Existence of value functions of differential games with incomplete information in partially order spaces. (English) Zbl 1514.91028
Summary: In this paper, we consider a two-person zero-sum differential game with incomplete information on the initial state, namely, the first player has a private information while the second player knows only a probability distribution on the initial state, and obtain the existence of its value functions. The main novelty lies in the method for which we apply a generalized weak contraction for dynamic systems and terminal cost functions instead of the Lipschitz contractive condition on a partially ordered metric space.
MSC:
| 91A23 | Differential games (aspects of game theory) |
| 91A27 | Games with incomplete information, Bayesian games |
| 91A05 | 2-person games |
| 91A10 | Noncooperative games |
Keywords:
two-person zero-sum differential game; incomplete information; generalized contraction; probability distribution; value functionReferences:
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