This thesis investigates problem-solving in domains featuring incomplete information and multiple agents with opposing goals. In particular, we describe Finesse --- a system that forms plans for the problem of declarer play in the game of Bridge. We begin by examining the problem of search. We formalise a best defence model of incomplete information games in which equilibrium point strategies can be identified, and identify two specific problems that can affect algorithms in such domains. In Bridge, we show that the best defence model corresponds to the typical model analysed in expert texts, and examine search algorithms which overcome the problems we have identified. Next, we look at how planning algorithms can be made to cope with the difficulties of such domains. This calls for the development of new techniques for representing uncertainty and actions with disjunctive effects, for coping with an opposition, and for reasoning about compound actions. We tackle these problems with a..
