On the definition of stochastic differential games an the existence of value ond of saddle points

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We give a definition of stochastic differential games similar to that given by Friedman for deterministic games.

We consider systems described by stochastic differential equations of ITO-NISIO type with open loop controls entering multiplicatively.

The gane is supposed to start at t=t0 and to end at a finite random time T with probability1.

We find that the existence theorems for the value and for the saddle points are valid again if some new conditions are assumed about the uniform integrability of the pay-off.


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Work supported by the C.N.R. through the Centro per la Matematica e la Fisica Teorica, c/o Istituto Matematico, Via L. B. Alberti 4, Genova.

The author would like to thank ProfessorJ. P. Cecconi for having suggested to him the object of this research and for useful discussions, and ProfessorT. Zolezzi for critical reading of the manuscript.

Entrata in Redazione il 25 febbraio 1972.

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Bafico, R. On the definition of stochastic differential games an the existence of value ond of saddle points. Annali di Matematica 96, 41–67 (1973).

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  • Differential Equation
  • Saddle Point
  • Stochastic Differential Equation
  • Loop Control
  • Existence Theorem