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Information structures, causality, and nonsequential stochastic control. II: Design-dependent properties. (English) Zbl 0823.93057

In the previous part of this paper [SIAM J. Control Optimization 30, No. 6, 1447-1475 (1992; Zbl 0770.93085)], the authors introduced a nonsequential system as ‘causal’ if it is deadlock-free and they identified a property of the information structure which is necessary and sufficient for deadlock-freeness. This result assumes Witsenhausen’s design-independent causality condition [cf. H. S. Witsenhausen, SIAM J. Control 9, No. 2, 149-160 (1971; Zbl 0236.93040)].
In the present part, the authors study the relationship between deadlock- freeness and the properties of individual designs. Particularly, due to the fact that the information structure need not be causal in Witsenhausen’s sense, the authors introduce properties of a design’s information partition which are necessary and sufficient to ensure that the design is deadlock-free. The authors’ conditions provide an intuitive characterization of the cause/effect notion of causality. This suggests a framework for the optimization of constrained nonsequential stochastic control problems. The result also implies that this characterization is finer than the existing design-independent characterizations.

MSC:

93E03 Stochastic systems in control theory (general)
91A60 Probabilistic games; gambling
91A15 Stochastic games, stochastic differential games
93E20 Optimal stochastic control
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