SEQUENTIAL DECISIONS UNDER UNCERTAINTY AND THE MAXIMUM THEOREM

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 pr ocesses 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 analys is for the dynamic-programming approach to sequential decision-making under uncertainty, and for equilibrium existence proof strategies in s equential-market models and games.