Sequential decisions under uncertainty and the maximum theorem

Sequential decisions under uncertainty and the maximum theorem

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Article ID: iaor1999908
Country: United States
Volume: 25
Issue: 4
Start Page Number: 443
End Page Number: 464
Publication Date: Oct 1996
Journal: Journal of Mathematical Economics
Authors:
Abstract:

For sequential decision problems in which the decision-maker observes a process of state variables and chooses an adapted process of action variables, the paper defines a topology on the space of measures of processes of state variables which ensures the applicability of Berge's maximum theorem to the decision-maker's optimal behavior. The topology controls for the information available to the decision-maker at each decision date. The paper also discusses the implications of the analysis for the dynamic-programming approach to sequential decision-making under uncertainty, and for equilibrium existence proof strategies in sequential-market models and games.

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