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Stochastic nonzero-sum games: a new connection between singular control and optimal stopping. (English) Zbl 1443.91037

The paper studies a connection between singular stochastic control problem and question of optimal stopping by extending the existing results to non-zero-sum multi-agent optimisation problem. The main theorem establishes a differention link between the value functions relative to Nash equilibria in the two-player game of stopping and the value functions relative to Nash equilibria in the game of control.
These games involve two different underlying one-dimensional Itô diffusions.

MSC:

91A15 Stochastic games, stochastic differential games
91A05 2-person games
93E20 Optimal stochastic control
91A55 Games of timing
60G40 Stopping times; optimal stopping problems; gambling theory
60J60 Diffusion processes
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References:

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