We argue that bidding in the game of Contract Bridge can profitably be regarded as a micro-world suitable for experimenting with pragmatics. We sketch an analysis in which a "bidding system" is treated as the semantics of an artificial language, and show how this "language", despite its apparent simplicity, is capable of supporting a wide variety of common speech acts parallel to those in natural languages; we also argue that the reason for the relatively unsuccessful nature of previous attempts to write strong Bridge playing programs has been their failure to address the need to reason explicitly about knowledge, pragmatics, probabilities and plans. We give an overview of Pragma, a system currently under development at SICS, which embodies these ideas in concrete form, using a combination of rule-based inference, stochastic simulation, and "neural-net" learning. Examples are given illustrating the functionality of the system in its current form.