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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Nonzero-sum stochastic differential games with stopping times and free boundary problems


Authors: Alain Bensoussan and Avner Friedman
Journal: Trans. Amer. Math. Soc. 231 (1977), 275-327
MSC: Primary 93E05; Secondary 60G40, 60G10
DOI: https://doi.org/10.1090/S0002-9947-1977-0453082-7
MathSciNet review: 0453082
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Abstract: One is given a diffusion process and two payoffs which depend on the process and on two stopping times $ {\tau _1},{\tau _2}$. Two players are to choose their respective stopping times $ {\tau _1},{\tau _2}$ so as to achieve a Nash equilibrium point. The problem whether such times exist is reduced to finding a ``regular'' solution $ ({u_1},{u_2})$ of a quasi-variational inequality. Existence of a solution is established in the stationary case and, for one space dimension, in the nonstationary case; for the latter situation, the solution is shown to be regular if the game is of zero sum.


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DOI: https://doi.org/10.1090/S0002-9947-1977-0453082-7
Keywords: Stochastic differential games, stochastic differential equations, stopping time, payoff, Nash point, variational inequality, quasi-variational inequality, free boundary problem, nonzero-sum game, zero-sum game
Article copyright: © Copyright 1977 American Mathematical Society