In the summer of 1967, Secretary of Defense Robert McNamara commissioned a group of thirty-six scholars to write a secret history of the Vietnam War. The project took a year and a half, ran to seven thousand pages, and filled forty-seven volumes. Only a handful of copies were made, and most were kept under lock and key in and around the Beltway. One set, however, ended up at the RAND Corporation, in Santa Monica, where it was read, from start to finish, by a young analyst there named Daniel Ellsberg. Ellsberg was dismayed by what he learned. For a generation, the U.S. government had been lying to the American people about the Vietnam War. He put the first of the volumes in his briefcase, praying that the security guards at RAND would not stop him, and made his way to a small advertising agency in West Hollywood, where a friend told him there was a Xerox machine he could use. "It was a big one, advanced for its time, but very slow by today's standards," Ellsberg writes in his 2002 autobiography, "Secrets: A Memoir of Vietnam and the Pentagon Papers": It could do only one page at a time, and it took several seconds to do each page. I tried pressing the book down on the glass to do two pages at a time, but the middle section was faint and uneven. Fortunately the books were bound with metal tapes through holes so they could be taken apart. . . . The machine didn't collate, and the bar had to come back and travel just as slowly for each copy.

In the summer of 1967, Secretary of Defense Robert McNamara commissioned a group of thirty-six scholars to write a secret history of the Vietnam War. The project took a year and a half, ran to seven thousand pages, and filled forty-seven volumes. Only a handful of copies were made, and most were kept under lock and key in and around the Beltway. One set, however, ended up at the RAND Corporation, in Santa Monica, where it was read, from start to finish, by a young analyst there named Daniel Ellsberg. Ellsberg was dismayed by what he learned. For a generation, the U.S. government had been lying to the American people about the Vietnam War. He put the first of the volumes in his briefcase, praying that the security guards at RAND would not stop him, and made his way to a small advertising agency in West Hollywood, where a friend told him there was a Xerox machine he could use. "It was a big one, advanced for its time, but very slow by today's standards," Ellsberg writes in his 2002 autobiography, "Secrets: A Memoir of Vietnam and the Pentagon Papers": It could do only one page at a time, and it took several seconds to do each page. I tried pressing the book down on the glass to do two pages at a time, but the middle section was faint and uneven. Fortunately the books were bound with metal tapes through holes so they could be taken apart. . . . The machine didn't collate, and the bar had to come back and travel just as slowly for each copy.

This paper is devoted to sequential decision making under uncertainty, in the multi-prior framework of Gilboa and Schmeidler [1989]. In this setting, a set of probability measures (priors) is defined instead of a single one, and the decision maker selects a strategy that maximizes the minimum possible value of expected utility over this set of priors. We are interested here in the resolute choice approach, where one initially commits to a complete strategy and never deviates from it later. Given a decision tree representation with multiple priors, we study the problem of determining an optimal strategy from the root according to min expected utility. We prove the intractability of evaluating a strategy in the general case. We then identify different properties of a decision tree that enable to design dedicated resolution procedures. Finally, experimental results are presented that evaluate these procedures.