
the coalgebra literature, we have some new results.
We
show that every functor on the category of measurable spaces built
from constant functors, products, coproducts, and the probability
measure space functor has a final coalgebra. Moreover, we construct
this final coalgebra from the relevant version of coalgebraic modal
logic. Specifically, we consider the set of theories of points in all
coalgebras and endow this set with a measurable and coalgebra
structure.