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Z -equilibria in many-player stochastic differential games

Svatoslav Gaidov (1993)

Archivum Mathematicum

In this paper N -person nonzero-sum games are considered. The dynamics is described by Ito stochastic differential equations. The cost-functions are conditional expectations of functionals of Bolza type with respect to the initial situation. The notion of Z -equilibrium is introduced in many-player stochastic differential games. Some properties of Z -equilibria are analyzed. Sufficient conditions are established guaranteeing the Z -equilibrium for the strategies of the players. In a particular case...

Zone and double zone diagrams in abstract spaces

Daniel Reem, Simeon Reich (2009)

Colloquium Mathematicae

A zone diagram of order n is a relatively new concept which was first defined and studied by T. Asano, J. Matoušek and T. Tokuyama. It can be interpreted as a state of equilibrium between n mutually hostile kingdoms. Formally, it is a fixed point of a certain mapping. These authors considered the Euclidean plane with finitely many singleton-sites and proved the existence and uniqueness of zone diagrams there. In the present paper we generalize this concept in various ways. We consider general sites...

μ -bicomplete categories and parity games

Luigi Santocanale (2002)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

For an arbitrary category, we consider the least class of functors containing the projections and closed under finite products, finite coproducts, parameterized initial algebras and parameterized final coalgebras, i.e. the class of functors that are definable by μ -terms. We call the category μ -bicomplete if every μ -term defines a functor. We provide concrete examples of such categories and explicitly characterize this class of functors for the category of sets and functions. This goal is achieved...

μ-Bicomplete Categories and Parity Games

Luigi Santocanale (2010)

RAIRO - Theoretical Informatics and Applications

For an arbitrary category, we consider the least class of functors containing the projections and closed under finite products, finite coproducts, parameterized initial algebras and parameterized final coalgebras, i.e. the class of functors that are definable by μ-terms. We call the category μ-bicomplete if every μ-term defines a functor. We provide concrete examples of such categories and explicitly characterize this class of functors for the category of sets and functions. This goal is achieved...

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