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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...

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