It is well known that, in general, Nash equilibria in open-loop strategies do not coincide with those in closed-loop strategies. This note identifies a class of differential games in which the Nash equilibrium in closed-loop strategies is degenerate, in the sense that it depends on time only. Consequently, the closed-loop equilibrium is also an equilibrium in open-loop strategies.
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Communicated by G. Leitmann
The helpful comments of Professors Y. C. Ho, G. Leitmann, H. Y. Wan, Jr., and an anonymous referee are gratefully acknowledged.
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Reinganum, J.F. A class of differential games for which the closed-loop and open-loop Nash equilibria coincide. J Optim Theory Appl 36, 253–262 (1982). https://doi.org/10.1007/BF00933832
- Differential games
- Nash equilibria
- open-loop strategies
- closed-loop strategies