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Nash equilibria of threshold type for two-player nonzero-sum games of stopping. (English) Zbl 1390.91038

Summary: This paper analyses two-player nonzero-sum games of optimal stopping on a class of linear regular diffusions with not nonsingular boundary behaviour (in the sense of K. Itô and H. P. McKean jun. [Diffusion processes and their sample paths. Berlin-Heidelberg-New York: Springer-Verlag (1974; Zbl 0285.60063), p. 108]. We provide sufficient conditions under which Nash equilibria are realised by each player stopping the diffusion at one of the two boundary points of an interval. The boundaries of this interval solve a system of algebraic equations. We also provide conditions sufficient for the uniqueness of the equilibrium in this class.

MSC:

91A15 Stochastic games, stochastic differential games
60G40 Stopping times; optimal stopping problems; gambling theory
60J60 Diffusion processes
91A05 2-person games

Citations:

Zbl 0285.60063
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References:

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